(C2×C2) ⋊ C4
Statistics
Order of group
16
GAP identifier
16,3
Presentation
< r,g,e | r
2
, g
2
, e
4
, [r,g], ere
3
g, ege
3
r >
Orders of elements
1 of 1, 7 of 2, 8 of 4
Centre
C2×C2
Derived subgroup
C2
Automorphism group
a group of order 32
Inner automorphism group
C2×C2
"Out"
(quotient of above)
a group of order 8
Schur multiplier
C2×C2
Permutation Diagrams
Not transitive.
Not transitive.
Not transitive.
Cayley Graphs
{4,4}
(2,0)
, type II
{4,4}
(2,0)
, type IIa
Regular maps
with (C2×C2) ⋊ C4 symmetry
(C2×C2) ⋊ C4 is the rotational symmetry group of the regular map
{4,4}
(2,0)
.
Index to regular maps
Orientable
sphere
|
torus
|
2
|
3
|
4
|
5
|
6
Non-orientable
projective plane
|
4
|
5
|
6
|
7