Finite Group Databasebeta

C2×#19135393 #25100181

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135393

Splittings

FittingC22×#97×C43 ⋊ C2
SylowC43 ⋊ C2×#1955

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#97×C43C2
socleC24×C43C22×C4
prime radicalC23×D172C4
cosocleC22×C4×C43C24
hypercenterC22×#97D43
hypocenterC43C2×#1955
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×#97

2094 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 173152);