Finite Group Databasebeta

C2×#19135624 #25123481

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135624

Splittings

FittingC22×#124×C43 ⋊ C2
SylowC43 ⋊ C2×#2004

Subgroups

subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#124×C43C2
socleC23×C43#120
prime radicalC2×#14583466C2
hypercenterC22×#124D43
hypocenterC43C2×#2004
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#124

2190 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 196452);