Finite Group Databasebeta

C2×#19135612 #25123475

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

Aliases

direct productC2×#19135612

Splittings

FittingC22×#100×C43 ⋊ C2
SylowC43 ⋊ C2×#2002

Subgroups

subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#100×C43C2
socleC23×C43#120
hypercenterC22×#100D43
hypocenterC43C2×#2002
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#100

2750 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

976 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 196446);