Finite Group Databasebeta

C2×#19135639 #25123553

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

Aliases

direct productC2×#19135639

Splittings

FittingC2×C43×#343 ⋊ C2
SylowC43 ⋊ C2×#2006

Subgroups

subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#343C2
socleC23×C43#120
hypercenterC2×#343D43
hypocenterC43C2×#2006
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

2254 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, 196524);