Finite Group Databasebeta

C2×#19134260 #25084376

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C8

Aliases

direct productC2×#19134260

Splittings

FittingC2×C43×#493 ⋊ C2
SylowC43 ⋊ C2×#1721

Subgroups

subgroupG/H
centerC23#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#493C2
socleC23×C43#127
hypercenterC2×#493D43
hypocenterC43C2×#1721
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

1146 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, 157347);