Finite Group Databasebeta

C2×#19136712 #25251151

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19136712

Splittings

FittingC22×D16×C43 ⋊ C2
SylowC43 ⋊ C2×#2221

Subgroups

subgroupG/H
centerC22#14583132
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC22×D16×C43C2
socleC22×C43#466
hypercenterC22×D16D43
hypocenterC43C2×#2221
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

678 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, 324122);