Finite Group Databasebeta

C2×#19136808 #25251480

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

Aliases

direct productC2×#19136808

Splittings

FittingC2×C43×#361 ⋊ C2
SylowC43 ⋊ C2×#2238

Subgroups

subgroupG/H
centerC22#14583216
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#361C2
socleC22×C43#481
prime radicalC2×#14583149C2
hypercenterC2×#361D43
hypocenterC43C2×#2238
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

604 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

712 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 324451);