Finite Group Databasebeta

C2×#19136710 #25251057

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

Aliases

direct productC2×#19136710

Splittings

FittingC2×C43×#467 ⋊ C2
SylowC43 ⋊ C2×#2220

Subgroups

subgroupG/H
centerC23C2×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#467C2
socleC23×C43C2×D8
prime radicalC2×#14583135C2
hypercenterC2×#467D43
hypocenterC43C2×#2220
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

734 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, 324028);