Finite Group Databasebeta

C2×#19137917 #25264147

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19137917

Splittings

FittingC2×C43×#394 ⋊ C2
SylowC43 ⋊ C2×#2405

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#394C2
socleC24×C43C24
prime radicalC23×D4×D43C2
hypercenterC2×#394D43
hypocenterC43C2×#2405
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#394

7822 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1000 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 337118);