Finite Group Databasebeta

C2×#19132917 #25062402

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#19132917

Splittings

SylowC43 ⋊ C2×#1461

Subgroups

subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C43C23×C8
FrattiniC22×C4C23×D43
FittingC2×C43×#324C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenterC2×#324D43
hypocenterC43C2×#1461
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

1282 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 135373);