Finite Group Databasebeta

C2×#19136214 #25249285

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19136214

Splittings

FittingC2×C43×#349 ⋊ C2
SylowC43 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC22×C43C23×C8
FrattiniC2×C8C23×D43
FittingC2×C43×#349C2
socleC22×C43C2×C22⋊C8
prime radicalC22×#10621898C4
cosocleC2×C8×C43C24
hypercenterC2×#349D43
hypocenterC43C2×#2115
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#349

1154 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, 322256);