Finite Group Databasebeta

C2×#19143649 #25961354

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19143649

Splittings

FittingC22×C22⋊C8×C43 ⋊ C2
SylowC43 ⋊ C2×#2977

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×C22⋊C8×C43C2
socleC23×C43C23×C4
prime radicalC2×#14583410C2
cosocleC2×C4×C43C25
hypercenterC22×C22⋊C8D43
hypocenterC43C2×#2977
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8

2362 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1034325);