Finite Group Databasebeta

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C22×#14582642 #25064876

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#14582642

Splittings

FittingC22×C4⋊C8×C43 ⋊ C2
SylowC43 ⋊ C22×#331

Subgroups

subgroupG/H
centerC24(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC22×C4⋊C8×C43C2
socleC24×C43C22⋊C4
prime radicalC22×#13063322C2
cosocleC42×C43C24
hypercenterC22×C4⋊C8D43
hypocenterC43C22×#331
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

2022 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 137847);