Finite Group Databasebeta

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C22×#14582955 #25960308

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#14582955

Splittings

FittingC22×C4⋊C8×C43 ⋊ C2
SylowC43 ⋊ C22×#432

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×C4⋊C8×C43C2
socleC24×C43C22×C4
prime radicalC24×D43C2×C4
cosocleC2×C4×C43C25
hypercenterC22×C4⋊C8D43
hypocenterC43C22×#432
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

2830 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033279);