Finite Group Databasebeta

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C22×#14582750 #25254774

order11008
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×#14582750

Splittings

SylowC43 ⋊ C22×C4×C4⋊C4

Subgroups

subgroupG/H
centerC25C22×D43
commutatorC2×C43C23×C42
FrattiniC23C24×D43
FittingC22×#95×C43C2
socle, prime radicalC25×C43C23
cosocleC23×C43C25
hypercenterC22×#95D43
hypocenterC43C22×C4×C4⋊C4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C22×#95

5758 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327745);