Finite Group Databasebeta

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C22×#14582661 #25093992

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productC22×#14582661

Splittings

SylowC43 ⋊ C22×#340

Subgroups

subgroupG/H
centerC25C22⋊D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC23×C4⋊C4×C43C2
socle, prime radicalC25×C43D4
cosocleC22×C4×C43C24
hypercenterC23×C4⋊C4D43
hypocenterC43C22×#340
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

3006 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, 166963);