Finite Group Databasebeta

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C22⋊C4×#10621872 #25094225

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22⋊C4×#10621872

Splittings

FittingC8×C22⋊C4×C43 ⋊ C2
SylowC43 ⋊ C22⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C22×C42
FittingC8×C22⋊C4×C43C2
socleC23×C43C23×C4
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenterC8×C22⋊C4D43
hypocenterC43C22⋊C4×M16
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

1774 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, 167196);