Finite Group Databasebeta

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C22×D4⋊(C43⋊C8) #25062939

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×D4⋊(C43⋊C8)

Splittings

SylowC43 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC23×C4C22⋊D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC22×C4×D4×C43C2
socleC24×C43C22⋊C4
prime radicalC23×D4×C43C4
cosocleC42×C43C24
hypercenterC22×C4×D4D43
hypocenterC43C22×D4⋊C8
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×D4

1886 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, 135910);