Finite Group Databasebeta

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C2×C4⋊(C43⋊C32) #25017077

order11008
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊(C43⋊C32)

Splittings

SylowC43 ⋊ C2×C4⋊C32

Subgroups

subgroupG/H
centerC22×C16C2×D43
commutatorC2×C43C22×C32
FrattiniC2×C16C22×D43
FittingC2×C4×C16×C43C2
socle, prime radicalC23×C43C2×C16
cosocleC2×C16×C43C23
hypercenterC2×C4×C16D43
hypocenterC43C2×C4⋊C32
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C16 ◁ C2×C4×C16

230 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 90048);