Finite Group Databasebeta

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M32×C43⋊C8 #25005574

order11008
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C2×C8

Aliases

direct productM32×C43⋊C8

Splittings

SylowC43 ⋊ C8×M32

Subgroups

subgroupG/H
center, FrattiniC4×C8C22×D43
commutatorC2×C43C2×C82
FittingC4×M32×C43C2
socleC22×C43C2×C4×C8
prime radicalC23×C43C4×C8
cosocleC4×C8×C43C23
hypercenterC4×M32D43
hypocenterC43C8×M32
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C4×C8 ◁ C4×M32

354 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, 78545);