Finite Group Databasebeta

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C8×C4⋊(C43⋊C8) #24987718

order11008
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8

Aliases

direct productC8×C4⋊(C43⋊C8)

Splittings

SylowC43 ⋊ C8×C4⋊C8

Subgroups

subgroupG/H
centerC2×C4×C8C2×D43
commutatorC2×C43C2×C82
FrattiniC2×C42C22×D43
FittingC42×C8×C43C2
socle, prime radicalC23×C43C2×C42
cosocleC2×C42×C43C23
hypercenterC42×C8D43
hypocenterC43C8×C4⋊C8
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4×C8 ◁ C42×C8

550 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, 60689);