Finite Group Databasebeta

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C23×C4⋊(C43⋊C8) #25960205

order11008
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC23×C4⋊(C43⋊C8)

Splittings

SylowC43 ⋊ C23×C4⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D43
commutatorC2×C43C24×C8
FrattiniC2×C4C24×D43
FittingC23×C42×C43C2
socle, prime radicalC25×C43C2×C4
cosocleC2×C4×C43C25
hypercenterC23×C42D43
hypocenterC43C23×C4⋊C8
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24×C4 ◁ C23×C42

3870 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, 1033176);