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C4×D4⋊(C43⋊C8) #24987189

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×D4⋊(C43⋊C8)

Splittings

SylowC43 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC2×C42C22⋊D43
commutatorC4×C43C2×C4×C8
FrattiniC2×C42C22×D43
FittingC42×D4×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenterC42×D4D43
hypocenterC43C4×D4⋊C8
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×D4

774 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, 60160);