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C4×C22⋊C8×D43 #25094106

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC4×C22⋊C8×D43

Splittings

FittingC4×C22⋊C8×C43 ⋊ C2
SylowC43 ⋊ C2×C4×C22⋊C8

Subgroups

subgroupG/H
centerC2×C42C22×D43
commutatorC2×C43C22×C4×C8
FrattiniC22×C4C23×D43
FittingC4×C22⋊C8×C43C2
socleC23×C43C23×C4
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenterC4×C22⋊C8D43
hypocenterC43C2×C4×C22⋊C8
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C4×C22⋊C8

2414 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, 167077);