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D8×(C2×D43)⋊C4 #25112416

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD8×(C2×D43)⋊C4

Splittings

FittingC2×C4×D8×C43 ⋊ C2
SylowC43 ⋊ C22⋊C4×D8

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
prime radicalC22×D8×D43C2
cosocleC22×C4×C43C24
hypercenterC2×C4×D8D43
hypocenterC43C22⋊C4×D8
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

1830 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1246 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 185387);