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Q8⋊C8×Dic43 #24987196

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productQ8⋊C8×Dic43

Splittings

SylowC43 ⋊ C4×Q8⋊C8

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC4×C43C2×C4×C8
FrattiniC2×C42C22×D43
FittingC2×C43×Q8⋊C8C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×Q8⋊C8D43
hypocenterC43C4×Q8⋊C8
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

654 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 60167);