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C2×Q8×Dic43⋊C4 #25255897

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×Q8×Dic43⋊C4

Splittings

SylowC43 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC22×C4×Q8×C43C2
socle, prime radicalC24×C43C24
cosocleC23×C43C25
hypercenterC22×C4×Q8D43
hypocenterC43C2×Q8×C4⋊C4
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4×Q8

3246 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328868);