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C24×#10587739 #22578484

order8768
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC24×#10587739
unambiguous semidirect productD137⋊(C23×C4)

Splittings

Fitting, socleC24×C137 ⋊ C4
derived, SylowC137 ⋊ C24×C4

Subgroups

subgroupG/H
center, hypercenterC24#10587739
commutator, hypocenterC137C24×C4
FrattiniC1G
Fitting, socleC24×C137C4
LCSG ▷ C137
UCSC1 ◁ C24

1362 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#31795962, C22×(C2×#10587739)⋊C4, C2×C22⋊C4×#10587739, …
maximal normal subgroup of#31795962, C22×(C2×#10587739)⋊C4, C2×C22⋊C4×#10587739, …
maximal quotient ofC23×C4×#10587739, C23×C22⋊#10587739, C23×C4⋊#10587739, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 1630);