Finite Group Databasebeta

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C42×#10587739 #22578337

order8768
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C43

Aliases

direct productC42×#10587739

Splittings

FittingC42×C137 ⋊ C4
derived, SylowC137 ⋊ C43

Subgroups

subgroupG/H
center, hypercenterC42#10587739
commutator, hypocenterC137C43
FrattiniC22C22×#10587739
FittingC42×C137C4
socleC22×C137C22×C4
LCSG ▷ C137
UCSC1 ◁ C42

258 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#31795616, C4×C8×#10587739, #97×#10587739, …
maximal normal subgroup of#31795616, C4×C8×#10587739, #97×#10587739, …
maximal quotient of#95×#10587739, C4×(C2×#10587739)⋊C4, C4×C8×#10587739, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 1483);