Finite Group Databasebeta

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C22×C4×#10587739 #22578463

order8768
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×#10587739
unambiguous semidirect productD137⋊(C2×C42)

Splittings

FittingC22×C4×C137 ⋊ C4
derived, SylowC137 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4#10587739
commutator, hypocenterC137C22×C42
FrattiniC2C23×#10587739
FittingC22×C4×C137C4
socleC23×C137C2×C4
LCSG ▷ C137
UCSC1 ◁ C22×C4

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#95×#10587739, C4×(C2×#10587739)⋊C4, #31795964, …
maximal normal subgroup of#95×#10587739, C4×(C2×#10587739)⋊C4, #31795964, …
maximal quotient ofC2×C42×#10587739, C22×(C2×#10587739)⋊C4, C2×#22578339, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 1609);