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C3×C3⋊(D71⋊C7) #22582129

order8946
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(D71⋊C7)
unambiguous semidirect productC3⋊(C3×D71⋊C7)
unambiguous semidirect productD213⋊(C3×C7)
unambiguous semidirect product(C71⋊C7)⋊(C3×D3)
unambiguous semidirect product(C3×D213)⋊C7

Splittings

Fitting, socle, HallC32×C71 ⋊ C2×C7
derivedC3×C71 ⋊ C2×C3×C7
HallC32×C71⋊C7 ⋊ C2
HallC3×D213 ⋊ C7
HallC71⋊C7 ⋊ C3×D3
SylowC71 ⋊ C3×D3×C7
SylowC32 ⋊ D71⋊C7

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(D71⋊C7)
commutator, hypocenterC3×C71C2×C3×C7
FrattiniC1G
Fitting, socleC32×C71C2×C7
LCSG ▷ C3×C71
UCSC1 ◁ C3

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×D71⋊C7, D3×C3⋊(D71⋊C7), (C3⋊D3)⋊(D71⋊C7), …
maximal normal subgroup ofC3×D3×D71⋊C7, D3×C3⋊(D71⋊C7), (C3⋊D3)⋊(D71⋊C7), …
maximal quotient ofC3×C3⋊(Dic71⋊C7), C2×C3×C3⋊(D71⋊C7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8946, 19);