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C2×C3×(C127⋊C3)⋊C7 #30630680

order16002
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×(C127⋊C3)⋊C7
unambiguous semidirect product(C2×C127⋊C3)⋊(C3×C7)
unambiguous semidirect product(C2×C127⋊C7)⋊C32
unambiguous semidirect product(C2×C3×C127⋊C3)⋊C7
unambiguous semidirect product(C2×C3×C127⋊C7)⋊C3

Splittings

Fitting, socleC2×C3×C127 ⋊ C3×C7
derived, SylowC127 ⋊ C2×C32×C7
HallC2×C3×C127⋊C3 ⋊ C7
HallC2×C127⋊C7 ⋊ C32
HallC3×C127⋊C3 ⋊ C2×C7
HallC127⋊C7 ⋊ C2×C32
HallC2×C127 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3(C127⋊C3)⋊C7
commutator, cosocle, hypocenterC127C2×C32×C7
FrattiniC1G
Fitting, socleC2×C3×C127C3×C7
LCSG ▷ C127
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×((C127⋊C3)⋊C4)⋊C7, C3⋊(((C127⋊C3)⋊C4)⋊C7), Dic3×(C127⋊C3)⋊C7, …
maximal normal subgroup ofC3×((C127⋊C3)⋊C4)⋊C7, C3⋊(((C127⋊C3)⋊C4)⋊C7), Dic3×(C127⋊C3)⋊C7, …
maximal quotient ofC3×C4×(C127⋊C3)⋊C7, C22×C3×(C127⋊C3)⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 37);