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C2×C3×(C71⋊C5)⋊C7 #28415841

order14910
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×(C71⋊C5)⋊C7
unambiguous semidirect product(C2×C71⋊C5)⋊(C3×C7)
unambiguous semidirect product(C2×C71⋊C7)⋊(C3×C5)
unambiguous semidirect product(C2×C3×C71⋊C5)⋊C7
unambiguous semidirect product(C2×C3×C71⋊C7)⋊C5

Splittings

Fitting, socle, HallC2×C3×C71 ⋊ C5×C7
derived, SylowC71 ⋊ C2×C3×C5×C7
HallC2×C3×C71⋊C7 ⋊ C5
HallC2×C3×C71⋊C5 ⋊ C7
HallC3×C71⋊C7 ⋊ C2×C5
HallC3×C71⋊C5 ⋊ C2×C7
HallC2×C71⋊C7 ⋊ C3×C5
HallC2×C71⋊C5 ⋊ C3×C7
HallC71⋊C7 ⋊ C2×C3×C5
HallC71⋊C5 ⋊ C2×C3×C7
HallC3×C71 ⋊ C2×C5×C7
HallC2×C71 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3(C71⋊C5)⋊C7
commutator, cosocle, hypocenterC71C2×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C71C5×C7
LCSG ▷ C71
UCSC1 ◁ C2×C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 426

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×(C71⋊C5)⋊C7, C3×(Dic71⋊C5)⋊C7, Dic3×(C71⋊C5)⋊C7, …
maximal normal subgroup ofC3×C4×(C71⋊C5)⋊C7, C3×(Dic71⋊C5)⋊C7, Dic3×(C71⋊C5)⋊C7, …
maximal quotient ofC3×C4×(C71⋊C5)⋊C7, C22×C3×(C71⋊C5)⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 4);