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C2×C32×C71⋊C5 #20264138

order6390
isoclinismisoclinic class of C71⋊C5
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C32×C71⋊C5
unambiguous semidirect product(C2×C71)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C71)⋊(C3×C5)
unambiguous semidirect product(C2×C32×C71)⋊C5

Splittings

Fitting, socle, HallC2×C32×C71 ⋊ C5
derived, SylowC71 ⋊ C2×C32×C5
HallC32×C71 ⋊ C2×C5
HallC2×C71 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32C71⋊C5
commutator, hypocenterC71C2×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C71C5
LCSG ▷ C71
UCSC1 ◁ C2×C32

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

342 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×Dic71⋊C5, C3×C3⋊(Dic71⋊C5), C3×Dic3×C71⋊C5, …
maximal normal subgroup ofC32×Dic71⋊C5, C3×C3⋊(Dic71⋊C5), C3×Dic3×C71⋊C5, …
maximal quotient ofC32×C4×C71⋊C5, C22×C32×C71⋊C5, C2×C32×C71⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6390, 19);