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C32×D71⋊C5 #20264133

order6390
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×D71⋊C5
unambiguous semidirect productD71⋊(C32×C5)
unambiguous semidirect product(C71⋊C5)⋊(C2×C32)
unambiguous semidirect product(C3×D71)⋊(C3×C5)
unambiguous semidirect product(C32×D71)⋊C5

Splittings

Fitting, socle, HallC32×C71 ⋊ C2×C5
derived, SylowC71 ⋊ C2×C32×C5
HallC32×C71⋊C5 ⋊ C2
HallC32×D71 ⋊ C5
HallC71⋊C5 ⋊ C2×C32
HallD71 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC32D71⋊C5
commutator, hypocenterC71C2×C32×C5
FrattiniC1G
Fitting, socleC32×C71C2×C5
LCSG ▷ C71
UCSC1 ◁ C32

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×D71⋊C5, C3⋊D3×D71⋊C5, C2×C32×D71⋊C5, …
maximal normal subgroup ofC3×D3×D71⋊C5, C3⋊D3×D71⋊C5, C2×C32×D71⋊C5, …
maximal quotient ofC32×Dic71⋊C5, C2×C32×D71⋊C5, C32×D71⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6390, 14);