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C2×C13×C71⋊C5 #22604366

order9230
isoclinismisoclinic class of C71⋊C5
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC2×C13×C71⋊C5
unambiguous semidirect product(C2×C71)⋊(C5×C13)
unambiguous semidirect product(C2×C13×C71)⋊C5

Splittings

Fitting, socle, HallC2×C13×C71 ⋊ C5
derived, SylowC71 ⋊ C2×C5×C13
HallC13×C71 ⋊ C2×C5
HallC2×C71 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13C71⋊C5
commutator, hypocenterC71C2×C5×C13
FrattiniC1G
Fitting, socleC2×C13×C71C5
LCSG ▷ C71
UCSC1 ◁ C2×C13

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C13×C71⋊C5, C13×Dic71⋊C5, Dic13×C71⋊C5, …
maximal normal subgroup ofC4×C13×C71⋊C5, C13×Dic71⋊C5, Dic13×C71⋊C5, …
maximal quotient ofC4×C13×C71⋊C5, C22×C13×C71⋊C5, C2×C3×C13×C71⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9230, 2);