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C3×C13⋊C3×C71 #22552183

order8307
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C32×C71 · Schur multiplier (H2) = C3

Aliases

direct productC3×C13⋊C3×C71
unambiguous semidirect productC13⋊(C32×C71)
unambiguous semidirect product(C3×C13)⋊(C3×C71)
unambiguous semidirect product(C13×C71)⋊C32
unambiguous semidirect product(C3×C13×C71)⋊C3

Splittings

Fitting, socleC3×C13×C71 ⋊ C3
derived, SylowC13 ⋊ C32×C71
HallC13×C71 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C71C13⋊C3
commutator, hypocenterC13C32×C71
FrattiniC1G
Fitting, socleC3×C13×C71C3
LCSG ▷ C13
UCSC1 ◁ C3×C71

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1491 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C71×D13⋊C3, C3×(C13⋊C3)⋊D71, C3×C13⋊C3×D71, …
maximal normal subgroup ofC3×C71×D13⋊C3, C3×(C13⋊C3)⋊D71, C3×C13⋊C3×D71, …
maximal quotient ofC2×C3×C13⋊C3×C71, A4×C13⋊C3×C71, C3×C71×C22⋊(C13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8307, 4);