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C3×C13⋊C3×C79 #22604463

order9243
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C32×C79 · Schur multiplier (H2) = C3

Aliases

direct productC3×C13⋊C3×C79
unambiguous semidirect productC13⋊(C32×C79)
unambiguous semidirect product(C3×C13)⋊(C3×C79)

Splittings

Fitting, socleC3×C13×C79 ⋊ C3
derived, SylowC13 ⋊ C32×C79
HallC13×C79 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C79C13⋊C3
commutator, hypocenterC13C32×C79
FrattiniC1G
Fitting, socleC3×C13×C79C3
LCSG ▷ C13
UCSC1 ◁ C3×C79

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1659 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D13⋊C3×C79, C3×(C13⋊C3)⋊D79, C3×C13⋊C3×D79, …
maximal normal subgroup ofC3×D13⋊C3×C79, C3×(C13⋊C3)⋊D79, C3×C13⋊C3×D79, …
maximal quotient ofC2×C3×C13⋊C3×C79, A4×C13⋊C3×C79, C3×C79×C22⋊(C13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9243, 14);