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C3×(C79⋊C3)⋊C13 #22604458

order9243
automorphism?
homologyAbelianization (H1) = C32×C13 · Schur multiplier (H2) = C3

Aliases

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

Splittings

Fitting, socleC3×C79 ⋊ C3×C13
derived, SylowC79 ⋊ C32×C13
HallC79⋊C13 ⋊ C32
HallC3×C79⋊C3 ⋊ C13

Subgroups

subgroupG/H
center, hypercenterC3(C79⋊C3)⋊C13
commutator, hypocenterC79C32×C13
FrattiniC1G
Fitting, socleC3×C79C3×C13
LCSG ▷ C79
UCSC1 ◁ C3

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

123 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽79), C3⋊AGL(1,𝔽79), D3×(C79⋊C3)⋊C13, …
maximal normal subgroup ofC3×AGL(1,𝔽79), C3⋊AGL(1,𝔽79), D3×(C79⋊C3)⋊C13, …
maximal quotient ofC2×C3×(C79⋊C3)⋊C13, A4×(C79⋊C3)⋊C13, C3×C22⋊((C79⋊C3)⋊C13)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9243, 9);