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C3⋊(C3⋊(D79⋊C13)) #32914876

order18486
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊(D79⋊C13))
unambiguous semidirect product(C79⋊C13)⋊(C3⋊D3)
unambiguous semidirect product(C3⋊D237)⋊C13

Splittings

Fitting, socle, derived, HallC32×C79 ⋊ C2×C13
HallC32×C79⋊C13 ⋊ C2
HallC3⋊D237 ⋊ C13
HallC79⋊C13 ⋊ C3⋊D3
SylowC79 ⋊ C13×C3⋊D3
SylowC32 ⋊ D79⋊C13

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C79C2×C13
LCSG ▷ C32×C79
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 711

Polycyclic presentation:

2,13,3^2,79|c^a=c^2,d^a=d^2,e^a=e^78,e^b=e^18

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C3⋊(D79⋊C13), C3⋊D3×D79⋊C13, C2×C3⋊(C3⋊(D79⋊C13))
maximal normal subgroup ofD3×C3⋊(D79⋊C13), C3⋊D3×D79⋊C13, C2×C3⋊(C3⋊(D79⋊C13))
maximal quotient ofC3⋊(C3⋊(Dic79⋊C13)), C2×C3⋊(C3⋊(D79⋊C13))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 39);