Finite Group Databasebeta

← Prev (#32914871) Next (#32914873) →

C2×C3×(C79⋊C3)⋊C13 #32914872

order18486
automorphism?
homologyAbelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×(C79⋊C3)⋊C13
unambiguous semidirect product(C2×C79⋊C3)⋊(C3×C13)
unambiguous semidirect product(C2×C3×C79⋊C3)⋊C13
unambiguous semidirect product(C2×C79⋊C13)⋊C32
unambiguous semidirect product(C2×C3×C79⋊C13)⋊C3

Splittings

Fitting, socleC2×C3×C79 ⋊ C3×C13
derived, SylowC79 ⋊ C2×C32×C13
HallC2×C79⋊C13 ⋊ C32
HallC2×C3×C79⋊C3 ⋊ C13
HallC79⋊C13 ⋊ C2×C32
HallC3×C79⋊C3 ⋊ C2×C13
HallC2×C79 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3(C79⋊C3)⋊C13
commutator, cosocle, hypocenterC79C2×C32×C13
FrattiniC1G
Fitting, socleC2×C3×C79C3×C13
LCSG ▷ C79
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 474

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×((C79⋊C3)⋊C4)⋊C13, C3⋊(((C79⋊C3)⋊C4)⋊C13), Dic3×(C79⋊C3)⋊C13, …
maximal normal subgroup ofC3×((C79⋊C3)⋊C4)⋊C13, C3⋊(((C79⋊C3)⋊C4)⋊C13), Dic3×(C79⋊C3)⋊C13, …
maximal quotient ofC3×C4×(C79⋊C3)⋊C13, C22×C3×(C79⋊C3)⋊C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 35);