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C2×(C79⋊C9)⋊C13 #32914844

order18486
automorphism?
homologyAbelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC2×(C79⋊C9)⋊C13
unambiguous semidirect product(C2×C79⋊C9)⋊C13
unambiguous semidirect product(C2×C79⋊C13)⋊C9

Splittings

derived, SylowC79 ⋊ C2×C9×C13
HallC2×C79⋊C13 ⋊ C9
HallC2×C79⋊C9 ⋊ C13
HallC79⋊C13 ⋊ C2×C9
HallC79⋊C9 ⋊ C2×C13
HallC2×C79 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3(C79⋊C3)⋊C13
commutator, hypocenterC79C2×C9×C13
FrattiniC3C2×(C79⋊C3)⋊C13
Fitting, socleC2×C3×C79C3×C13
prime radicalC2×C3×C79⋊C13C3
cosocleC3×C79C2×C3×C13
LCSG ▷ C79
UCSC1 ◁ C2×C3

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1422

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×(C79⋊C9)⋊C13, (Dic79⋊C9)⋊C13, C2×(D79⋊C9)⋊C13, …
maximal normal subgroup ofC4×(C79⋊C9)⋊C13, (Dic79⋊C9)⋊C13, C2×(D79⋊C9)⋊C13, …
maximal quotient ofC4×(C79⋊C9)⋊C13, C22×(C79⋊C9)⋊C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 7);