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C2×C3×(C67⋊C3)⋊C11 #27210709

order13266
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×(C67⋊C3)⋊C11
unambiguous semidirect product(C2×C67⋊C3)⋊(C3×C11)
unambiguous semidirect product(C2×C3×C67⋊C3)⋊C11
unambiguous semidirect product(C2×C67⋊C11)⋊C32
unambiguous semidirect product(C2×C3×C67⋊C11)⋊C3

Splittings

Fitting, socleC2×C3×C67 ⋊ C3×C11
derived, SylowC67 ⋊ C2×C32×C11
HallC2×C67⋊C11 ⋊ C32
HallC2×C3×C67⋊C3 ⋊ C11
HallC67⋊C11 ⋊ C2×C32
HallC3×C67⋊C3 ⋊ C2×C11
HallC2×C67 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3(C67⋊C3)⋊C11
commutator, cosocle, hypocenterC67C2×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C67C3×C11
LCSG ▷ C67
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 72
transitive degreeμt(G) = 402

A minimal faithful permutation representation — 2 generators on 72 points:

(2,7,22,20,41,52,43,33,65,50,21,6,4,10,35,37,58,36,16,49,64,59,3,14,9,23,30,34,19,57,28,48,39)(5,25,63,47,32,46,66,54,51,15,18,24,12,44,60,45,38,53,31,56,17,29,11,42,27,61,26,62,40,67,55,8,13)(71,72);(1,2,5,13,30,53,23,11,26,9,21,40,61,47,37,50,49,33,27,48,18,35,59,7,16,34,57,42,45,6,15,32,56,64,54,39,36,3,8,19,20,38,60,46,29,51,25,14,31,41,62,66,67,63,58,52,65,55,24,43,22,12,28,44,4,10,17)(68,69,70)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×((C67⋊C3)⋊C4)⋊C11, C3⋊(((C67⋊C3)⋊C4)⋊C11), Dic3×(C67⋊C3)⋊C11, …
maximal normal subgroup ofC3×((C67⋊C3)⋊C4)⋊C11, C3⋊(((C67⋊C3)⋊C4)⋊C11), Dic3×(C67⋊C3)⋊C11, …
maximal quotient ofC3×C4×(C67⋊C3)⋊C11, C22×C3×(C67⋊C3)⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 23);