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C3×C11⋊(D67⋊C3) #27210717

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

Aliases

direct productC3×C11⋊(D67⋊C3)
unambiguous semidirect productC11⋊(C3×D67⋊C3)
unambiguous semidirect product(C67⋊C3)⋊(C3×D11)
unambiguous semidirect productD737⋊C32
unambiguous semidirect product(C3×D737)⋊C3

Splittings

Fitting, socleC3×C11×C67 ⋊ C2×C3
derived, HallC11×C67 ⋊ C2×C32
HallC3×C11×C67⋊C3 ⋊ C2
HallD737 ⋊ C32
HallC3×C67⋊C3 ⋊ D11
SylowC67 ⋊ C32×D11
SylowC11 ⋊ C3×D67⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C11⋊(D67⋊C3)
commutator, cosocle, hypocenterC11×C67C2×C32
FrattiniC1G
Fitting, socleC3×C11×C67C2×C3
LCSG ▷ C11×C67
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 81
transitive degreeμt(G) = 2211

A minimal faithful permutation representation — 2 generators on 81 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,59)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,55,54,40,49,65)(34,62,63,50,48,56)(37,42,61,51,52,57)(53,60,66,58,64,67)(69,70)(71,72)(73,74)(75,76)(77,78);(1,2,5,11,19,32,36,10,16,24,38,54,66,64,31,48,55,57,59,63,28,43,44,27,42,58,51,35,22,7,6,12,21,34,50,33,20,4,8,13,23,37,53,52,18,29,39,41,56,47,61,49,62,46,60,67,65,45,15,26,14,25,40,30,17,9,3)(68,69,71,73,75,77,78,76,74,72,70)(79,80,81)

Conjugacy classes & character table

426 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D11×D67⋊C3, D3×C11⋊(D67⋊C3), D33⋊(D67⋊C3), …
maximal normal subgroup ofC3×D11×D67⋊C3, D3×C11⋊(D67⋊C3), D33⋊(D67⋊C3), …
maximal quotient ofC3×C11⋊((C67⋊C3)⋊C4), C2×C3×C11⋊(D67⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 31);