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C11×C3⋊(D67⋊C3) #27210719

order13266
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(D67⋊C3)
unambiguous semidirect productC3⋊(C11×D67⋊C3)
unambiguous semidirect product(C11×D201)⋊C3

Splittings

Fitting, socleC3×C11×C67 ⋊ C2×C3
derivedC3×C67 ⋊ C2×C3×C11
HallC3×C11×C67⋊C3 ⋊ C2
HallC11×C67 ⋊ C3×D3
HallC3×C67⋊C3 ⋊ C2×C11
SylowC67 ⋊ C3×D3×C11

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(D67⋊C3)
commutator, cosocle, hypocenterC3×C67C2×C3×C11
FrattiniC1G
Fitting, socleC3×C11×C67C2×C3
LCSG ▷ C3×C67
UCSC1 ◁ C11

36 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)(71,72,73,74,75,76,77,78,79,80,81);(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)(68,69,70)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C11×D67⋊C3, D11×C3⋊(D67⋊C3), D33⋊(D67⋊C3), …
maximal normal subgroup ofD3×C11×D67⋊C3, D11×C3⋊(D67⋊C3), D33⋊(D67⋊C3), …
maximal quotient ofC11×C3⋊((C67⋊C3)⋊C4), C2×C11×C3⋊(D67⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 33);