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C9×D67⋊C11 #27210698

order13266
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×D67⋊C11
unambiguous semidirect product(C9×D67)⋊C11

Splittings

Fitting, HallC9×C67 ⋊ C2×C11
derived, SylowC67 ⋊ C2×C9×C11
HallC9×C67⋊C11 ⋊ C2
HallC9×D67 ⋊ C11
HallC67⋊C11 ⋊ C2×C9
HallD67 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC9D67⋊C11
commutator, hypocenterC67C2×C9×C11
FrattiniC3C3×D67⋊C11
FittingC9×C67C2×C11
socle, cosocleC3×C67C2×C3×C11
prime radicalC3×D67⋊C11C3
LCSG ▷ C67
UCSC1 ◁ C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 76
transitive degreeμt(G) = 603

A minimal faithful permutation representation — 2 generators on 76 points:

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×D67⋊C11, C2×C9×D67⋊C11
maximal normal subgroup ofD9×D67⋊C11, C2×C9×D67⋊C11
maximal quotient ofC9×Dic67⋊C11, C2×C9×D67⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 12);