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D9×C67⋊C11 #27210699

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

Aliases

direct productD9×C67⋊C11
unambiguous semidirect productC9⋊(C2×C67⋊C11)
unambiguous semidirect product(D9×C67)⋊C11

Splittings

Fitting, derived, HallC9×C67 ⋊ C2×C11
HallC9×C67⋊C11 ⋊ C2
HallD9×C67 ⋊ C11
SylowC67 ⋊ C11×D9
SylowC9 ⋊ C2×C67⋊C11

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C67C2×C11
FrattiniC3D3×C67⋊C11
socleC3×C67D3×C11
LCSG ▷ C9×C67
UCSC1

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:

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×D67⋊C11, C2×D9×C67⋊C11
maximal normal subgroup ofD9×D67⋊C11, C2×D9×C67⋊C11
maximal quotient ofDic9×C67⋊C11, C2×D9×C67⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 13);