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C9⋊(D67⋊C11) #27210700

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

Aliases

unambiguous semidirect productC9⋊(D67⋊C11)
unambiguous semidirect product(C67⋊C11)⋊D9
unambiguous semidirect productD603⋊C11

Splittings

Fitting, derived, HallC9×C67 ⋊ C2×C11
HallC9×C67⋊C11 ⋊ C2
HallD603 ⋊ C11
HallC67⋊C11 ⋊ D9
SylowC67 ⋊ C11×D9
SylowC9 ⋊ D67⋊C11

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C67C2×C11
FrattiniC3C3⋊(D67⋊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:

(2,6,7,17,22,43,18,57,16,40,53,3,4,10,12,32,41,34,35,21,31,61)(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)(69,71)(70,74)(72,73)(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)(68,76,71,74,73,72,70,69,75)

Polycyclic presentation:

2,3,11,67,3|b^3=e^2,b^a=b^2e,d^a=d^66,e^a=e^2,d^c=d^64

Conjugacy classes & character table

93 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, 14);