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(D67⋊C9)⋊C11 #27210704

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

Aliases

unambiguous semidirect product(D67⋊C9)⋊C11
unambiguous semidirect product(D67⋊C11)⋊C9
unambiguous semidirect product((C67⋊C9)⋊C11)⋊C2

Splittings

derived, SylowC67 ⋊ C2×C9×C11
Hall(C67⋊C9)⋊C11 ⋊ C2
HallD67⋊C11 ⋊ C9
HallD67⋊C9 ⋊ C11
HallC67⋊C11 ⋊ C2×C9
HallC67⋊C9 ⋊ C2×C11
HallD67 ⋊ C9×C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC3AGL(1,𝔽67)
commutator, hypocenterC67C2×C9×C11
Fitting, socle, cosocleC3×C67C2×C3×C11
prime radicalC3×D67⋊C11C3
LCSG ▷ C67
UCSC1 ◁ C3

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:

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

Polycyclic presentation:

2,3,11,67,3|b^3=e,d^a=d^66,d^b=d^37,d^c=d^64

Conjugacy classes & character table

201 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(D67⋊C9)⋊C11
maximal normal subgroup ofC2×(D67⋊C9)⋊C11
maximal quotient of(Dic67⋊C9)⋊C11, C2×(D67⋊C9)⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 18);