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C11⋊(#87604⋊C3) #27165378

order12804
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊(#87604⋊C3)
unambiguous semidirect product(C11⋊#87604)⋊C3

Splittings

Fitting, socle, derived, HallC11×C97 ⋊ C3×C4
HallC11⋊#87604 ⋊ C3
HallC11×C97⋊C3 ⋊ C4
HallC97⋊C3 ⋊ Dic11
SylowC97 ⋊ C3×Dic11
SylowC11 ⋊ #87604⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC11×C97C3×C4
prime radicalC11×D97⋊C3C2
cosocleC11×D97C2×C3
LCSG ▷ C11×C97
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 108
transitive degreeμt(G) = 1067

A minimal faithful permutation representation — 2 generators on 108 points:

(2,7,12,8,4,17,5,18,10,3,11,26)(6,28,66,29,14,58,15,59,31,13,32,87)(9,45,49,20,22,48,23,43,24,21,46,61)(16,70,95,71,35,92,36,85,72,34,73,97)(19,47,96,80,41,84,42,65,81,40,82,54)(25,69,27,68,33,57,52,93,56,51,67,55)(30,86,37,44,63,94,64,53,75,62,91,74)(38,76,83,88,60,50,78,39,89,77,90,79)(99,100)(101,102)(103,104)(105,106)(107,108);(1,2,6,16,37,76,7,19,35,74,93,95,28,60,77,84,17,38,70,79,49,23,8,20,44,31,67,32,68,43,83,34,58,86,52,4,12,27,57,81,40,22,47,64,29,61,82,63,92,97,91,41,48,13,30,65,46,80,96,55,56,10,11,25,53,87,71,89,45,51,14,33,66,62,21,3,9,24,50,85,78,26,54,88,90,59,72,69,94,73,42,18,39,75,36,15,5)(98,99,101,103,105,107,108,106,104,102,100)

Polycyclic presentation:

2,3,2,11,97|a^2=c,d^a=d^10,e^a=e^75,e^b=e^35,e^c=e^96

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊(#87604⋊C3), C3⋊(C11⋊(#87604⋊C3))
maximal normal subgroup ofC3×C11⋊(#87604⋊C3)
maximal quotient ofC11⋊(#87604⋊C9), C3×C11⋊(#87604⋊C3), C3⋊(C11⋊(#87604⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12804, 15);