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C3⋊#16864282 #27166167

order12876
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊#16864282

Splittings

Fitting, socle, derived, HallC3×C29×C37 ⋊ C4
HallC29×C37 ⋊ Dic3
HallC3×C37 ⋊ #1181
HallC3×C29 ⋊ Dic37
SylowC37 ⋊ C3⋊#1181
SylowC29 ⋊ Dic111
SylowC3 ⋊ #16864282

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C29×C37C4
prime radical, cosocleC3×C37×D29C2
LCSG ▷ C3×C29×C37
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 69
transitive degreeμt(G) = 3219

A minimal faithful permutation representation — 2 generators on 69 points:

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

Polycyclic presentation:

2^2,3,29,37|a^2=b,c^a=c^2,d^a=d^17,e^a=e^36,d^b=d^28

Conjugacy classes & character table

891 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9⋊#16864282, C3⋊(#16864282⋊C3), C3×C3⋊#16864282, …
maximal normal subgroup ofC3⋊(#16864282⋊C3), C3×C3⋊#16864282
maximal quotient ofC9⋊#16864282, C3×C3⋊#16864282, C3⋊(C3⋊#16864282)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 36);