Finite Group Databasebeta

← Prev (#27166167) Next (#27166169) →

C3⋊#16864283 #27166168

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

Aliases

unambiguous semidirect productC3⋊#16864283

Splittings

Fitting, socle, derived, HallC3×C29×C37 ⋊ C4
HallC29×C37 ⋊ Dic3
HallC3×C37 ⋊ Dic29
HallC3×C29 ⋊ #3866
SylowC37 ⋊ Dic87
SylowC29 ⋊ C3⋊#3866
SylowC3 ⋊ #16864283

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C29×C37C4
prime radical, cosocleC3×C29×D37C2
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:

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

Polycyclic presentation:

2^2,3,29,37|a^2=b,c^a=c^2,d^a=d^28,e^a=e^31,e^b=e^36

Conjugacy classes & character table

873 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9⋊#16864283, C3⋊(#16864283⋊C3), C3×C3⋊#16864283, …
maximal normal subgroup ofC3⋊(#16864283⋊C3), C3×C3⋊#16864283
maximal quotient ofC9⋊#16864283, C3×C3⋊#16864283, C3⋊(C3⋊#16864283)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 37);