Finite Group Databasebeta

← Prev (#27166164) Next (#27166166) →

C3⋊#16864280 #27166165

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

Aliases

unambiguous semidirect productC3⋊#16864280

Splittings

Fitting, socle, derived, HallC3×C29×C37 ⋊ C4
HallC29×C37 ⋊ Dic3
HallC3×C37 ⋊ #1181
HallC3×C29 ⋊ #3866
SylowC37 ⋊ C3⋊#1181
SylowC29 ⋊ C3⋊#3866
SylowC3 ⋊ #16864280

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C29×C37C4
prime radical, cosocleC3×D1073C2
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)(39,40,41,43)(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);(1,2,5,10,19,13,6,11,20,28,31,24,15,22,29,35,37,33,26,17,27,34,36,30,21,8,16,25,32,23,12,3,7,14,18,9,4)(38,39,42,47,56,45,53,63,66,65,58,50,43,48,57,61,49,40,44,51,59,64,54,62,52,60,55,46,41)(67,68,69)

Polycyclic presentation:

2^2,3,29,37|a^2=b,c^a=c^2,d^a=d^17,e^a=e^31,d^b=d^28,e^b=e^36

Conjugacy classes & character table

810 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9⋊#16864280, C3⋊(#16864280⋊C3), C3×C3⋊#16864280, …
maximal normal subgroup ofC3⋊(#16864280⋊C3), C3×C3⋊#16864280
maximal quotient ofC9⋊#16864280, C3×C3⋊#16864280, C3⋊(C3⋊#16864280)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 34);