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C3×#15105 #10633712

order768
nilpotency class2
isoclinismisoclinic class of #14715
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C24

Aliases

direct productC3×#15105

Subgroups

subgroupG/H
center, socle, prime radicalC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

1226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 768

A minimal faithful permutation representation — 4 generators on 31 points:

(1,2,3)(5,7)(10,14)(13,15)(16,17,19,20)(18,22,23,21)(24,25,27,29)(26,28,30,31);(4,5)(6,7)(9,12)(13,15)(17,20)(21,22)(24,25,27,29)(26,28,30,31);(8,9,11,12)(10,13,14,15)(16,17)(18,21)(19,20)(22,23)(24,25)(26,28)(27,29)(30,31);(8,10)(9,13)(11,14)(12,15)(16,18,19,23)(17,21,20,22)(24,26,27,30)(25,28,29,31)

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 8093);