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C3×#15087 #10633694

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

Aliases

direct productC3×#15087

Subgroups

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

1138 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)(8,9,12,10)(11,14,15,13)(17,20)(18,22)(24,25,29,27)(26,31,28,30);(9,10)(13,14)(16,17)(18,21)(19,20)(22,23)(24,26,29,28)(25,30,27,31);(4,5)(6,7)(8,10,12,9)(11,14,15,13)(16,17)(18,21)(19,20)(22,23)(24,27,29,25)(26,30,28,31);(8,11,12,15)(9,13,10,14)(16,18,19,22)(17,21,20,23)(24,28,29,26)(25,30,27,31)

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, 8075);