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C3×C5×#2514 #14275548

order1920
nilpotency class2
isoclinismisoclinic class of #2403
automorphism?
homologyAbelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C23

Aliases

direct productC3×C5×#2514

Subgroups

subgroupG/H
center, socle, prime radicalC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 4 generators on 32 points:

(1,2,3)(4,5,6,7,8)(10,12)(11,15)(17,18,22,20)(19,24,23,21)(27,31)(29,32);(9,10,13,12)(11,14,15,16)(17,19)(18,21)(20,24)(22,23)(25,26,28,30)(27,32,31,29);(9,11)(10,14)(12,16)(13,15)(17,20,22,18)(19,24,23,21)(25,27,28,31)(26,29,30,32);(9,12,13,10)(11,16,15,14)(17,21,22,24)(18,23,20,19)

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 1246);