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C3×C5×#2528 #14275562

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

Aliases

direct productC3×C5×#2528

Subgroups

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

728 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)(9,10,12,14)(11,13,15,16)(19,23)(22,24)(26,30)(28,32);(9,10,12,14)(11,13,15,16)(17,18,21,20)(19,22,23,24)(25,26,29,30)(27,28,31,32);(9,10)(11,13)(12,14)(15,16)(17,19)(18,22)(20,24)(21,23)(25,27,29,31)(26,28,30,32);(9,11,12,15)(10,13,14,16)(17,20,21,18)(19,24,23,22)(25,28)(26,31)(27,30)(29,32)

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, 1260);