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C3×C5×#2511 #14275545

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

Aliases

direct productC3×C5×#2511

Subgroups

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

776 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)(18,21)(19,23)(25,26,29,32)(27,31,28,30);(9,10,13,12)(11,16,15,14)(17,18)(19,22)(20,21)(23,24)(25,27,29,28)(26,30,32,31);(9,11,13,15)(10,14,12,16)(25,27,29,28)(26,30,32,31);(9,12,13,10)(11,16,15,14)(17,19,20,23)(18,22,21,24)(25,28,29,27)(26,31,32,30)

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, 1243);