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C3×C5×#2660 #14275694

order1920
nilpotency class2
isoclinismisoclinic class of #2613
automorphism?
homologyAbelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×C5×#2660

Subgroups

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

896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 4 generators on 28 points:

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

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 1392);