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C3×C5×#2451 #14275485

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

Aliases

direct productC3×C5×#2451

Subgroups

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

968 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)(15,19)(16,17)(18,20)(21,22,25,28)(23,27,24,26);(10,12)(14,17)(18,19)(21,23,25,24)(22,26,28,27);(9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,23,25,24)(22,26,28,27);(13,15,16,20)(14,18,17,19)(21,24,25,23)(22,27,28,26)

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, 1183);