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C3×C5×#1661 #14274695

order1920
nilpotency class3
isoclinismisoclinic class of #1655
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC3×C5×#1661

Subgroups

subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC3×C5×#562C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

300 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 393);