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C3×C5×#1700 #14274734

order1920
nilpotency class3
isoclinismisoclinic class of #1685
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C5×#1700

Subgroups

subgroupG/H
center, socle, prime radicalC22×C3×C5#121
commutator, Frattini, cosocleC42C23×C3×C5
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1920

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

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

Conjugacy classes & character table

345 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 432);