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C3×C5×#1653 #14274687

order1920
nilpotency class3
isoclinismisoclinic class of #1619
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC3×C5×#1653

Subgroups

subgroupG/H
center, socle, prime radicalC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

388 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)(10,13)(11,15)(14,16)(17,18,22,26)(19,27,30,31)(20,23,21,25)(24,28,32,29);(9,10,12,14)(11,16,15,13)(18,23)(20,21)(24,31)(25,26)(27,32)(28,29);(17,19,22,30)(18,24,26,32)(20,29,21,28)(23,31,25,27)

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 385);