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C3×C5×#1637 #14274671

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

Aliases

direct productC3×C5×#1637

Subgroups

subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC2×C3×C5×D4D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

456 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)(9,10,12,15)(11,13,16,14)(17,18,23,27)(19,28,20,31)(21,26,22,25)(24,30,32,29);(10,13)(11,16)(14,15)(17,19,23,20)(18,24,27,32)(21,30,22,29)(25,31,26,28);(17,20,23,19)(18,24,27,32)(21,29,22,30)(25,31,26,28)

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, 369);