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C3×C5×#2090 #14275124

order1920
nilpotency class3
isoclinismisoclinic class of #2018
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C5×#2090

Subgroups

subgroupG/H
center, socleC22×C3×C5#121
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC23×C3×C5#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G

352 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)(11,16)(12,14)(13,15)(17,18,21,24,22,26,20,25)(19,23,27,32,29,30,28,31);(9,11,13,12)(10,14,15,16)(17,19)(18,23)(20,28)(21,27)(22,29)(24,32)(25,31)(26,30);(9,12,13,11)(10,14,15,16)(18,24)(19,27)(20,21)(23,30)(25,26)(28,29)

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, 822);