Finite Group Databasebeta

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C3×C5×#2004 #14275038

order1920
nilpotency class3
isoclinismisoclinic class of #2002
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C24

Aliases

direct productC3×C5×#2004

Subgroups

subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC3×C5×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

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, 736);