Finite Group Databasebeta

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C3×C5×#1837 #14274871

order1920
nilpotency class3
isoclinismisoclinic class of #465
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×C5×#1837

Subgroups

subgroupG/H
centerC2×C3×C4×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×C5C2×Q8
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C4×C5 ◁ C2×C3×C42×C5 ◁ G

376 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)(11,14)(12,13)(15,16)(17,18,21,27,23,28,22,26)(19,25,20,24,30,31,29,32);(10,13)(14,16)(17,19,22,29,23,30,21,20)(18,24,27,31,28,32,26,25);(9,11,12,15)(10,14,13,16)(17,20,21,30,23,29,22,19)(18,25,26,32,28,31,27,24)

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 569);