Finite Group Databasebeta

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C3×C5×#1995 #14275029

order1920
nilpotency class3
isoclinismisoclinic class of #468
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×C5×#1995

Subgroups

subgroupG/H
centerC2×C3×C4×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C4×C5 ◁ C2×C3×C42×C5 ◁ G

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3)(4,5,6,7,8)(9,10)(11,15)(12,13)(14,16)(17,18,21,24,22,25,20,30)(19,26,29,31,27,32,28,23);(10,13)(14,15)(17,19)(18,23,25,31)(20,28)(21,29)(22,27)(24,26,30,32);(9,11,12,16)(10,14,13,15)(19,27)(23,31)(26,32)(28,29)

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 727);