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C3×C5×#1497 #14274531

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

Aliases

direct productC3×C5×#1497

Subgroups

subgroupG/H
centerC2×C3×C4×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC42C23×C3×C5
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C4×C5 ◁ C2×C3×C42×C5 ◁ G

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3)(4,5,6,7,8)(9,10)(11,18)(12,16)(13,22)(14,17)(15,20)(19,23)(21,24)(25,26,28,32,29,31,35,38)(27,30,34,36,33,37,39,40);(9,11,14,21)(10,15,17,23)(12,20,13,19)(16,24,22,18)(25,27)(26,30)(28,34)(29,33)(31,37)(32,36)(35,39)(38,40);(9,12,14,13)(10,16,17,22)(11,19,21,20)(15,18,23,24)(26,31)(27,33)(32,38)(34,39)

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, 229);