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C3×C5×#1544 #14274578

order1920
nilpotency class3
isoclinismisoclinic class of #327
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC3×C5×#1544

Subgroups

subgroupG/H
centerC2×C3×C4×C5C22⋊C4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC42C23×C3×C5
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ 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)(9,10,12,16,13,15,21,23)(11,17,18,24,19,14,20,22)(25,26)(27,34)(28,32)(29,37)(30,33)(31,35)(36,39)(38,40);(9,11,13,19)(10,14,15,17)(12,20,21,18)(16,24,23,22)(25,27,30,36)(26,31,33,40)(28,35,29,38)(32,39,37,34);(25,28,30,29)(26,32,33,37)(27,35,36,38)(31,39,40,34)

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 276);