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C3×C5×#1849 #14274883

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

Aliases

direct productC3×C5×#1849

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

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

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

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

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, 581);