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C3×C5×#2101 #14275135

order1920
nilpotency class3
isoclinismisoclinic class of #1999
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC3×C5×#2101

Subgroups

subgroupG/H
center, socle, prime radicalC23×C3×C5C2×D4
commutator, Frattini, cosocleC22×C4C23×C3×C5
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G

396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1920

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

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

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, 833);