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C3×C5×#2645 #14275679

order1920
nilpotency class2
isoclinismisoclinic class of #2613
automorphism?
homologyAbelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C23

Aliases

direct productC3×C5×#2645

Subgroups

subgroupG/H
center, socle, prime radicalC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 32 points:

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

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, 1377);