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C3×C5×#401 #11751376

order960
nilpotency class2
isoclinismisoclinic class of #392
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC3×C5×#401

Subgroups

subgroupG/H
center, socle, prime radicalC23×C3×C5C23
commutator, Frattini, cosocleC23C23×C3×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

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

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

Conjugacy classes & character table

330 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofC5×D3×#401, C3×D5×#401, D15×#401, …
maximal subgroup ofC2×C3×C5×#401, C3×C5×#2401, C3×C5×#2493, …
maximal normal subgroup ofC2×C3×C5×#401, C3×C5×#2401, C3×C5×#2493, …
maximal quotient ofC3×C5×#1443, C3×C5×#2104, C2×C3×C5×#401

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 5571);