C₃×C₅×#2245 #14275279

order	1920
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₃×C₅×#2245

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ C₃×C₄×C₅×C₈ ◁ G

264 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 3 generators on 48 points:

(1,2,3)(4,5,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,18,24,30)(19,26,34,45)(20,25,36,43)(21,28,38,40)(22,27,31,46)(23,39,37,29)(32,44,47,42)(33,48,35,41);(10,13)(14,16)(17,19,31,47,23,33,21,20,24,34,22,32,37,35,38,36)(18,25,40,48,29,42,27,26,30,43,28,41,39,44,46,45);(9,11,12,15)(10,14,13,16)(17,20,21,35,37,47,31,34,24,36,38,33,23,32,22,19)(18,26,27,44,39,48,40,43,30,45,46,42,29,41,28,25)

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 977);