C₃×C₅×#1716 #14274750

order	1920
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₃×C₅×#1716

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₃×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

352 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 160 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) = 32
transitive degree	μ_t(G) = 1920

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

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

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, 448);