C₃×C₅×#2070 #14275104

order	1920
nilpotency class	3
isoclinism	isoclinic class of #2069
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃×C₅×#2070

Subgroups

	subgroup	G/H
center, socle	C₂×C₃×C₅	#396
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂³×C₃×C₅	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

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

normal subgroups only

This group has 392 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) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

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

Conjugacy classes & character table

345 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 802);