C₃×C₅×#2247 #14275281

order	1920
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃×C₅×#2247

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

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) = 44
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 3 generators on 44 points:

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

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 979);