C₃×C₅×#1307 #14274341

order	1920
nilpotency class	3
isoclinism	isoclinic class of #1304
automorphism	?
homology	Abelianization (H₁) = C₃×C₄²×C₅ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₃×C₅×#1307

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#95
commutator	C₂³	C₃×C₄²×C₅
Frattini, cosocle	C₂×C₄²	C₂²×C₃×C₅
prime radical	C₂³×C₃×C₅	C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

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

normal subgroups only

This group has 260 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) = 32
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 2 generators on 32 points:

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

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, 39);