C₃×C₅×#1349 #14274383

order	1920
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×C₅×#1349

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#102
commutator	C₂×C₈	C₂×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₈	C₂²×C₃×C₅
prime radical	C₃×C₅×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ C₂²×C₃×C₅×C₈ ◁ G

228 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 80 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)(11,15,16,13)(12,14)(17,18,20,25,22,27,21,26)(19,28,30,24,31,23,29,32);(9,11)(10,13)(12,16)(14,15)(18,23)(19,29)(20,21)(24,25)(26,32)(27,28)(30,31)

Conjugacy classes & character table

435 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 81);