C₃×C₅×#1365 #14274399

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×#1365

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	#102
commutator	C₂×C₈	C₂×C₃×C₄×C₅
Frattini, cosocle	C₄×C₈	C₂²×C₃×C₅
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ C₃×C₄×C₅×C₈ ◁ G

172 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 96 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 — 2 generators on 32 points:

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

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, 97);