C₃×C₅×#1839 #14274873

order	1920
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅×C₈ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃×C₅×#1839

Subgroups

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂²	C₂²×C₃×C₅×C₈
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄×C₅ ◁ G

480 conjugacy classes of subgroups; only the 272 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 272 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 — 3 generators on 32 points:

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

Conjugacy classes & character table

840 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 571);