C₃×C₅×#1348 #14274382

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×#1348

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	C₂³×C₃×C₅	D₈
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ C₂²×C₃×C₅×C₈ ◁ G

232 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 480

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)(18,22)(19,25)(20,27)(23,32)(24,31)(26,29)(28,30);(9,11)(10,13)(12,16)(14,15)(17,18,21,24)(19,26,28,32)(20,29,27,23)(22,30,31,25)

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, 80);