C₃×C₅×#1418 #14274452

order	1920
nilpotency class	5
isoclinism	isoclinic class of #1418
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×C₅×#1418

Subgroups

	subgroup	G/H
center, socle	C₂×C₃×C₅	#357
commutator	C₁₆	C₂×C₃×C₄×C₅
Frattini, cosocle	C₂×C₁₆	C₂²×C₃×C₅
prime radical	C₃×C₅×#508	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂×C₃×C₄×C₅ ◁ C₂×C₃×C₅×C₈ ◁ C₂×C₃×C₅×C₁₆ ◁ G

148 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3)(4,5,6,7,8)(10,15,16,31)(11,19)(12,24)(13,26)(17,35,34,39)(18,36,28,33)(20,25,32,30)(21,27)(22,40)(23,29)(37,38);(9,10)(11,20)(12,25)(13,28)(14,16)(15,29)(17,24)(18,26)(19,31)(21,34)(22,35)(23,32)(27,30)(33,38)(36,40)(37,39)

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, 150);