C₃×C₅×#2242 #14275276

order	1920
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₃×C₅×#2242

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃×C₅
prime radical	C₂×C₃×C₅×D₈	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ C₃×C₄×C₅×C₈ ◁ G

276 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 128 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) = 48
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 48 points:

(1,2,3)(4,5,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,18)(19,31)(20,25)(21,39)(22,42)(23,43)(24,30)(26,35)(27,32)(28,41)(29,40)(33,45)(34,44)(36,48)(37,47)(38,46);(10,13)(14,16)(17,19,32,37,23,34,41,38,24,35,22,33,40,36,21,20)(18,25,39,48,29,45,42,26,30,46,28,44,43,47,27,31);(9,11,12,15)(10,14,13,16)(17,20,21,36,40,33,22,35,24,38,41,34,23,37,32,19)(18,26,27,45,43,48,28,25,30,31,42,47,29,44,39,46)

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 974);