C₃×C₅×#1843 #14274877

order	1920
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃×C₅×#1843

Subgroups

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

512 conjugacy classes of subgroups; only the 304 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 304 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)(10,12)(14,16)(17,18,20,23,21,24,27,30)(19,22,26,29,25,28,31,32);(9,10,11,12)(17,19)(18,22)(20,26)(21,25)(23,29)(24,28)(27,31)(30,32);(13,14,15,16)(19,25)(22,28)(26,31)(29,32)

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 575);