C₃₁×#2052 #16841985

order	3968
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₁×#2052

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₁	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃₁
prime radical	C₂×#41×C₃₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

262 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 51
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(32,33)(34,35)(36,37)(38,46)(39,40)(41,44)(42,45)(43,48)(47,50)(49,51);(36,38,42,50)(37,43,45,51)(39,46,44,47)(40,49,41,48);(33,35)(36,39,40,37,42,44,41,45)(38,47,48,43,50,46,49,51)

Conjugacy classes & character table

806 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₃₁×#2052, C₃₁×#23530, C₃₁×#23532, …
maximal normal subgroup of	C₂×C₃₁×#2052, C₃₁×#23530, C₃₁×#23532, …
maximal quotient of	C₃₁×#10458, C₃₁×#10459, C₃₁×#10462, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 784);