C₃₁×#2063 #16841996

order	3968
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₁×#2063

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₁	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

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

normal subgroups only

This group has 228 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) = 992

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)(36,37,39,45,41,43,40,44)(38,46,47,42,49,50,48,51);(32,33)(34,35)(36,38,39,47,41,49,40,48)(37,42,44,46,43,51,45,50);(33,35)(37,43)(38,47)(39,40)(42,50)(46,51)(48,49)

Conjugacy classes & character table

806 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₃₁×#2063, C₃₁×#23601, C₃₁×#23602, …
maximal normal subgroup of	C₂×C₃₁×#2063, C₃₁×#23601, C₃₁×#23602, …
maximal quotient of	C₃₁×#10587, C₃₁×#10589, C₃₁×#10591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 795);