C₃₁×#2519 #16842452

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₁×#2519

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 4 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)(33,34)(37,40)(41,43)(44,45,48,47)(46,50,51,49);(32,33,35,34)(46,51)(49,50);(32,33,35,34)(36,37)(38,41)(39,40)(42,43)(44,46)(45,49)(47,50)(48,51);(32,34,35,33)(36,38,39,42)(37,41,40,43)(44,47,48,45)(46,50,51,49)

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₁×#2519, C₃₁×#34763, C₃₁×#34808, …
maximal normal subgroup of	C₂×C₃₁×#2519, C₃₁×#34763, C₃₁×#34808, …
maximal quotient of	C₃₁×#13889, C₃₁×#13914, C₃₁×#14010, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1251);

C31×#2519 #16842452