C₃₁×#2506 #16842439

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

Aliases

direct product

C₃₁×#2506

Subgroups

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

436 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 3968

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#26752, C₃₁×#26756, C₃₁×#26761, …
maximal normal subgroup of	C₃₁×#26752, C₃₁×#26756, C₃₁×#26761, …
maximal quotient of	C₃₁×#13884, C₃₁×#13918, C₃₁×#14005, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1238);

C31×#2506 #16842439