C₃₁×#2484 #16842417

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

Aliases

direct product

C₃₁×#2484

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

512 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)(33,35)(37,38)(39,43)(44,45,47,49)(46,48,51,50);(36,37,40,38)(39,41,43,42)(44,46)(45,48)(47,51)(49,50);(32,33)(34,35)(36,38,40,37)(39,42,43,41)(44,45)(46,50)(47,49)(48,51);(36,39)(37,41)(38,42)(40,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9478, C₃₁×#9482, C₃₁×#9514, …
maximal normal subgroup of	C₃₁×#9478, C₃₁×#9482, C₃₁×#9514, …
maximal quotient of	C₃₁×#13870, C₃₁×#13958, C₃₁×#13992, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1216);

C31×#2484 #16842417