C₃₁×#2581 #16842514

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

Aliases

direct product

C₃₁×#2581

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

468 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)(33,35)(36,37,39,41)(38,42,43,40);(36,37)(38,40)(39,41)(42,43)(44,45,47,49)(46,50,51,48);(32,33)(34,35)(36,37)(38,40)(39,41)(42,43)(44,46,47,51)(45,48,49,50);(36,38,39,43)(37,40,41,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9484, C₃₁×#9488, C₃₁×#9999, …
maximal normal subgroup of	C₃₁×#9484, C₃₁×#9488, C₃₁×#9999, …
maximal quotient of	C₃₁×#13925, C₃₁×#13942, C₃₁×#14017, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1313);

C31×#2581 #16842514