C₃₁×#2509 #16842442

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₁×#2509

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

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 3968

A minimal faithful permutation representation — 4 generators on 55 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)(33,36)(34,38)(40,41,44,47)(42,46,43,45)(48,49,53,51)(50,55,54,52);(32,33,35,36)(34,37,38,39)(40,42,44,43)(41,45,47,46)(48,50)(49,52)(51,55)(53,54);(32,33)(34,37)(35,36)(38,39)(40,41)(42,45)(43,46)(44,47)(48,51,53,49)(50,55,54,52);(32,34,35,38)(33,37,36,39)(40,43,44,42)(41,46,47,45)(48,52,53,55)(49,54,51,50)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#26755, C₃₁×#26759, C₃₁×#26762, …
maximal normal subgroup of	C₃₁×#26755, C₃₁×#26759, C₃₁×#26762, …
maximal quotient of	C₃₁×#13885, C₃₁×#13933, C₃₁×#14006, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1241);

C31×#2509 #16842442