C₃₁×#2513 #16842446

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₃₁×#2513

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1984

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)(32,33,36,34)(35,38,39,37)(41,44)(42,46)(48,49,52,55)(50,54,51,53);(33,34)(37,38)(40,41,43,44)(42,45,46,47)(48,50,52,51)(49,53,55,54);(32,34,36,33)(35,38,39,37)(40,41)(42,45)(43,44)(46,47)(48,49)(50,53)(51,54)(52,55);(32,35,36,39)(33,37,34,38)(40,42,43,46)(41,45,44,47)(48,51,52,50)(49,54,55,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#27065, C₃₁×#27069, C₃₁×#27072, …
maximal normal subgroup of	C₃₁×#27065, C₃₁×#27069, C₃₁×#27072, …
maximal quotient of	C₃₁×#13885, C₃₁×#13936, C₃₁×#14002, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1245);

C31×#2513 #16842446