C₃₁×#2252 #16842185

order	3968
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₁×#2252

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ C₄×C₈×C₃₁ ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(32,33,35,37)(34,38,39,36)(41,45)(42,46)(43,49)(47,55)(48,53)(50,54)(51,52);(32,34,35,39)(33,36,37,38);(40,41,46,52,43,47,50,53,44,48,54,55,49,51,42,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#7450, C₃₁×#7451, C₃₁×#12392, …
maximal normal subgroup of	C₃₁×#7450, C₃₁×#7451, C₃₁×#12392, …
maximal quotient of	C₃₁×#12905, C₃₁×#13165, C₃₁×#13282, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 984);

C31×#2252 #16842185