C₃₁×#1917 #16841850

order	3968
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₁×#1917

Subgroups

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

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 3968

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

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₁×#1917, C₃₁×#21021, C₃₁×#21022, …
maximal normal subgroup of	C₂×C₃₁×#1917, C₃₁×#21021, C₃₁×#21022, …
maximal quotient of	C₃₁×#9537, C₃₁×#9538, C₃₁×#9539, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 649);

C31×#1917 #16841850