C₃₁×#1925 #16841858

order	3968
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₃₁×#1925

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂³×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1984

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₁×#1925, C₃₁×#21058, C₃₁×#21059, …
maximal normal subgroup of	C₂×C₃₁×#1925, C₃₁×#21058, C₃₁×#21059, …
maximal quotient of	C₃₁×#9541, C₃₁×#9545, C₃₁×#9561, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 657);

C31×#1925 #16841858