C₃₁×#1869 #16841802

order	3968
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₁×#1869

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂³
commutator	C₂²	C₂²×C₈×C₃₁
Frattini, cosocle	C₂²×C₄	C₂³×C₃₁
socle	C₂³×C₃₁	C₂²×C₄
prime radical	C₂²×D₄×C₃₁	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

432 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)(33,35)(36,37)(38,39)(40,41,43,46,44,42,45,47);(32,33,34,35)(40,42,43,47,44,41,45,46);(37,39)

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#7203, C₃₁×#7204, C₃₁×#7236, …
maximal normal subgroup of	C₃₁×#7203, C₃₁×#7204, C₃₁×#7236, …
maximal quotient of	C₃₁×#8937, C₃₁×#8938, C₃₁×#8939, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 601);

C31×#1869 #16841802