C₃₁×#2360 #16842293

order	3968
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₁×#2360

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(36,37,39,38)(40,41)(42,43)(44,45)(46,47);(36,38,39,37)(41,45)(43,46);(32,33)(34,35)(40,42)(41,46)(43,45)(44,47);(40,43,44,46)(41,42,45,47)

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#22854, C₃₁×#22859, C₃₁×#22862, …
maximal normal subgroup of	C₃₁×#22854, C₃₁×#22859, C₃₁×#22862, …
maximal quotient of	C₂²⋊C₄×C₄⋊C₄×C₃₁, C₃₁×#13814, C₃₁×#13817, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1092);

C31×#2360 #16842293