C₃₁×#2857 #16842790

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₁×#2857

Subgroups

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

644 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)(37,39)(40,41,44,47)(42,46,43,45);(40,42,44,43)(41,45,47,46);(36,37,38,39)(40,43,44,42)(41,46,47,45);(32,33)(34,35)(40,41)(42,45)(43,46)(44,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#7665, C₃₁×#7667, C₃₁×#7668, …
maximal normal subgroup of	C₃₁×#7665, C₃₁×#7667, C₃₁×#7668, …
maximal quotient of	C₃₁×#14686, C₃₁×#14697, C₃₁×#14699, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1589);

C31×#2857 #16842790