C₃₁×#2851 #16842784

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

Aliases

direct product

C₃₁×#2851

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

556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 4 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)(33,35)(36,37,40,43)(38,42,39,41)(44,45,48,47)(46,50,51,49);(36,38,40,39)(37,41,43,42)(44,46)(45,49)(47,50)(48,51);(36,39,40,38)(37,42,43,41)(44,47,48,45)(46,50,51,49);(32,33)(34,35)(36,37)(38,41)(39,42)(40,43)(44,46)(45,49)(47,50)(48,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#7671, C₃₁×#7691, C₃₁×#7711, …
maximal normal subgroup of	C₃₁×#7671, C₃₁×#7691, C₃₁×#7711, …
maximal quotient of	C₃₁×#14682, C₃₁×#14695, C₃₁×#14697, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1583);

C31×#2851 #16842784