C₃₁×#2471 #16842404

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₃₁×#2471

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₃₁×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

582 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)(36,37,39,40)(38,42,43,41)(44,45,48,50)(46,47,51,49);(33,35)(37,40)(41,42)(44,46,48,51)(45,49,50,47);(32,33)(34,35)(36,37)(38,41)(39,40)(42,43)(44,46)(45,47)(48,51)(49,50);(36,38,39,43)(37,41,40,42)(44,47)(45,46)(48,49)(50,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₁×#2471, C₃₁×#34727, C₃₁×#34732, …
maximal normal subgroup of	C₂×C₃₁×#2471, C₃₁×#34727, C₃₁×#34732, …
maximal quotient of	C₃₁×#13895, C₃₁×#13944, C₃₁×#13984, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1203);

C31×#2471 #16842404