C₃₁×#2477 #16842410

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×#2477

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

540 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)(36,37,39,41)(38,42,43,40)(44,45)(46,47)(48,50)(49,51);(33,35)(36,38,39,43)(37,40,41,42)(44,46,48,51)(45,47,50,49);(32,33)(34,35)(36,38)(37,40)(39,43)(41,42)(44,46)(45,49)(47,50)(48,51);(36,37)(38,40)(39,41)(42,43)(44,47,48,49)(45,46,50,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₁×#2477, C₃₁×#34720, C₃₁×#34732, …
maximal normal subgroup of	C₂×C₃₁×#2477, C₃₁×#34720, C₃₁×#34732, …
maximal quotient of	C₃₁×#13898, C₃₁×#13944, C₃₁×#13988, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1209);

C31×#2477 #16842410