C₃₁×#2499 #16842432

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×#2499

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

484 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)(37,40)(38,42)(44,45,48,50)(46,47,49,51);(36,37)(38,41)(39,40)(42,43)(44,46)(45,47)(48,49)(50,51);(32,33,34,35)(44,47)(45,49)(46,50)(48,51);(36,38,39,42)(37,41,40,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9444, C₃₁×#11552, C₃₁×#11556, …
maximal normal subgroup of	C₃₁×#9444, C₃₁×#11552, C₃₁×#11556, …
maximal quotient of	C₃₁×#13879, C₃₁×#13939, C₃₁×#14000, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1231);

C31×#2499 #16842432