C₃₁×#2592 #16842525

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×#2592

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

520 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)(32,33,34,35)(36,37,39,41)(38,42,43,40)(45,47)(46,50);(36,37)(38,40)(39,41)(42,43)(44,45,48,47)(46,51,50,49);(32,33)(34,35)(36,37)(38,40)(39,41)(42,43)(44,46,48,50)(45,49,47,51);(36,38,39,43)(37,40,41,42)(44,47,48,45)(46,51,50,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#10006, C₃₁×#10010, C₃₁×#18273, …
maximal normal subgroup of	C₃₁×#10006, C₃₁×#10010, C₃₁×#18273, …
maximal quotient of	C₃₁×#13925, C₃₁×#13955, C₃₁×#14021, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1324);

C31×#2592 #16842525