C₃₁×#2545 #16842478

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₁×#2545

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

576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1984

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9448, C₃₁×#11565, C₃₁×#13228, …
maximal normal subgroup of	C₃₁×#9448, C₃₁×#11565, C₃₁×#13228, …
maximal quotient of	C₃₁×#13909, C₃₁×#13942, C₃₁×#14001, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1277);

C31×#2545 #16842478