C₂³×M₁₆×C₃₁ #16843503

order	3968
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₃₁ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂³×M₁₆×C₃₁

1720 conjugacy classes of subgroups.

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 5 generators on 45 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(3,4);(5,6);(7,8,9,10,11,12,13,14);(8,12)(10,14)

2480 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2302);