C₈×C₄⋊C₄×C₃₁ #16841702

order	3968
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₃₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₈×C₄⋊C₄×C₃₁

296 conjugacy classes of subgroups.

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 3968

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(10,12)(13,14,15,16);(9,10,11,12)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 501);