Q₈×C₄⋊C₄×C₁₉ #14560207

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

Q₈×C₄⋊C₄×C₁₉

568 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 4 generators on 35 points:

(1,2,3,4)(5,8,7,6)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(1,5,3,7)(2,6,4,8);(10,12)(13,14,15,16);(9,10,11,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1082);