C₇×#99 #6416

order	224
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	Aut(G) = C₂×C₃×B(4,𝔽₂) (order 384) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂²

Aliases

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 56

A minimal faithful permutation representation — 2 generators on 15 points:

(1,2)(3,7,8,5)(4,6)(9,10,11,12,13,14,15);(1,3)(2,5)(4,8)(6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 48);