C₇×#101 #6418

order	224
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	Aut(G) = C₂×C₃×#2196 (order 768) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂×C₃×D₄
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂

Aliases

38 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,4,8,5,7,13,15)(3,9,10,16,11,6,12,14)(17,18,19,20,21,22,23);(1,3,5,11)(2,6,7,9)(4,12,13,10)(8,16,15,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 50);