C₇×#102 #6419

order	224
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂⁴×C₃×D₄ (order 384) · Inn(G) = D₄ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂²

Aliases

50 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 51);