C₇×#97 #6414

order	224
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₂×C₃×#2021 (order 768) · Inn(G) = C₂² · Out(G) = C₂×C₃×#120
homology	Abelianization (H₁) = C₄²×C₇ · Schur multiplier (H₂) = C₂

Aliases

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 224

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 46);