C₂²×C₇⋊C₈ #6483

order	224
isoclinism	isoclinic class of D₇
automorphism	Aut(G) = C₂×AGL(1,𝔽₇)×#5934 (order 16128) · Inn(G) = D₇ · Out(G) = C₂×C₃×#5934
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₇⋊C₈

C₇ ⋊ C₂²×C₈

76 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 115);