C₄×#1131 #89459

order	448
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

Fitting	C₄×C₇×C₈ ⋊ C₂
Sylow	C₇ ⋊ C₄×M₁₆

142 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 221);