C₄×C₈×D₇ #89456

order	448
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₄×C₈×D₇

Fitting	C₄×C₇×C₈ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₄×C₈

162 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 218);