C₂×C₄²×D₇ #90162

order	448
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

C₂×C₄²×D₇

Fitting	C₂×C₄²×C₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂²×C₄²

498 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 4 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 924);