C₂²×(C₂×D₇)⋊C₄ #90478

order	448
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

Fitting	C₂³×C₄×C₇ ⋊ C₂
Sylow	C₇ ⋊ C₂²×C₂²⋊C₄

674 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1240);