C₂²×#1131 #90428

order	448
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₂²×C₇×C₈ ⋊ C₂
Sylow	C₇ ⋊ C₂²×M₁₆

298 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1190);