C₂×#3663 #63463

order	288
isoclinism	isoclinic class of Dic₁₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₂×C₈×C₉ ⋊ C₂
Sylow	C₉ ⋊ C₂×M₁₆

102 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 111);