C₂×#611 #3703

order	144
isoclinism	isoclinic class of Dic₁₈
automorphism	Aut(G) = #120×AGL(1,ℤ/9) (order 1728) · Inn(G) = C₂×D₉ · Out(G) = C₂×C₃×D₄
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

Fitting	C₂³×C₉ ⋊ C₂
Sylow	C₉ ⋊ C₂×D₄

81 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 46);