C₅×Dic₁₈ #67090

order	360
isoclinism	isoclinic class of Dic₁₈
automorphism	Aut(G) = C₄×D₄×AGL(1,ℤ/9) (order 1728) · Inn(G) = C₂×D₉ · Out(G) = C₂²×C₃×C₄
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×Dic₁₈
unambiguous semidirect product	C₉⋊(C₅×Q₈)

Hall	C₅×C₉ ⋊ Q₈
Sylow	C₉ ⋊ C₅×Q₈

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 360

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3,4,5)(6,7,8,9)(10,13,12,11)(14,15,16,17,18,19,20,21,22);(6,10,8,12)(7,11,9,13)(15,22)(16,21)(17,20)(18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 20);