C₄×#1088 #88628

order	432
isoclinism	isoclinic class of #1088
automorphism	Aut(G) = D₄×AΓL(1,𝔽₉) (order 1152) · Inn(G) = #157 · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

Fitting	C₄×H(3,𝔽₃) ⋊ C₄
derived, Sylow	H(3,𝔽₃) ⋊ C₄²

77 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 72

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 275);