C₂×#6188 #88630

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) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

65 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 28 points:

(3,4,5,7,6,8,9,10)(11,12)(13,17,18,25)(14,16)(15,20,22,28)(19,26,27,23)(21,24);(1,2)(11,18,19)(12,16,24)(13,21,20)(14,27,28)(15,26,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 277);