C₁₁×#216 #10587191

order	528
isoclinism	isoclinic class of #213
automorphism	Aut(G) = C₂²×C₅×D₃×D₄ (order 960) · Inn(G) = #67 · Out(G) = C₂³×C₅
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₁₁ ⋊ Q₁₆
Sylow	C₃ ⋊ C₁₁×Q₁₆

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 528

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14)(15,17,19,25)(16,20,22,29)(18,27,28,24)(21,30,26,23);(13,14)(15,16,19,22)(17,23,25,30)(18,26,28,21)(20,27,29,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 61);