C₁₁×C₃⋊C₁₆ #10587131

order	528
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₁₁×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×C₃⋊C₁₆
unambiguous semidirect product	C₃⋊(C₁₁×C₁₆)

derived, Sylow	C₃ ⋊ C₁₁×C₁₆
Hall	C₃×C₁₁ ⋊ C₁₆

20 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)(13,14)(15,16,17,20,18,21,23,26,19,22,24,27,25,28,29,30);(12,13,14)

264 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 1);