C₁₁×C₃⋊C₃₂ #11760464

order	1056
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₁₁×C₃₂ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×C₃⋊C₃₂
unambiguous semidirect product	C₃⋊(C₁₁×C₃₂)

derived, Sylow	C₃ ⋊ C₁₁×C₃₂
Hall	C₃×C₁₁ ⋊ C₃₂

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 1056

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14)(15,16,17,21,18,22,25,31,19,23,26,32,28,34,37,41,20,24,27,33,29,35,38,42,30,36,39,43,40,44,45,46);(12,13,14)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1056, 1);