C₁₁×#819 #11760598

order	1056
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₁₁ ⋊ #108
Sylow	C₃ ⋊ C₁₁×#108

60 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)(15,17,19,26,20,27,18,25)(16,21,22,24,23,29,28,30);(13,14)(15,16,18,22,20,23,19,28)(17,24,25,29,27,30,26,21)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1056, 135);