C₁₁×C₇⋊C₁₆ #11927618

order	1232
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₁₁×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×C₇⋊C₁₆
unambiguous semidirect product	C₇⋊(C₁₁×C₁₆)

derived, Sylow	C₇ ⋊ C₁₁×C₁₆
Hall	C₇×C₁₁ ⋊ C₁₆

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1232

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14)(15,16)(17,18)(19,20,21,24,22,25,27,30,23,26,28,31,29,32,33,34);(12,13,15,17,18,16,14)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1232, 1);