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C₆₁×#61091 #29564524

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 97 points:

(1,2)(3,4)(5,6,12,17)(7,18,22,34)(8,9,14,27)(10,16,11,15)(13,29,33,21)(19,20,23,36)(24,30,28,26)(25,35,31,32)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(5,7,12,22)(6,13,17,33)(8,23,14,19)(9,25,27,31)(10,21,11,29)(15,18,16,34)(20,30,36,26)(24,35,28,32);(2,4)(5,8,12,14)(6,9,17,27)(7,19,22,23)(10,28,11,24)(13,31,33,25)(15,30,16,26)(18,20,34,36)(21,35,29,32);(5,9)(6,14)(7,20)(8,17)(10,26)(11,30)(12,27)(13,32)(15,28)(16,24)(18,23)(19,34)(21,31)(22,36)(25,29)(33,35);(5,10,12,11)(6,15,17,16)(7,21,22,29)(8,24,14,28)(9,26,27,30)(13,18,33,34)(19,32,23,35)(20,31,36,25)

Conjugacy classes & character table

3538 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 54079);