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C₇₉×#61349 #34173038

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 103 points:

(2,5)(6,7)(10,14)(11,18)(12,21)(15,23)(19,20)(22,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,2,4,5)(3,7,8,6)(9,10,13,14)(11,15,20,22)(12,17,21,16)(18,24,19,23);(9,11)(10,15)(12,19)(13,20)(14,22)(16,24)(17,23)(18,21);(1,3,4,8)(2,6,5,7)(10,14)(15,22)(16,17)(23,24);(9,12,13,21)(10,16,14,17)(11,19,20,18)(15,24,22,23)

Conjugacy classes & character table

4345 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 54337);