Finite Group Databasebeta

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C₈₃×#61808 #35289632

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 115 points:

(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,22,27)(19,23,20,25)(21,24,30,26)(28,31,29,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19)(18,23)(20,22)(21,28)(24,31)(25,27)(26,32)(29,30);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(18,24)(21,30)(23,31)(25,32)(26,27)(28,29);(3,11)(6,9)(10,16)(13,15)(17,20,22,19)(18,25,27,23)(21,29,30,28)(24,32,26,31);(2,8)(6,9)(7,14)(13,15)(19,20)(23,25)(28,29)(31,32)

Conjugacy classes & character table

4067 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 54796);