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#508×C₂₁₁ #27212786

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 243 points:

(1,2)(3,12)(4,8)(5,19)(6,11)(7,14)(9,17)(10,18)(13,25)(15,31)(16,28)(20,27)(21,24)(22,29)(23,30)(26,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243);(1,3)(2,7)(4,13)(5,20)(6,16)(8,22)(9,25)(10,27)(11,23)(12,19)(14,17)(15,18)(21,29)(24,28)(26,31)(30,32);(1,4,6,18)(2,8,11,10)(3,13,16,15)(5,17,21,32)(7,22,23,27)(9,24,26,19)(12,25,28,31)(14,29,30,20)

Conjugacy classes & character table

4642 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13504, 189);