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C₂×Q₆₄×C₂₃₃ #44448293

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 299 points:

(1,2)(67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299);(3,4,9,14)(5,15,19,46)(6,20,25,44)(7,26,29,60)(8,30,28,13)(10,32,35,16)(11,36,39,23)(12,40,42,22)(17,48,49,65)(18,50,31,45)(21,41,55,66)(24,58,57,52)(27,37,61,64)(33,59,62,54)(34,47,43,53)(38,56,51,63);(3,5,9,19)(4,10,14,35)(6,21,25,55)(7,27,29,61)(8,31,28,18)(11,37,39,64)(12,41,42,66)(13,43,30,34)(15,44,46,20)(16,36,32,23)(17,40,49,22)(24,59,57,54)(26,33,60,62)(38,65,51,48)(45,52,50,58)(47,56,53,63)

Conjugacy classes & character table

8854 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29824, 993);