Finite Group Databasebeta

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C₇₉×#62161 #34173850

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 127 points:

(1,2,5,8)(3,9,10,6)(4,12,13,7)(11,14,16,15)(17,18)(19,23)(20,31)(21,25)(22,27)(24,33)(26,35)(28,42)(29,37)(30,38)(32,40)(34,41)(36,45)(39,46)(43,47)(44,48)(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);(1,3)(2,6)(4,11)(5,10)(7,14)(8,9)(12,15)(13,16)(17,19)(18,23)(20,28)(21,29)(22,30)(24,36)(25,37)(26,39)(27,38)(31,42)(32,43)(33,45)(34,44)(35,46)(40,47)(41,48);(17,20,22,34)(18,24,27,40)(19,28,30,44)(21,32,35,33)(23,36,38,47)(25,31,26,41)(29,43,46,45)(37,42,39,48);(3,10)(6,9)(11,16)(14,15)(17,21,22,35)(18,25,27,26)(19,29,30,46)(20,32,34,33)(23,37,38,39)(24,31,40,41)(28,43,44,45)(36,42,47,48);(1,4,5,13)(2,7,8,12)(3,11,10,16)(6,14,9,15)(19,30)(23,38)(28,44)(29,46)(36,47)(37,39)(42,48)(43,45)

Conjugacy classes & character table

3871 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 55149);