Finite Group Databasebeta

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C₂×#20266223 #27187901

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

464 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 119 points:

(1,2,7,3)(4,11,14,8)(5,16,12,6)(9,24,23,17)(10,29,25,15)(13,20,27,21)(18,41,36,30)(19,46,42,28)(22,37,40,34)(26,33,44,38)(31,62,53,47)(32,65,49,45)(35,58,57,51)(39,54,61,55)(43,50,64,59)(48,80,68,63)(52,77,72,66)(56,73,76,70)(60,69,79,74)(67,91,83,78)(71,88,87,81)(75,84,90,85)(82,98,94,89)(86,95,97,92)(93,101,99,96)(104,107,108,115,109,116,113,117)(105,110,112,119,106,114,111,118);(2,4)(3,6)(5,9)(7,13)(8,15)(10,18)(11,12)(14,22)(16,26)(17,28)(19,31)(20,25)(21,24)(23,35)(27,39)(29,43)(30,45)(32,48)(33,42)(34,41)(36,52)(37,38)(40,56)(44,60)(46,63)(47,65)(49,50)(51,62)(53,67)(54,59)(55,58)(57,71)(61,75)(64,78)(66,80)(68,69)(70,77)(72,82)(73,74)(76,86)(79,89)(81,91)(83,84)(85,88)(87,93)(90,96)(92,98)(94,95)(97,100)(99,101)(104,106)(105,109)(107,114)(108,111)(110,116)(112,113)(115,118)(117,119);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,65)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,49,63,50)(53,66,67,80)(57,70,71,77)(61,74,75,73)(64,68,78,69)(72,81,82,91)(76,85,86,88)(79,83,89,84)(87,92,93,98)(90,94,96,95)(97,99,100,101)(104,105,108,112,109,106,113,111)(107,114,115,118,116,110,117,119);(102,103)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 21279);