Finite Group Databasebeta

← Group #99020

Character table — Group #99020

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888244488888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ91111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-1
χ101111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-1
χ111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111ii−i−iii−i−i−i−iii−i−iii-1-111
χ121111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111−i−iii−i−iiiii−i−iii−i−i-1-111
χ131111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1ii−i−i−i−iiiii−i−i−i−iii-1-111
χ141111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1−i−iiiii−i−i−i−iiiii−i−i-1-111
χ151111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111ii−i−i−i−iii−i−iiiii−i−i11-1-1
χ161111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111−i−iiiii−i−iii−i−i−i−iii11-1-1
χ1722222222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-2222222-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ202222222222-2-2-2-2222222-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2122222222-2-222222222-2-2-2-2-2-222-2-200000000000000002-22-200000000000000000000
χ2222222222-2-222222222-2-2-2-2-2-222-2-20000000000000000-22-2200000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-22222-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-2-2-22222-2-222-2-2-2-2220000000000000000000000000000000000002i−2i−2i2i
χ2622222222-2-2-2-2-2-22222-2-222-2-2-2-222000000000000000000000000000000000000−2i2i2i−2i
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-200000000000000002-2-2200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000-222-200000000000000000000
χ29222-2-22-2-22-200002i2i−2i−2i2-2002i−2i000000002i2i−2i−2i22-2-2000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ30222-2-22-2-22-200002i2i−2i−2i2-2002i−2i000000002i2i−2i−2i22-2-200000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ31222-2-22-2-22-200002i2i−2i−2i2-2002i−2i00000000−2i−2i2i2i-2-222000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000
χ32222-2-22-2-22-200002i2i−2i−2i2-2002i−2i00000000−2i−2i2i2i-2-22200000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000
χ33222-2-22-2-22-20000−2i−2i2i2i2-200−2i2i000000002i2i−2i−2i-2-222000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000
χ34222-2-22-2-22-20000−2i−2i2i2i2-200−2i2i000000002i2i−2i−2i-2-22200000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000
χ35222-2-22-2-22-20000−2i−2i2i2i2-200−2i2i00000000−2i−2i2i2i22-2-2000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ36222-2-22-2-22-20000−2i−2i2i2i2-200−2i2i00000000−2i−2i2i2i22-2-200000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ372-2-2222-2-22-22i2i−2i−2i0000-222i−2i00000022-2-200002i−2i2i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ382-2-2222-2-22-22i2i−2i−2i0000-222i−2i00000022-2-200002i−2i2i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ392-2-2222-2-22-22i2i−2i−2i0000-222i−2i000000-2-2220000−2i2i−2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ402-2-2222-2-22-22i2i−2i−2i0000-222i−2i000000-2-2220000−2i2i−2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ412-2-2222-2-22-2−2i−2i2i2i0000-22−2i2i00000022-2-20000−2i2i−2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ422-2-2222-2-22-2−2i−2i2i2i0000-22−2i2i00000022-2-20000−2i2i−2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ432-2-2222-2-22-2−2i−2i2i2i0000-22−2i2i000000-2-22200002i−2i2i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ442-2-2222-2-22-2−2i−2i2i2i0000-22−2i2i000000-2-22200002i−2i2i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ45444-4-44-4-4-4400004i4i−4i−4i-4400−4i4i00000000000000000000000000000000000000000000
χ46444-4-44-4-4-440000−4i−4i4i4i-44004i−4i00000000000000000000000000000000000000000000
χ4744-44-4-44-40000000000000000004i−4i2i2−2i22i2−2i222−2222−2200000000000000000000000000000000
χ4844-44-4-44-40000000000000000004i−4i−2i22i2−2i22i2−2222−222200000000000000000000000000000000
χ4944-44-4-44-4000000000000000000−4i4i2i2−2i22i2−2i2−2222−222200000000000000000000000000000000
χ5044-44-4-44-4000000000000000000−4i4i−2i22i2−2i22i222−2222−2200000000000000000000000000000000
χ5144-4-44-4-44004-44-40000000000000000002i2−2i2−2i22i200002i22i2−2i2−2i2000000000000000000000000
χ5244-4-44-4-44004-44-4000000000000000000−2i22i22i2−2i20000−2i2−2i22i22i2000000000000000000000000
χ5344-4-44-4-4400-44-440000000000000000002i2−2i2−2i22i20000−2i2−2i22i22i2000000000000000000000000
χ5444-4-44-4-4400-44-44000000000000000000−2i22i22i2−2i200002i22i2−2i2−2i2000000000000000000000000
χ554-444-4-4-440000004-44-400000000002i2−2i2−2i22i2000000002i2−2i22i2−2i2000000000000000000000000
χ564-444-4-4-440000004-44-40000000000−2i22i22i2−2i200000000−2i22i2−2i22i2000000000000000000000000
χ574-444-4-4-44000000-44-4400000000002i2−2i2−2i22i200000000−2i22i2−2i22i2000000000000000000000000
χ584-444-4-4-44000000-44-440000000000−2i22i22i2−2i2000000002i2−2i22i2−2i2000000000000000000000000
χ594-44-44-44-4004i−4i−4i4i4i−4i−4i4i0000004-4000000000000000000000000000000000000000000
χ604-44-44-44-4004i−4i−4i4i−4i4i4i−4i000000-44000000000000000000000000000000000000000000
χ614-44-44-44-400−4i4i4i−4i4i−4i−4i4i000000-44000000000000000000000000000000000000000000
χ624-44-44-44-400−4i4i4i−4i−4i4i4i−4i0000004-4000000000000000000000000000000000000000000
χ634-4-4444-4-4-444i4i−4i−4i00004-4−4i4i0000000000000000000000000000000000000000000000
χ644-4-4444-4-4-44−4i−4i4i4i00004-44i−4i0000000000000000000000000000000000000000000000
χ654-4-4-4-44444400000000-4-400000000000000004i−4i−4i4i0000000000000000000000000000
χ664-4-4-4-44444400000000-4-40000000000000000−4i4i4i−4i0000000000000000000000000000
χ674-4-4-4-4444-4-40000000044000000000000000000004-4-44000000000000000000000000
χ684-4-4-4-4444-4-4000000004400000000000000000000-444-4000000000000000000000000

Here i is the imaginary unit (i² = −1).