Finite Group Databasebeta

← Group #99080

Character table — Group #99080

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888224488888888888888888888
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
χ911111111-1-1-1-1111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1ii−i−iii−i−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-1111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1−i−iii−i−iii−i−iii−i−iii11-1-1
χ1111111111-1-1-1-1111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11ii−i−iii−i−i−i−iii−i−iii-1-111
χ1211111111-1-1-1-1111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11−i−iii−i−iiiii−i−iii−i−i-1-111
χ1311111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1ii−i−i−i−iiiii−i−i−i−iii-1-111
χ1411111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1−i−iiiii−i−i−i−iiiii−i−i-1-111
χ1511111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11ii−i−i−i−iii−i−iiiii−i−i11-1-1
χ1611111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11−i−iiiii−i−iii−i−i−i−iii11-1-1
χ17222222222222-2-2-22222-222-2-2-2-2-2-200000000000000002-2-2200000000000000000000
χ18222222222222-2-2-22222-222-2-2-2-2-2-20000000000000000-222-200000000000000000000
χ192222222222-2-222222-2-22-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ202222222222-2-222222-2-22-2-2-2-222-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000
χ212222222222-2-2-2-2-222-2-2-2-2-222-2-2220000000000000000000000000000000000002i−2i2i−2i
χ222222222222-2-2-2-2-222-2-2-2-2-222-2-222000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-222222-2-2222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2422222222-2-222222-2-2222-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2522222222-2-222-2-2-2-2-222-2-2-22222-2-20000000000000000000000000000000000002i−2i−2i2i
χ2622222222-2-222-2-2-2-2-222-2-2-22222-2-2000000000000000000000000000000000000−2i2i2i−2i
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000022-2-200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000-2-22200000000000000000000
χ29222-2-2-2-2200222-2-200-2-220000002-222-2-20000000022-2-20000i2−i2i2−i2i2−i2i2−i2000000000000
χ30222-2-2-2-2200222-2-200-2-220000002-222-2-20000000022-2-20000−i2i2−i2i2−i2i2−i2i2000000000000
χ31222-2-2-2-2200222-2-200-2-220000002-2-2-22200000000-2-2220000i2−i2i2−i2−i2i2−i2i2000000000000
χ32222-2-2-2-2200222-2-200-2-220000002-2-2-22200000000-2-2220000−i2i2−i2i2i2−i2i2−i2000000000000
χ33222-2-2-2-2200-2-22-2-200222000000-2222-2-200000000-2-22200002−2−222−2−22000000000000
χ34222-2-2-2-2200-2-22-2-200222000000-2222-2-200000000-2-2220000−222−2−222−2000000000000
χ35222-2-2-2-2200-2-22-2-200222000000-22-2-2220000000022-2-200002−2−22−222−2000000000000
χ36222-2-2-2-2200-2-22-2-200222000000-22-2-2220000000022-2-20000−222−22−2−22000000000000
χ372-2-222-2-222200-22-2-2-200200002-200000022-2-200002-22-2000000000000i2−i2i2−i2i2−i2i2−i20000
χ382-2-222-2-222200-22-2-2-200200002-200000022-2-200002-22-2000000000000−i2i2−i2i2−i2i2−i2i20000
χ392-2-222-2-222200-22-2-2-200200002-2000000-2-2220000-22-22000000000000i2−i2i2−i2−i2i2−i2i20000
χ402-2-222-2-222200-22-2-2-200200002-2000000-2-2220000-22-22000000000000−i2i2−i2i2i2−i2i2−i20000
χ412-2-222-2-22-2-200-22-2220020000-2200000022-2-20000-22-220000000000002−2−222−2−220000
χ422-2-222-2-22-2-200-22-2220020000-2200000022-2-20000-22-22000000000000−222−2−222−20000
χ432-2-222-2-22-2-200-22-2220020000-22000000-2-22200002-22-20000000000002−2−22−222−20000
χ442-2-222-2-22-2-200-22-2220020000-22000000-2-22200002-22-2000000000000−222−22−2−220000
χ45444-4-4-4-440044-44400-4-4-4000000-440000000000000000000000000000000000000000
χ46444-4-4-4-4400-4-4-4440044-40000004-40000000000000000000000000000000000000000
χ4744-44-44-4-4000000000000004i−4i00002i2−2i22i2−2i222−2222−2200000000000000000000000000000000
χ4844-44-44-4-4000000000000004i−4i0000−2i22i2−2i22i2−2222−222200000000000000000000000000000000
χ4944-44-44-4-400000000000000−4i4i00002i2−2i22i2−2i2−2222−222200000000000000000000000000000000
χ5044-44-44-4-400000000000000−4i4i0000−2i22i2−2i22i222−2222−2200000000000000000000000000000000
χ5144-4-44-44-44i−4i000004i−4i000000000002i2−2i2−2i22i200002222−22−220000000000000000000000000000
χ5244-4-44-44-44i−4i000004i−4i00000000000−2i22i22i2−2i20000−22−2222220000000000000000000000000000
χ5344-4-44-44-4−4i4i00000−4i4i000000000002i2−2i2−2i22i20000−22−2222220000000000000000000000000000
χ5444-4-44-44-4−4i4i00000−4i4i00000000000−2i22i22i2−2i200002222−22−220000000000000000000000000000
χ554-444-4-44-4004i−4i000004i−4i000000000000022−22−22222i2−2i22i2−2i20000000000000000000000000000
χ564-444-4-44-4004i−4i000004i−4i0000000000000−222222−22−2i22i2−2i22i20000000000000000000000000000
χ574-444-4-44-400−4i4i00000−4i4i000000000000022−22−2222−2i22i2−2i22i20000000000000000000000000000
χ584-444-4-44-400−4i4i00000−4i4i0000000000000−222222−222i2−2i22i2−2i20000000000000000000000000000
χ594-44-444-4-44i−4i4i−4i000−4i4i−4i4i04-40000000000000000000000000000000000000000000000
χ604-44-444-4-44i−4i−4i4i000−4i4i4i−4i0-440000000000000000000000000000000000000000000000
χ614-44-444-4-4−4i4i4i−4i0004i−4i−4i4i0-440000000000000000000000000000000000000000000000
χ624-44-444-4-4−4i4i−4i4i0004i−4i4i−4i04-40000000000000000000000000000000000000000000000
χ634-4-444-4-4444004-44-4-400-40000-44000000000000000000000000000000000000000000
χ644-4-444-4-44-4-4004-444400-400004-4000000000000000000000000000000000000000000
χ654-4-4-4-4444000044-40000-400000000000000004i−4i−4i4i0000000000000000000000000000
χ664-4-4-4-4444000044-40000-40000000000000000−4i4i4i−4i0000000000000000000000000000
χ674-4-4-4-44440000-4-4400004000000000000000000004-4-44000000000000000000000000
χ684-4-4-4-44440000-4-440000400000000000000000000-444-4000000000000000000000000

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