Finite Group Databasebeta

← Group #97136

Character table — Group #97136

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888882222444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1-111-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1ii−i−i−i−iii
χ1722222222222222222222-2-22222-2-222-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-222-2-200000000000000000000000000000000
χ2122222222-2-2-2-2222-2-2-2-222-200002-2002-200000000000000000000002200-2-200000000
χ2222222222-2-2-2-2222-2-2-2-222-200002-2002-20000000000000000000000-2-2002200000000
χ2322222222-2-2-2-2222-2-2-2-22-220000-2200-22000000000000000000002200-2-20000000000
χ2422222222-2-2-2-2222-2-2-2-22-220000-2200-2200000000000000000000-2-200220000000000
χ2522222222-2-2-2-2-2-2-22222-22-200002-200-22000000000000000000002-200-220000000000
χ2622222222-2-2-2-2-2-2-22222-22-200002-200-2200000000000000000000-22002-20000000000
χ2722222222-2-2-2-2-2-2-22222-2-220000-22002-200000000000000000000002-200-2200000000
χ2822222222-2-2-2-2-2-2-22222-2-220000-22002-20000000000000000000000-22002-200000000
χ2922-2-2-22-2222-2-2000000002222-2-2-2-20000002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3022-2-2-22-2222-2-2000000002222-2-2-2-20000002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3122-2-2-22-2222-2-20000000022-2-222-2-2000000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3222-2-2-22-2222-2-20000000022-2-222-2-2000000-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3322-2-2-22-2222-2-200000000-2-222-2-222000000-2222−2−2−2−22222−2−2−2−2220000000000000000
χ3422-2-2-22-2222-2-200000000-2-222-2-222000000-22−2−22222−2−2−2−22222−2−20000000000000000
χ3522-2-2-22-2222-2-200000000-2-2-2-222220000002-222−2−2−2−222−2−22222−2−20000000000000000
χ3622-2-2-22-2222-2-200000000-2-2-2-222220000002-2−2−22222−2−222−2−2−2−2220000000000000000
χ372-2-222-2-222-22-222-222-2-2-2002-22-2002-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ382-2-222-2-222-22-222-222-2-2-2002-22-2002-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ392-2-222-2-222-22-222-222-2-2-200-22-2200-22000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ402-2-222-2-222-22-222-222-2-2-200-22-2200-22000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ412-2-222-2-222-22-2-2-22-2-2222002-22-200-220000000000000000000000000000002−2−222−2−22
χ422-2-222-2-222-22-2-2-22-2-2222002-22-200-22000000000000000000000000000000−222−2−222−2
χ432-2-222-2-222-22-2-2-22-2-222200-22-22002-20000000000000000000000000000002−2−22−222−2
χ442-2-222-2-222-22-2-2-22-2-222200-22-22002-2000000000000000000000000000000−222−22−2−22
χ454444-4-4-4-400004-440000-400000000000000002-22-22-22-2000000000000000000000000
χ464444-4-4-4-400004-440000-40000000000000000-22-22-22-22000000000000000000000000
χ474444-4-4-4-40000-44-40000400000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ484444-4-4-4-40000-44-4000040000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4944-4-44-44-400000004i−4i4i−4i000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ5044-4-44-44-400000004i−4i4i−4i00000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ5144-4-44-44-40000000−4i4i−4i4i000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ5244-4-44-44-40000000−4i4i−4i4i00000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ5344-4-4-44-44-4-444000000004-40000-440000000000000000000000000000000000000000
χ5444-4-4-44-44-4-44400000000-4400004-40000000000000000000000000000000000000000
χ554-44-444-4-400000004i−4i−4i4i00000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ564-44-444-4-400000004i−4i−4i4i0000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ574-44-444-4-40000000−4i4i4i−4i00000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ584-44-444-4-40000000−4i4i4i−4i0000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ594-44-4-4-4444-4-4400000000004-4-44000000000000000000000000000000000000000000
χ604-44-4-4-4444-4-440000000000-444-4000000000000000000000000000000000000000000
χ614-44-4-4-444-444-4000000000000000000004-40000000000000000000000000000000000
χ624-44-4-4-444-444-400000000000000000000-440000000000000000000000000000000000
χ634-4-444-4-44-44-4444-4-4-444-4000000000000000000000000000000000000000000000000
χ644-4-444-4-44-44-44-4-4444-4-44000000000000000000000000000000000000000000000000
χ654-4-44-444-400004-4-4000040000000000000000000000002-2-222-2-220000000000000000
χ664-4-44-444-400004-4-400004000000000000000000000000-222-2-222-20000000000000000
χ674-4-44-444-40000-4440000-40000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ684-4-44-444-40000-4440000-4000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.