Finite Group Databasebeta

← Group #98008

Character table — Group #98008

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-11-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1-11-11ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1-11-11−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-111-1-11−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-111-1-11ii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1ii−i−i−i−iii
χ172222222222222222-2-222-2-2-2-222-2220000000000000000000000-2-2000000000000
χ182222222222222222-2-222-2-2-2-2-2-2-2-2-2000000000000000000000022000000000000
χ192222222222-2-2-222-222-2-22-22-200-20022-2-200000000000000000000-220000000000
χ202222222222-2-2-222-222-2-22-22-200-200-2-222000000000000000000002-20000000000
χ212222222222-2-2-222-2-2-2-2-2-22-2200200000000000000000000002-20000-2200000000
χ222222222222-2-2-222-2-2-2-2-2-22-220020000000000000000000000-2200002-200000000
χ2322222222-2-2222-2-2222-2-2-22-2200-200222200000000000000000000-2-20000000000
χ2422222222-2-2222-2-2222-2-2-22-2200-200-2-2-2-200000000000000000000220000000000
χ2522222222-2-2222-2-22-2-2-2-22-22-20020000000000000000000000220000-2-200000000
χ2622222222-2-2222-2-22-2-2-2-22-22-20020000000000000000000000-2-200002200000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222222-2-2-20000000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222-2-2-22200000000000000000000002-2000000000000
χ2922-2-2-222-20022-200-22-2000-202000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3022-2-2-222-20022-200-22-2000-202000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000
χ3122-2-2-222-20022-200-22-2000-20200000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3222-2-2-222-20022-200-22-2000-20200000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000
χ3322-2-2-222-200-2-220022-200020-2000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ3422-2-2-222-200-2-220022-200020-2000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ3522-2-2-222-200-2-220022-200020-200000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ3622-2-2-222-200-2-220022-200020-200000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ372-222-22-2-2222-2-2-2-22002-200002i−2i02i−2i0000000000002−22−22−22−2000000000000i2−i2i2−i2
χ382-222-22-2-2222-2-2-2-22002-200002i−2i02i−2i000000000000−22−22−22−22000000000000−i2i2−i2i2
χ392-222-22-2-2222-2-2-2-22002-20000−2i2i0−2i2i0000000000002−22−22−22−2000000000000−i2i2−i2i2
χ402-222-22-2-2222-2-2-2-22002-20000−2i2i0−2i2i000000000000−22−22−22−22000000000000i2−i2i2−i2
χ412-222-22-2-2-2-2-22222-2002-200002i−2i0−2i2i000000000000i2−i2i2−i2−i2i2−i2i2000000000000−222−2
χ422-222-22-2-2-2-2-22222-2002-200002i−2i0−2i2i000000000000−i2i2−i2i2i2−i2i2−i20000000000002−2−22
χ432-222-22-2-2-2-2-22222-2002-20000−2i2i02i−2i000000000000i2−i2i2−i2−i2i2−i2i20000000000002−2−22
χ442-222-22-2-2-2-2-22222-2002-20000−2i2i02i−2i000000000000−i2i2−i2i2i2−i2i2−i2000000000000−222−2
χ45444-44-4-4-400000000000040-400000000002-22-22-22-2000000000000000000000000
χ46444-44-4-4-400000000000040-40000000000-22-22-22-22000000000000000000000000
χ47444-44-4-4-4000000000000-40400000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ48444-44-4-4-4000000000000-4040000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4944-44-4-4-444i−4i0004i−4i0000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ5044-44-4-4-444i−4i0004i−4i000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ5144-44-4-4-44−4i4i000−4i4i0000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ5244-44-4-4-44−4i4i000−4i4i000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ5344-4-4-444-40044-400-4-4400040-400000000000000000000000000000000000000000
χ5444-4-4-444-400-4-44004-44000-40400000000000000000000000000000000000000000
χ554-444-44-4-444-444-4-4-400-44000000000000000000000000000000000000000000000
χ564-444-44-4-4-4-44-4-444400-44000000000000000000000000000000000000000000000
χ574-4-444-44-44i−4i000−4i4i0000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ584-4-444-44-44i−4i000−4i4i000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ594-4-444-44-4−4i4i0004i−4i0000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ604-4-444-44-4−4i4i0004i−4i000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ614-4-4-444-44004-4400-400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ624-4-4-444-44004-4400-40000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ634-4-4-444-4400-44-400400000000000000000000000002-2-22-222-20000000000000000
χ644-4-4-444-4400-44-40040000000000000000000000000-222-22-2-220000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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