Finite Group Databasebeta

← Group #98299

Character table — Group #98299

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422444444444888888888888888844444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111-1-1111-1-1-1-11111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ7111111111111111111111-1-1-1-111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ8111111111111111111111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-11111-111-1-1-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-11111-111-1-1-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-11111-111-1-1-1-11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-1-111ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-11111-111-1-1-1-11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1111−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1111ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii111-1-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i111-1-1-1ii−i−i−i−iii
χ1722222222222222-2-222-2-222222-2-2-22-222-200-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-222-2-22-2-2-2-2-2-2-22-2-2-2-200222200000000000000000000000000000000
χ19222222222222-2-222-2-222-222222-2-2-22-2-2-200-2-22200000000000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-22-2-2-2222-20022-2-200000000000000000000000000000000
χ2122222222-2-2-2-222222222-20000-222-2-200-2220000220000000000000000-200-20000000000
χ2222222222-2-2-2-222222222-20000-222-2-200-2-2-20000-2-2000000000000000020020000000000
χ2322222222-2-2-2-222-2-222-2-2-200002-2-2-2200200000000000000000000000002-202-200000000
χ2422222222-2-2-2-222-2-222-2-2-200002-2-2-220020000000000000000000000000-220-2200000000
χ2522222222-2-2-2-2-2-222-2-22220000-2-2-22-200200000000000000000000000002-20-2200000000
χ2622222222-2-2-2-2-2-222-2-22220000-2-2-22-20020000000000000000000000000-2202-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2200002222200-2220000-2-20000000000000000200-20000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2200002222200-2-2-20000220000000000000000-20020000000000
χ292222-2-2-2-222-2-22200-2-200222-2-2000-202-20000000000000000022−2−222−2−200000000002−22−2
χ302222-2-2-2-222-2-22200-2-200222-2-2000-202-200000000000000000−2−222−2−2220000000000−22−22
χ312222-2-2-2-222-2-22200-2-2002-2-222000-20-220000000000000000022−2−222−2−20000000000−22−22
χ322222-2-2-2-222-2-22200-2-2002-2-222000-20-2200000000000000000−2−222−2−22200000000002−22−2
χ332222-2-2-2-222-2-2-2-2002200-222-2-200020-2200000000000000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i2
χ342222-2-2-2-222-2-2-2-2002200-222-2-200020-2200000000000000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i2
χ352222-2-2-2-222-2-2-2-2002200-2-2-222000202-200000000000000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i2
χ362222-2-2-2-222-2-2-2-2002200-2-2-222000202-200000000000000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i2
χ3722-2-22-22-200002i−2i2i−2i2i−2i2i−2i0000002-2000002-200002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ3822-2-22-22-200002i−2i2i−2i2i−2i2i−2i0000002-2000002-200002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ3922-2-22-22-200002i−2i2i−2i2i−2i2i−2i0000002-200000-220000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ4022-2-22-22-200002i−2i2i−2i2i−2i2i−2i0000002-200000-220000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ4122-2-22-22-20000−2i2i−2i2i−2i2i−2i2i0000002-2000002-20000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ4222-2-22-22-20000−2i2i−2i2i−2i2i−2i2i0000002-2000002-20000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ4322-2-22-22-20000−2i2i−2i2i−2i2i−2i2i0000002-200000-2200002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ4422-2-22-22-20000−2i2i−2i2i−2i2i−2i2i0000002-200000-2200002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ452-22-22-2-222-22-2002200-2-202i−2i2i−2i-2000200000002i−2i002−22−22−22−200000000000000i2−i2i2−i20000
χ462-22-22-2-222-22-2002200-2-202i−2i2i−2i-2000200000002i−2i00−22−22−22−2200000000000000−i2i2−i2i20000
χ472-22-22-2-222-22-2002200-2-20−2i2i−2i2i-200020000000−2i2i002−22−22−22−200000000000000−i2i2−i2i20000
χ482-22-22-2-222-22-2002200-2-20−2i2i−2i2i-200020000000−2i2i00−22−22−22−2200000000000000i2−i2i2−i20000
χ492-22-22-2-222-22-200-2-2002202i−2i2i−2i2000-20000000−2i2i00i2−i2i2−i2−i2i2−i2i200000000000000−222−20000
χ502-22-22-2-222-22-200-2-2002202i−2i2i−2i2000-20000000−2i2i00−i2i2−i2i2i2−i2i2−i2000000000000002−2−220000
χ512-22-22-2-222-22-200-2-200220−2i2i−2i2i2000-200000002i−2i00i2−i2i2−i2−i2i2−i2i2000000000000002−2−220000
χ522-22-22-2-222-22-200-2-200220−2i2i−2i2i2000-200000002i−2i00−i2i2−i2i2i2−i2i2−i200000000000000−222−20000
χ534444-4-4-4-4-4-4444400-4-400-400000004000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-444-4-400440040000000-4000000000000000000000000000000000000000000
χ5544-4-44-44-400004i−4i−4i4i4i−4i−4i4i000000-440000000000000000000000000000000000000000000
χ5644-4-44-44-40000−4i4i4i−4i−4i4i4i−4i000000-440000000000000000000000000000000000000000000
χ5744-4-4-44-4400004i−4i00−4i4i00000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ5844-4-4-44-4400004i−4i00−4i4i0000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5944-4-4-44-440000−4i4i004i−4i00000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ6044-4-4-44-440000−4i4i004i−4i0000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000
χ614-44-44-4-44-44-44004400-4-4000004000-400000000000000000000000000000000000000000
χ624-44-44-4-44-44-4400-4-4004400000-4000400000000000000000000000000000000000000000
χ634-44-4-444-44-4-440000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ644-44-4-444-44-4-44000000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ654-44-4-444-4-444-4000000000000000000000004i−4i0000000000000000000000000000000000
χ664-44-4-444-4-444-400000000000000000000000−4i4i0000000000000000000000000000000000
χ674-4-4444-4-40000004i−4i00−4i4i0000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ684-4-4444-4-40000004i−4i00−4i4i000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ694-4-4444-4-4000000−4i4i004i−4i0000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ704-4-4444-4-4000000−4i4i004i−4i000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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