Finite Group Databasebeta

← Group #98290

Character table — Group #98290

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888844444488888888
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
χ51111111111111111111111-1-1-1-111111-1-111-1-1-1-11111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ71111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ81111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1111ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii111-1-1-1ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i111-1-1-1−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-1−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-1ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111ii−i−i−i−iii
χ1722222222222222-2-222-2-2-2-222222-22-2-2-2-20022-2-200000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-22-22-2-22200-2-22200000000000000000000000000000000
χ19222222222222-2-222-2-222-2-22222-22-22-2-2-200-2-22200000000000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-22-22-2220022-2-200000000000000000000000000000000
χ2122222222-2-2-2-222222222220000-2-2-2-2-200220000220000000000000000-200-20000000000
χ2222222222-2-2-2-222222222220000-2-2-2-2-200-2-20000-2-2000000000000000020020000000000
χ2322222222-2-2-2-222-2-222-2-2-2-20000-22-2220000000000000000000000000002-202-200000000
χ2422222222-2-2-2-222-2-222-2-2-2-20000-22-222000000000000000000000000000-220-2200000000
χ2522222222-2-2-2-2-2-222-2-222-2-200002-22-220000000000000000000000000002-20-2200000000
χ2622222222-2-2-2-2-2-222-2-222-2-200002-22-22000000000000000000000000000-2202-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200002222-200220000-2-20000000000000000200-20000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200002222-200-2-20000220000000000000000-20020000000000
χ2922-2-2-2-22200002i−2i2i−2i2i−2i2i−2i2-2000000000002i−2i00002-21+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ3022-2-2-2-22200002i−2i2i−2i2i−2i2i−2i2-2000000000002i−2i00002-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ3122-2-2-2-22200002i−2i2i−2i2i−2i2i−2i2-200000000000−2i2i0000-221+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ3222-2-2-2-22200002i−2i2i−2i2i−2i2i−2i2-200000000000−2i2i0000-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ3322-2-2-2-2220000−2i2i−2i2i−2i2i−2i2i2-2000000000002i−2i0000-221−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ3422-2-2-2-2220000−2i2i−2i2i−2i2i−2i2i2-2000000000002i−2i0000-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ3522-2-2-2-2220000−2i2i−2i2i−2i2i−2i2i2-200000000000−2i2i00002-21−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ3622-2-2-2-2220000−2i2i−2i2i−2i2i−2i2i2-200000000000−2i2i00002-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ372-22-22-22-222-2-2002200-2-2002i2i−2i−2i0-20200000002i−2i002−22−22−22−200000000000000i2−i2i2−i20000
χ382-22-22-22-222-2-2002200-2-2002i2i−2i−2i0-20200000002i−2i00−22−22−22−2200000000000000−i2i2−i2i20000
χ392-22-22-22-222-2-2002200-2-200−2i−2i2i2i0-2020000000−2i2i002−22−22−22−200000000000000−i2i2−i2i20000
χ402-22-22-22-222-2-2002200-2-200−2i−2i2i2i0-2020000000−2i2i00−22−22−22−2200000000000000i2−i2i2−i20000
χ412-22-22-22-222-2-200-2-20022002i2i−2i−2i020-20000000−2i2i00i2−i2i2−i2−i2i2−i2i200000000000000−222−20000
χ422-22-22-22-222-2-200-2-20022002i2i−2i−2i020-20000000−2i2i00−i2i2−i2i2i2−i2i2−i2000000000000002−2−220000
χ432-22-22-22-222-2-200-2-2002200−2i−2i2i2i020-200000002i−2i00i2−i2i2−i2−i2i2−i2i2000000000000002−2−220000
χ442-22-22-22-222-2-200-2-2002200−2i−2i2i2i020-200000002i−2i00−i2i2−i2i2i2−i2i2−i200000000000000−222−20000
χ452-22-2-22-222-22-22200-2-200002i−2i2i−2i-2020000002i−2i000000000000i2−i2i2−i2i2−i2i2−i200000000002−22−2
χ462-22-2-22-222-22-22200-2-200002i−2i2i−2i-2020000002i−2i000000000000−i2i2−i2i2−i2i2−i2i20000000000−22−22
χ472-22-2-22-222-22-22200-2-20000−2i2i−2i2i-202000000−2i2i000000000000i2−i2i2−i2i2−i2i2−i20000000000−22−22
χ482-22-2-22-222-22-22200-2-20000−2i2i−2i2i-202000000−2i2i000000000000−i2i2−i2i2−i2i2−i2i200000000002−22−2
χ492-22-2-22-222-22-2-2-2002200002i−2i2i−2i20-2000000−2i2i0000000000002−22−2−22−220000000000−i2i2i2−i2
χ502-22-2-22-222-22-2-2-2002200002i−2i2i−2i20-2000000−2i2i000000000000−22−222−22−20000000000i2−i2−i2i2
χ512-22-2-22-222-22-2-2-200220000−2i2i−2i2i20-20000002i−2i0000000000002−22−2−22−220000000000i2−i2−i2i2
χ522-22-2-22-222-22-2-2-200220000−2i2i−2i2i20-20000002i−2i000000000000−22−222−22−20000000000−i2i2i2−i2
χ534444-4-4-4-44-4-4400000000004-4-44000000000000000000000000000000000000000000000
χ544444-4-4-4-44-4-440000000000-444-4000000000000000000000000000000000000000000000
χ554444-4-4-4-4-444-400000000000000000004-400000000000000000000000000000000000000
χ564444-4-4-4-4-444-40000000000000000000-4400000000000000000000000000000000000000
χ5744-4-4-4-44400004i−4i−4i4i4i−4i−4i4i-440000000000000000000000000000000000000000000000000
χ5844-4-4-4-4440000−4i4i4i−4i−4i4i4i−4i-440000000000000000000000000000000000000000000000000
χ594-44-44-44-4-4-444004400-4-4000000040-400000000000000000000000000000000000000000
χ604-44-44-44-4-4-44400-4-400440000000-40400000000000000000000000000000000000000000
χ614-44-4-44-44-44-444400-4-40000000040-4000000000000000000000000000000000000000000
χ624-44-4-44-44-44-44-4-4004400000000-404000000000000000000000000000000000000000000
χ634-4-444-4-4400004i−4i00−4i4i00000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ644-4-444-4-4400004i−4i00−4i4i0000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ654-4-444-4-440000−4i4i004i−4i00000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ664-4-444-4-440000−4i4i004i−4i0000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ674-4-44-444-40000004i−4i00−4i4i0000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ684-4-44-444-40000004i−4i00−4i4i000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ694-4-44-444-4000000−4i4i004i−4i0000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ704-4-44-444-4000000−4i4i004i−4i000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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