Finite Group Databasebeta

← Group #98039

Character table — Group #98039

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888882444444488888888
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
χ3111111111111111111111111111-1-111-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111
χ5111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1-1-1-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-11-11-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-11-111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-111-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-111-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-111-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-11-111-1-11−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-11-111-1-11ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-11111iiii−i−i−i−i−i−i−i−iiiii1-11-111-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-11-111-1-1ii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-200-222002200000000000000000000-20-2000000000
χ18222222222222222222-2-2-2-2-2-200-2-2-200-2-200000000000000000000202000000000
χ192222222222-2-222-2-2-2-22-2222-222-200-2-20000000000000000000-220000000000000
χ202222222222-2-222-2-2-2-22-2222-2-2-2-2002200000000000000000002-20000000000000
χ212222222222-2-222-2-2-2-2-22-2-2-22002000000000000000000000020020-20-200000000
χ222222222222-2-222-2-2-2-2-22-2-2-220020000000000000000000000-200-2020200000000
χ2322222222-2-222-2-222-2-22-2-2-22-20020000000000000000000000200-20-20200000000
χ2422222222-2-222-2-222-2-22-2-2-22-20020000000000000000000000-2002020-200000000
χ2522222222-2-222-2-222-2-2-2222-2222-200220000000000000000000-2-20000000000000
χ2622222222-2-222-2-222-2-2-2222-22-2-2-200-2-20000000000000000000220000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-22200-22200-2-20000000000000000000020-2000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-22200-2-2-2002200000000000000000000-202000000000
χ2922-22-2-22-22i−2i2i−2i2i−2i2i−2i2-20000000002-2002i−2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000001+i−1−i1−i−1+i
χ3022-22-2-22-22i−2i2i−2i2i−2i2i−2i2-20000000002-2002i−2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000−1−i1+i−1+i1−i
χ3122-22-2-22-22i−2i2i−2i2i−2i2i−2i2-2000000000-2200−2i2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000−1−i1+i−1+i1−i
χ3222-22-2-22-22i−2i2i−2i2i−2i2i−2i2-2000000000-2200−2i2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000001+i−1−i1−i−1+i
χ3322-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-20000000002-200−2i2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000001−i−1+i1+i−1−i
χ3422-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-20000000002-200−2i2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000−1+i1−i−1−i1+i
χ3522-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-2000000000-22002i−2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000−1+i1−i−1−i1+i
χ3622-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-2000000000-22002i−2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000001−i−1+i1+i−1−i
χ372-2-2-22-222002200-2-200022-20-22-20002-200i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-2-22-222002200-2-200022-20-22-20002-200−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-2-22-222002200-2-200022-20-2-22000-2200i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-2-2-22-222002200-2-200022-20-2-22000-2200−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-2-2-22-22200-2-20022000-22-2022-2000-220022−2−2−2−2222−22−2−22−220000000000000000
χ422-2-2-22-22200-2-20022000-22-2022-2000-2200−2−22222−2−2−22−222−22−20000000000000000
χ432-2-2-22-22200-2-20022000-22-202-220002-20022−2−2−2−222−22−222−22−20000000000000000
χ442-2-2-22-22200-2-20022000-22-202-220002-200−2−22222−2−22−22−2−22−220000000000000000
χ45444-4-4-4-444i−4i00−4i4i00000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ46444-4-4-4-444i−4i00−4i4i0000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ47444-4-4-4-44−4i4i004i−4i00000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ48444-4-4-4-44−4i4i004i−4i0000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ4944-44-4-44-44i−4i−4i4i4i−4i−4i4i-4400000000000000000000000000000000000000000000000
χ5044-44-4-44-4−4i4i4i−4i−4i4i4i−4i-4400000000000000000000000000000000000000000000000
χ5144-4-444-4-44400-4-400000000000000000000000000000000000000000002-22-20000
χ5244-4-444-4-44400-4-40000000000000000000000000000000000000000000-22-220000
χ5344-4-444-4-4-4-4004400000000000000000000000000000000000000000002i−2i−2i2i0000
χ5444-4-444-4-4-4-400440000000000000000000000000000000000000000000−2i2i2i−2i0000
χ554-44-4-444-4004i−4i00−4i4i00000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ564-44-4-444-4004i−4i00−4i4i0000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ574-44-4-444-400−4i4i004i−4i00000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ584-44-4-444-400−4i4i004i−4i0000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ594-4-44-44-4400000000004000-400000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ604-4-44-44-4400000000004000-40000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ614-4-44-44-440000000000-4000400000000002-2-222-2-22000000000000000000000000
χ624-4-44-44-440000000000-400040000000000-222-2-222-2000000000000000000000000
χ634-4-4-44-444004400-4-4000-4-440400000000000000000000000000000000000000000
χ644-4-4-44-44400-4-400440004-440-400000000000000000000000000000000000000000
χ658-8888-8-8-8000000000000000000000000000000000000000000000000000000000

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