Finite Group Databasebeta

← Group #98014

Character table — Group #98014

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422224444488888888888888882444444488888888
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
χ311111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-111-1-1-111-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111-111-1-1-111-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111-111-1-1-111-1-11-1-111iiii−i−i−i−iiiii−i−i−i−i-111-1-1-111−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111-111-1-1-111-1-11-1-111−i−i−i−iiiii−i−i−i−iiiii-111-1-1-111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111-111-1-1-1-1-111111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111-111-1-1-1-1-111111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11-1-111−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1ii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-20000-222220000000000000000-2-200000000000000
χ18222222222222222222-2-2-2-2-2-20000-2-2-2-2-200000000000000002200000000000000
χ1922222222222-2-2-2-22-2-22-2-2-22-2000020000000000000000000000002-22-200000000
χ2022222222222-2-2-2-22-2-22-2-2-22-200002000000000000000000000000-22-2200000000
χ2122222222222-2-2-2-22-2-2-2222-222222-20000000000000000000000-2-2000000000000
χ2222222222222-2-2-2-22-2-2-2222-22-2-2-2-2-2000000000000000000000022000000000000
χ2322222222-2-2-22222-2-2-2222-22-222-2-2-20000000000000000000000-22000000000000
χ2422222222-2-2-22222-2-2-2222-22-2-2-222-200000000000000000000002-2000000000000
χ2522222222-2-2-22222-2-2-2-2-2-22-22000020000000000000000000000002-2-2200000000
χ2622222222-2-2-22222-2-2-2-2-2-22-2200002000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2222-2-22220000-222-2-20000000000000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-2222-2-22220000-2-2-22200000000000000002-200000000000000
χ2922-2-222-2-222-2-2-222-22-2000000000002i−2i2i−2i0000000022−2−222−2−2000000000000i2−i2i2−i2
χ3022-2-222-2-222-2-2-222-22-2000000000002i−2i2i−2i00000000−2−222−2−222000000000000−i2i2−i2i2
χ3122-2-222-2-222-2-2-222-22-200000000000−2i2i−2i2i0000000022−2−222−2−2000000000000−i2i2−i2i2
χ3222-2-222-2-222-2-2-222-22-200000000000−2i2i−2i2i00000000−2−222−2−222000000000000i2−i2i2−i2
χ3322-2-222-2-2-2-2222-2-222-2000000000002i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i2000000000000−222−2
χ3422-2-222-2-2-2-2222-2-222-2000000000002i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i20000000000002−2−22
χ3522-2-222-2-2-2-2222-2-222-200000000000−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i20000000000002−2−22
χ3622-2-222-2-2-2-2222-2-222-200000000000−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i2000000000000−222−2
χ372-2-2-22-2222-220000-20002-220-22-22-200000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-2-22-2222-220000-20002-220-22-22-200000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-2-22-2222-220000-20002-220-2-22-2200000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-2-2-22-2222-220000-20002-220-2-22-2200000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-2-2-22-222-22-2000020002-2-2022-2-220000022−2−2−2−2222−22−2−22−220000000000000000
χ422-2-2-22-222-22-2000020002-2-2022-2-2200000−2−22222−2−2−22−222−22−20000000000000000
χ432-2-2-22-222-22-2000020002-2-202-222-20000022−2−2−2−222−22−222−22−20000000000000000
χ442-2-2-22-222-22-2000020002-2-202-222-200000−2−22222−2−22−22−2−22−220000000000000000
χ45444-4-4-44-40004i−4i4i−4i0000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ46444-4-4-44-40004i−4i4i−4i000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ47444-4-4-44-4000−4i4i−4i4i0000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ48444-4-4-44-4000−4i4i−4i4i000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ4944-44-4-4-440004i−4i−4i4i0000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ5044-44-4-4-440004i−4i−4i4i000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ5144-44-4-4-44000−4i4i4i−4i0000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ5244-44-4-4-44000−4i4i4i−4i000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ5344-4-444-4-444-444-4-4-4-4400000000000000000000000000000000000000000000000
χ5444-4-444-4-4-4-44-4-4444-4400000000000000000000000000000000000000000000000
χ554-4444-4-4-44-4-40000400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ564-4444-4-4-44-4-4000040000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ574-4444-4-4-4-4440000-400000000000000000000000002-2-22-222-20000000000000000
χ584-4444-4-4-4-4440000-40000000000000000000000000-222-22-2-220000000000000000
χ594-44-4-44-4400000000004000-400000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ604-44-4-44-4400000000004000-40000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ614-44-4-44-440000000000-4000400000000002-2-222-2-22000000000000000000000000
χ624-44-4-44-440000000000-400040000000000-222-2-222-2000000000000000000000000
χ634-4-4-44-4444-440000-4000-44-40400000000000000000000000000000000000000000
χ644-4-4-44-444-44-400004000-4440-400000000000000000000000000000000000000000
χ658-8-88-888-8000000000000000000000000000000000000000000000000000000000

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