Finite Group Databasebeta

← Group #97895

Character table — Group #97895

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444444444888888882444444488888888
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
χ3111111111111111111111111111-1-111-1-11111111111111111-11-1-1-1-1-11-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111111
χ51111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111-11111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-1-11ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-1-11−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1-11-1111−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1-11-1111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1-111-1ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-111-1-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-111-1-1-1ii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-2-200220022000000000000000000-2-2000000000000
χ18222222222222222222-2-2-2-2-2-2-200-2-200-2-200000000000000000022000000000000
χ19222222222222-2-2-2-2-2-2222-2-22-22200-2-20000000000000000000200000-200000000
χ20222222222222-2-2-2-2-2-2222-2-22-2-2-200220000000000000000000-200000200000000
χ21222222222222-2-2-2-2-2-2-2-2-222-220000000000000000000000002000-22-2000000000
χ22222222222222-2-2-2-2-2-2-2-2-222-22000000000000000000000000-20002-22000000000
χ2322222222-2-2-2-22222-2-222-222-2-22200220000000000000000000-200000-200000000
χ2422222222-2-2-2-22222-2-222-222-2-2-2-200-2-20000000000000000000200000200000000
χ2522222222-2-2-2-22222-2-2-2-22-2-2220000000000000000000000002000-2-22000000000
χ2622222222-2-2-2-22222-2-2-2-22-2-222000000000000000000000000-200022-2000000000
χ2722222222-2-2-2-2-2-2-2-222-2-22222-2002200-2-2000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22222-200-2-200220000000000000000002-2000000000000
χ29222-2-2-2-2200002i−2i2i−2i002-202i−2i002i−2i002-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ30222-2-2-2-2200002i−2i2i−2i002-202i−2i002i−2i002-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ31222-2-2-2-2200002i−2i2i−2i002-202i−2i00−2i2i00-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ32222-2-2-2-2200002i−2i2i−2i002-202i−2i00−2i2i00-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ33222-2-2-2-220000−2i2i−2i2i002-20−2i2i002i−2i00-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ34222-2-2-2-220000−2i2i−2i2i002-20−2i2i002i−2i00-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ35222-2-2-2-220000−2i2i−2i2i002-20−2i2i00−2i2i002-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ36222-2-2-2-220000−2i2i−2i2i002-20−2i2i00−2i2i002-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ372-2222-2-2-222-2-2-2-2222-20000000002i−2i002i−2i000000002−22−22−22−2000000000000i2−i2i2−i2
χ382-2222-2-2-222-2-2-2-2222-20000000002i−2i002i−2i00000000−22−22−22−22000000000000−i2i2−i2i2
χ392-2222-2-2-222-2-2-2-2222-2000000000−2i2i00−2i2i000000002−22−22−22−2000000000000−i2i2−i2i2
χ402-2222-2-2-222-2-2-2-2222-2000000000−2i2i00−2i2i00000000−22−22−22−22000000000000i2−i2i2−i2
χ412-2222-2-2-2-2-22222-2-22-20000000002i−2i00−2i2i00000000i2−i2i2−i2−i2i2−i2i2000000000000−222−2
χ422-2222-2-2-2-2-22222-2-22-20000000002i−2i00−2i2i00000000−i2i2−i2i2i2−i2i2−i20000000000002−2−22
χ432-2222-2-2-2-2-22222-2-22-2000000000−2i2i002i−2i00000000i2−i2i2−i2−i2i2−i2i20000000000002−2−22
χ442-2222-2-2-2-2-22222-2-22-2000000000−2i2i002i−2i00000000−i2i2−i2i2i2−i2i2−i2000000000000−222−2
χ45444-4-4-4-4400004i−4i4i−4i00-440−4i4i000000000000000000000000000000000000000000
χ46444-4-4-4-440000−4i4i−4i4i00-4404i−4i000000000000000000000000000000000000000000
χ4744-44-44-4-44-44-40000000000000000000000000000000000000000000002-22-20000
χ4844-44-44-4-44-44-4000000000000000000000000000000000000000000000-22-220000
χ4944-44-44-4-4-44-440000000000000000000000000000000000000000000002i−2i−2i2i0000
χ5044-44-44-4-4-44-44000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ514-4444-4-4-444-4-444-4-4-4400000000000000000000000000000000000000000000000
χ524-4444-4-4-4-4-444-4-444-4400000000000000000000000000000000000000000000000
χ534-44-4-444-400004i−4i−4i4i00000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ544-44-4-444-400004i−4i−4i4i0000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ554-44-4-444-40000−4i4i4i−4i00000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ564-44-4-444-40000−4i4i4i−4i0000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ574-4-44-4-4444-4-440000000000000000000002-22-22-22-2000000000000000000000000
χ584-4-44-4-4444-4-44000000000000000000000-22-22-22-22000000000000000000000000
χ594-4-44-4-444-444-40000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ604-4-44-4-444-444-4000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ614-4-4-444-44000000000000400-40000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ624-4-4-444-44000000000000400-4000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ634-4-4-444-44000000000000-40040000000002-2-222-2-22000000000000000000000000
χ644-4-4-444-44000000000000-4004000000000-222-2-222-2000000000000000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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