Finite Group Databasebeta

← Group #125313

Character table — Group #125313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ91111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ192222222222-2-2-2-222-2-222-2-2-2-2-2-222-2-222-2-22200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2222222-2-222-2-2-2-22200000000000000000000000000000000
χ21222-22-2-2-22222-2-2-2-22-20022000000-2-22-2000022−2−222−2−222−2−222−2−20000000000000000
χ22222-22-2-2-22222-2-2-2-22-20022000000-2-22-20000−2−222−2−222−2−222−2−2220000000000000000
χ23222-22-2-2-22222-2-2-2-22-200-2-200000022-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ24222-22-2-2-22222-2-2-2-22-200-2-200000022-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ25222-22-2-2-222-2-222-2-2-220022000000-2-2-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ26222-22-2-2-222-2-222-2-2-220022000000-2-2-220000−2−22222−2−2−2−22222−2−20000000000000000
χ27222-22-2-2-222-2-222-2-2-2200-2-2000000222-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ28222-22-2-2-222-2-222-2-2-2200-2-2000000222-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ29222-22-2-2-2-2-222-2-222-222i−2i002i2i−2i−2i2i−2i000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ30222-22-2-2-2-2-222-2-222-222i−2i002i2i−2i−2i2i−2i00000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ31222-22-2-2-2-2-222-2-222-22−2i2i00−2i−2i2i2i−2i2i000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ32222-22-2-2-2-2-222-2-222-22−2i2i00−2i−2i2i2i−2i2i00000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ33222-22-2-2-2-2-2-2-222222-22i−2i00−2i−2i2i2i2i−2i000000000000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ34222-22-2-2-2-2-2-2-222222-22i−2i00−2i−2i2i2i2i−2i00000000000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ35222-22-2-2-2-2-2-2-222222-2−2i2i002i2i−2i−2i−2i2i000000000000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ36222-22-2-2-2-2-2-2-222222-2−2i2i002i2i−2i−2i−2i2i00000000000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ3722-22-2-2-222-200002-2002i−2i2i−2i0000−2i2i2i−2i002-20000002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ0000000000000000
χ3822-22-2-2-222-200002-2002i−2i2i−2i0000−2i2i2i−2i002-2000000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ0000000000000000
χ3922-22-2-2-222-200002-2002i−2i−2i2i0000−2i2i−2i2i00-22002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ00000000000000000000
χ4022-22-2-2-222-200002-2002i−2i−2i2i0000−2i2i−2i2i00-2200−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ00000000000000000000
χ4122-22-2-2-222-200002-200−2i2i2i−2i00002i−2i2i−2i00-22002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ300000000000000000000
χ4222-22-2-2-222-200002-200−2i2i2i−2i00002i−2i2i−2i00-2200−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ300000000000000000000
χ4322-22-2-2-222-200002-200−2i2i−2i2i00002i−2i−2i2i002-20000002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ30000000000000000
χ4422-22-2-2-222-200002-200−2i2i−2i2i00002i−2i−2i2i002-2000000−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ30000000000000000
χ4522-2-2-222-22-20000-2200002i−2i2-22-200−2i2i00002i−2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ4622-2-2-222-22-20000-2200002i−2i2-22-200−2i2i00002i−2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ4722-2-2-222-22-20000-2200002i−2i-22-2200−2i2i0000−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ4822-2-2-222-22-20000-2200002i−2i-22-2200−2i2i0000−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ4922-2-2-222-22-20000-220000−2i2i2-22-2002i−2i0000−2i2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ5022-2-2-222-22-20000-220000−2i2i2-22-2002i−2i0000−2i2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ5122-2-2-222-22-20000-220000−2i2i-22-22002i−2i00002i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ5222-2-2-222-22-20000-220000−2i2i-22-22002i−2i00002i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ5344444444-4-44444-4-4-4-400000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ5544-44-4-4-44-440000-440000004i−4i−4i4i000000000000000000000000000000000000000000
χ5644-44-4-4-44-440000-44000000−4i4i4i−4i000000000000000000000000000000000000000000
χ5744-4-4-444-4-4400004-40044000000-4-40000000000000000000000000000000000000000
χ5844-4-4-444-4-4400004-400-4-4000000440000000000000000000000000000000000000000
χ594-4-4444-4-4004-44-40000000000000000000000000000000000000000002i−2i2i−2i00000000
χ604-4-4444-4-4004-44-4000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ614-4-4444-4-400-44-440000000000000000000000000000000000000000002i−2i−2i2i00000000
χ624-4-4444-4-400-44-44000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ634-4-4-44-444004-4-44000000000000000000000000000000000000002-22-2000000000000
χ644-4-4-44-444004-4-4400000000000000000000000000000000000000-22-22000000000000
χ654-4-4-44-44400-444-4000000000000000000000000000000000000002-2-22000000000000
χ664-4-4-44-44400-444-400000000000000000000000000000000000000-222-2000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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