Finite Group Databasebeta

← Group #125331

Character table — Group #125331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422444488888888888888882222444488888888
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
χ51111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ61111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222222222-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-222-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-22200000000000000000000000000000000
χ21222-2-2-2-2222-2-222-2-22i2i−2i−2i2-2002i2i−2i−2i000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ22222-2-2-2-2222-2-222-2-22i2i−2i−2i2-2002i2i−2i−2i00000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ23222-2-2-2-2222-2-222-2-2−2i−2i2i2i2-200−2i−2i2i2i000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ24222-2-2-2-2222-2-222-2-2−2i−2i2i2i2-200−2i−2i2i2i00000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ25222-2-2-2-2222-2-2-2-2222i2i−2i−2i-2200−2i−2i2i2i000000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ26222-2-2-2-2222-2-2-2-2222i2i−2i−2i-2200−2i−2i2i2i00000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ27222-2-2-2-2222-2-2-2-222−2i−2i2i2i-22002i2i−2i−2i000000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ28222-2-2-2-2222-2-2-2-222−2i−2i2i2i-22002i2i−2i−2i00000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ29222-2-2-2-22-2-22222-2-20000-22220000-2-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ30222-2-2-2-22-2-22222-2-20000-22220000-2-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ31222-2-2-2-22-2-22222-2-20000-22-2-2000022-22000022−2−222−2−2−2−222−2−2220000000000000000
χ32222-2-2-2-22-2-22222-2-20000-22-2-2000022-220000−2−222−2−22222−2−222−2−20000000000000000
χ33222-2-2-2-22-2-222-2-22200002-2220000-2-2-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ34222-2-2-2-22-2-222-2-22200002-2220000-2-2-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ35222-2-2-2-22-2-222-2-22200002-2-2-20000222-2000022−2−2−2−22222−2−2−2−2220000000000000000
χ36222-2-2-2-22-2-222-2-22200002-2-2-20000222-20000−2−22222−2−2−2−22222−2−20000000000000000
χ3722-222-2-2-22-22-200000000002i−2i2i−2i2i−2i2i−2i002-20000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ3822-222-2-2-22-22-200000000002i−2i2i−2i2i−2i2i−2i002-2000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ3922-222-2-2-22-22-200000000002i−2i−2i2i−2i2i2i−2i00-22002ζ3−2ζ32ζ3−2ζ3000000002ζ−2ζ2ζ−2ζ0000000000000000
χ4022-222-2-2-22-22-200000000002i−2i−2i2i−2i2i2i−2i00-2200−2ζ32ζ3−2ζ32ζ300000000−2ζ2ζ−2ζ2ζ0000000000000000
χ4122-222-2-2-22-22-20000000000−2i2i2i−2i2i−2i−2i2i00-22002ζ−2ζ2ζ−2ζ000000002ζ3−2ζ32ζ3−2ζ30000000000000000
χ4222-222-2-2-22-22-20000000000−2i2i2i−2i2i−2i−2i2i00-2200−2ζ2ζ−2ζ2ζ00000000−2ζ32ζ3−2ζ32ζ30000000000000000
χ4322-222-2-2-22-22-20000000000−2i2i−2i2i−2i2i−2i2i002-20000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ4422-222-2-2-22-22-20000000000−2i2i−2i2i−2i2i−2i2i002-2000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ4522-2-2-222-2-222-200002i−2i2i−2i002i−2i0000−2i2i00002-21+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i0000000000000000
χ4622-2-2-222-2-222-200002i−2i2i−2i002i−2i0000−2i2i00002-2−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i0000000000000000
χ4722-2-2-222-2-222-200002i−2i2i−2i00−2i2i00002i−2i0000-221−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i0000000000000000
χ4822-2-2-222-2-222-200002i−2i2i−2i00−2i2i00002i−2i0000-22−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i0000000000000000
χ4922-2-2-222-2-222-20000−2i2i−2i2i002i−2i0000−2i2i0000-221+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i0000000000000000
χ5022-2-2-222-2-222-20000−2i2i−2i2i002i−2i0000−2i2i0000-22−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i0000000000000000
χ5122-2-2-222-2-222-20000−2i2i−2i2i00−2i2i00002i−2i00002-21−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i0000000000000000
χ5222-2-2-222-2-222-20000−2i2i−2i2i00−2i2i00002i−2i00002-2−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i0000000000000000
χ5344444444-4-4-4-444440000-4-40000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ5544-444-4-4-4-44-4400004-4-44000000000000000000000000000000000000000000000000
χ5644-444-4-4-4-44-440000-444-4000000000000000000000000000000000000000000000000
χ5744-4-4-444-44-4-440000000000004-4-440000000000000000000000000000000000000000
χ5844-4-4-444-44-4-44000000000000-444-40000000000000000000000000000000000000000
χ594-4-44-44-4400004-44-400000000000000000000000000000000000000002-22-200000000
χ604-4-44-44-4400004-44-40000000000000000000000000000000000000000-22-2200000000
χ614-4-44-44-440000-44-4400000000000000000000000000000000000000002-2-2200000000
χ624-4-44-44-440000-44-440000000000000000000000000000000000000000-222-200000000
χ634-4-4-44-44400004-4-440000000000000000000000000000000000002-22-2000000000000
χ644-4-4-44-44400004-4-44000000000000000000000000000000000000-22-22000000000000
χ654-4-4-44-4440000-444-40000000000000000000000000000000000002-2-22000000000000
χ664-4-4-44-4440000-444-4000000000000000000000000000000000000-222-2000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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