Finite Group Databasebeta

← Group #139999

Character table — Group #139999

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order12222244444488888888224444444444488888888224488888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111
χ8111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ9111111-1-1-1-1-1-1iiii−i−i−i−i1-1111-1-111-1-11-1iiii−i−i−i−i1-11-1i−ii−i1-1i−i
χ10111111-1-1-1-1-1-1iiii−i−i−i−i1-1111-1-111-1-11-1iiii−i−i−i−i-11-11i−i−ii-11−ii
χ11111111-1-1-1-1-1-1iiii−i−i−i−i1-11-1-111-1-1111-1−i−i−i−iiiii1-11-1i−ii−i-11−ii
χ12111111-1-1-1-1-1-1iiii−i−i−i−i1-11-1-111-1-1111-1−i−i−i−iiiii-11-11i−i−ii1-1i−i
χ13111111-1-1-1-1-1-1−i−i−i−iiiii1-1111-1-111-1-11-1−i−i−i−iiiii1-11-1−ii−ii1-1−ii
χ14111111-1-1-1-1-1-1−i−i−i−iiiii1-1111-1-111-1-11-1−i−i−i−iiiii-11-11−iii−i-11i−i
χ15111111-1-1-1-1-1-1−i−i−i−iiiii1-11-1-111-1-1111-1iiii−i−i−i−i1-11-1−ii−ii-11i−i
χ16111111-1-1-1-1-1-1−i−i−i−iiiii1-11-1-111-1-1111-1iiii−i−i−i−i-11-11−iii−i1-1−ii
χ1722222222222222222222-2-2200000000-2-2000000000000-2-2000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2200000000-2-200000000000022000000
χ192222222222-2-2000000002-2-200000000-2222-2-222-2-2000000000000
χ202222222222-2-2000000002-2-200000000-22-2-222-2-222000000000000
χ212222222222-2-200000000-22-22222-2-2-2-22-200000000000000000000
χ222222222222-2-200000000-22-2-2-2-2-222222-200000000000000000000
χ23222222-2-2-2-2220000000022-200000000-2-22i2i−2i−2i−2i−2i2i2i000000000000
χ24222222-2-2-2-2220000000022-200000000-2-2−2i−2i2i2i2i2i−2i−2i000000000000
χ25222222-2-2-2-22200000000-2-2-222-2-2-2-2222200000000000000000000
χ26222222-2-2-2-22200000000-2-2-2-2-22222-2-22200000000000000000000
χ27222222-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i-22200000000-22000000000000−2i2i000000
χ28222222-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i-22200000000-220000000000002i−2i000000
χ294444-4-444-4-400000000000000000000000000000002-2-2200000000
χ304444-4-444-4-40000000000000000000000000000000-222-200000000
χ314444-4-4-4-444000000000000000000000000000000022-2-200000000
χ324444-4-4-4-4440000000000000000000000000000000-2-22200000000
χ3344-4-400004-40022-2-222-2-20002i−2i2i−2i000000002i−2i002i−2i000000000000
χ3444-4-400004-40022-2-222-2-2000−2i2i−2i2i00000000−2i2i00−2i2i000000000000
χ3544-4-400004-400-2-222-2-2220002i−2i2i−2i00000000−2i2i00−2i2i000000000000
χ3644-4-400004-400-2-222-2-222000−2i2i−2i2i000000002i−2i002i−2i000000000000
χ3744-4-40000-44002i2i−2i−2i−2i−2i2i2i0002i−2i−2i2i00000000-22002-2000000000000
χ3844-4-40000-44002i2i−2i−2i−2i−2i2i2i000−2i2i2i−2i000000002-200-22000000000000
χ3944-4-40000-4400−2i−2i2i2i2i2i−2i−2i0002i−2i−2i2i000000002-200-22000000000000
χ4044-4-40000-4400−2i−2i2i2i2i2i−2i−2i000−2i2i2i−2i00000000-22002-2000000000000
χ414-44-4004i−4i00002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000002-22i−2i002ζ−2ζ002ζ3−2ζ300000000000000
χ424-44-4004i−4i00002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000-22−2i2i00−2ζ2ζ00−2ζ32ζ300000000000000
χ434-44-4004i−4i0000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000002-22i−2i00−2ζ2ζ00−2ζ32ζ300000000000000
χ444-44-4004i−4i0000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000-22−2i2i002ζ−2ζ002ζ3−2ζ300000000000000
χ454-44-400−4i4i00002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000002-2−2i2i002ζ3−2ζ3002ζ−2ζ00000000000000
χ464-44-400−4i4i00002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000-222i−2i00−2ζ32ζ300−2ζ2ζ00000000000000
χ474-44-400−4i4i0000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000002-2−2i2i00−2ζ32ζ300−2ζ2ζ00000000000000
χ484-44-400−4i4i0000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000-222i−2i002ζ3−2ζ3002ζ−2ζ00000000000000
χ494-4-444-400004-42i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000
χ504-4-444-400004-4−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000
χ514-4-444-40000-4422−22−2222−222222−22000000000000000000000000000000000
χ524-4-444-40000-44−222222−2222−22−2222000000000000000000000000000000000
χ538-8-88-8800000000000000000000000000000000000000000000000

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