Finite Group Databasebeta

← Group #97884

Character table — Group #97884

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444444444888888882224444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-111111111-11-1-11-111-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-11-1-11-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111-1-11111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-1-1-11111-1-1iiii−i−i−i−i11-1-111-1-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-11-1-1-111-11ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii11-1-111-1-11-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-11-1-1-111-11−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i-11111-1-1-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i-1-1-11-11111-1−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii-11111-1-1-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii-1-1-11-11111-1ii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-2-2-222-2-200000000-2002000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22200000000200-2000000000000000000
χ19222222222222-2-2-2-222-2-2-2200000000000000200-2002-2000000000000
χ20222222222222-2-2-2-222-2-2-2200000000000000-200200-22000000000000
χ21222222222222-2-2-2-2-2-2222-20000000000000200-202-200000000000000
χ22222222222222-2-2-2-2-2-2222-20000000000000-20020-2200000000000000
χ2322222222-2-2-2-222-2-22222-2-2222200000000-200-2000000000000000000
χ2422222222-2-2-2-222-2-22222-2-2-2-2-2-2000000002002000000000000000000
χ2522222222-2-2-2-2-2-22222-2-22-20000000000000200-20-2200000000000000
χ2622222222-2-2-2-2-2-22222-2-22-20000000000000-200202-200000000000000
χ2722222222-2-2-2-2-2-222-2-222-2200000000000000200200-2-2000000000000
χ2822222222-2-2-2-2-2-222-2-222-2200000000000000-200-20022000000000000
χ29222-2-22-2-200002-2002i−2i2i−2i002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000001−i−1+i1+i−1−i00000000
χ30222-2-22-2-200002-2002i−2i2i−2i002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−1+i1−i−1−i1+i00000000
χ31222-2-22-2-200002-2002i−2i2i−2i00−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−1+i1−i−1−i1+i00000000
χ32222-2-22-2-200002-2002i−2i2i−2i00−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000001−i−1+i1+i−1−i00000000
χ33222-2-22-2-200002-200−2i2i−2i2i002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−1−i1+i−1+i1−i00000000
χ34222-2-22-2-200002-200−2i2i−2i2i002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000001+i−1−i1−i−1+i00000000
χ35222-2-22-2-200002-200−2i2i−2i2i00−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000001+i−1−i1−i−1+i00000000
χ36222-2-22-2-200002-200−2i2i−2i2i00−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−1−i1+i−1+i1−i00000000
χ37444-4-44-4-40000-44004i−4i−4i4i000000000000000000000000000000000000
χ38444-4-44-4-40000-4400−4i4i4i−4i000000000000000000000000000000000000
χ3944-44-4-44-40000004i−4i00000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000
χ4044-44-4-44-40000004i−4i0000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000
χ4144-44-4-44-4000000−4i4i00000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000
χ4244-44-4-44-4000000−4i4i0000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000
χ4344-4-44-4-444i−4i4i−4i000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ4444-4-44-4-444i−4i4i−4i00000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ4544-4-44-4-44−4i4i−4i4i000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ4644-4-44-4-44−4i4i−4i4i00000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ474-4444-4-4-44i−4i−4i4i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ484-4444-4-4-44i−4i−4i4i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ494-4444-4-4-4−4i4i4i−4i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ504-4444-4-4-4−4i4i4i−4i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ514-4-4-4444-444-4-40000000000000000000000000000000000002i−2i2i−2i0000
χ524-4-4-4444-444-4-4000000000000000000000000000000000000−2i2i−2i2i0000
χ534-4-4-4444-4-4-4440000000000000000000000000000000000002-2-220000
χ544-4-4-4444-4-4-444000000000000000000000000000000000000-222-20000
χ558-88-8-8-888000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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