Finite Group Databasebeta

← Group #97167

Character table — Group #97167

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444224444444444442444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-11-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-111111111
χ511111111111111111111-1-11-1-11111111111-111-1-1-11-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-11-1-1111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-11-1-11-1-1-1-1-1-1-1-11-111-1-1-11-1-11111-1-1-1-11111
χ811111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ911111111-1-1-1-1-1-111-1-1-1-1111-1-11iiii−i−i−i−i111-11-1-1-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-111-1-1-1-1111-1-11iiii−i−i−i−i-11-11-11-11-11ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1-1-111-1-1-1-1111-1-11−i−i−i−iiiii111-11-1-1-11-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-1-1-111-1-1-1-1111-1-11−i−i−i−iiiii-11-11-11-11-11−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i1-11-1-111-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i-1-1-111-1111-1−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiii1-11-1-111-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiii-1-1-111-1111-1ii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-222-2-2-2-2000000000-200002000000000000000
χ182222222222222222-2-2-2-2-2-2-222-200000000020000-2000000000000000
χ19222222222222-2-2-2-222-2-200-20020000000000002-200-22000000000000
χ20222222222222-2-2-2-222-2-200-2002000000000000-22002-2000000000000
χ21222222222222-2-2-2-2-2-22200200-20000000020-22000-200000000000000
χ22222222222222-2-2-2-2-2-22200200-200000000-202-2000200000000000000
χ2322222222-2-2-2-222-2-222-2-200200-20000000020-2-2000200000000000000
χ2422222222-2-2-2-222-2-222-2-200200-200000000-2022000-200000000000000
χ2522222222-2-2-2-222-2-2-2-22200-20020000000000002200-2-2000000000000
χ2622222222-2-2-2-222-2-2-2-22200-2002000000000000-2-20022000000000000
χ2722222222-2-2-2-2-2-222222222-222-2000000000-20000-2000000000000000
χ2822222222-2-2-2-2-2-2222222-2-2-2-2-2-2000000000200002000000000000000
χ2922-22-2-22-20000002-22i−2i2i−2i2-202i−2i01+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000001+i−1−i1−i−1+i00000000
χ3022-22-2-22-20000002-22i−2i2i−2i2-202i−2i0−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−1−i1+i−1+i1−i00000000
χ3122-22-2-22-20000002-22i−2i2i−2i-220−2i2i01+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−1−i1+i−1+i1−i00000000
χ3222-22-2-22-20000002-22i−2i2i−2i-220−2i2i0−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000001+i−1−i1−i−1+i00000000
χ3322-22-2-22-20000002-2−2i2i−2i2i2-20−2i2i01−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000001−i−1+i1+i−1−i00000000
χ3422-22-2-22-20000002-2−2i2i−2i2i2-20−2i2i0−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−1+i1−i−1−i1+i00000000
χ3522-22-2-22-20000002-2−2i2i−2i2i-2202i−2i01−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−1+i1−i−1−i1+i00000000
χ3622-22-2-22-20000002-2−2i2i−2i2i-2202i−2i0−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000001−i−1+i1+i−1−i00000000
χ3744-44-4-44-4000000-444i−4i−4i4i000000000000000000000000000000000000
χ3844-44-4-44-4000000-44−4i4i4i−4i000000000000000000000000000000000000
χ3944-4-44-4-444i−4i4i−4i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ4044-4-44-4-444i−4i4i−4i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ4144-4-44-4-44−4i4i−4i4i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4244-4-44-4-44−4i4i−4i4i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ434-4444-4-4-44i−4i−4i4i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ444-4444-4-4-44i−4i−4i4i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ454-4444-4-4-4−4i4i4i−4i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ464-4444-4-4-4−4i4i4i−4i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ474-44-4-4-44400004-40000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ484-44-4-4-44400004-4000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ494-44-4-4-4440000-440000000000002-22-2-22-220000000000000000000000
χ504-44-4-4-4440000-44000000000000-22-222-22-20000000000000000000000
χ514-4-4-4444-444-4-4000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ524-4-4-4444-444-4-400000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ534-4-4-4444-4-4-444000000000000002-2-22-222-20000000000000000000000
χ544-4-4-4444-4-4-44400000000000000-222-22-2-220000000000000000000000
χ55888-8-88-8-8000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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