Finite Group Databasebeta

← Group #97808

Character table — Group #97808

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444422444444442244444448888888824444444888888888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111-11-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-11-1-11111111111111-1-1-11-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-11-1-1-1-1-1-111111111-1-11-1-1111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-1111-1-11111iiii−i−i−i−i-11-1-1-11-11ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1111-1-11111−i−i−i−iiiii-11-1-1-11-11−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1iiii−i−i−i−i111-11-11-1−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1−i−i−i−iiiii111-11-11-1ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-11111111iiii−i−i−i−i-1-111-1-11-1ii−i−i−i−iii−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-11111111−i−i−i−iiiii-1-111-1-11-1−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1iiii−i−i−i−i1-1-1111-11−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1−i−i−i−iiiii1-1-1111-11ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-2-2-22222-2220000000000000-20-20000000000000000
χ1822222222222222-2-2-2-2-2-222-2-2-2-2-200000000000002020000000000000000
χ19222222222222-2-22222-2-2-2-200-20022-2-200000000-20002000000000000000
χ20222222222222-2-22222-2-2-2-200-200-2-222000000002000-2000000000000000
χ21222222222222-2-2-2-2-2-222-2-200200000000000000002002-2-2000000000000
χ22222222222222-2-2-2-2-2-222-2-20020000000000000000-200-222000000000000
χ2322222222-2-2-2-222-2-22222-2-222-2-2-20000000000000-2020000000000000000
χ2422222222-2-2-2-222-2-22222-2-2-2-2-222000000000000020-20000000000000000
χ2522222222-2-2-2-2-2-222-2-2222200-20022-2-2000000002000-2000000000000000
χ2622222222-2-2-2-2-2-222-2-2222200-200-2-22200000000-20002000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2220020000000000000000200-2-22000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2220020000000000000000-20022-2000000000000
χ2922-222-2-2-22i−2i2i−2i2-20000002i−2i2-202i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000001+i−1−i1−i−1+i0000
χ3022-222-2-2-22i−2i2i−2i2-20000002i−2i2-202i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000−1−i1+i−1+i1−i0000
χ3122-222-2-2-22i−2i2i−2i2-20000002i−2i-220−2i2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000−1−i1+i−1+i1−i0000
χ3222-222-2-2-22i−2i2i−2i2-20000002i−2i-220−2i2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000001+i−1−i1−i−1+i0000
χ3322-222-2-2-2−2i2i−2i2i2-2000000−2i2i2-20−2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000001−i−1+i1+i−1−i0000
χ3422-222-2-2-2−2i2i−2i2i2-2000000−2i2i2-20−2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000−1+i1−i−1−i1+i0000
χ3522-222-2-2-2−2i2i−2i2i2-2000000−2i2i-2202i−2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000−1+i1−i−1−i1+i0000
χ3622-222-2-2-2−2i2i−2i2i2-2000000−2i2i-2202i−2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000001−i−1+i1+i−1−i0000
χ37444-4-4-4-4400000000004i−4i000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ38444-4-4-4-4400000000004i−4i00000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ39444-4-4-4-440000000000−4i4i000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ40444-4-4-4-440000000000−4i4i00000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ4144-444-4-4-44i−4i4i−4i-44000000−4i4i0000000000000000000000000000000000000
χ4244-444-4-4-4−4i4i−4i4i-440000004i−4i0000000000000000000000000000000000000
χ4344-4-4-444-4000000004i−4i00000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ4444-4-4-444-4000000004i−4i0000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ4544-4-4-444-400000000−4i4i00000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ4644-4-4-444-400000000−4i4i0000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ474-444-44-4-40000004-400000000000004i−4i0000000000000000000000000000
χ484-444-44-4-40000004-40000000000000−4i4i0000000000000000000000000000
χ494-444-44-4-4000000-44000000000004i−4i000000000000000000000000000000
χ504-444-44-4-4000000-4400000000000−4i4i000000000000000000000000000000
χ514-44-44-44-44i−4i−4i4i00000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ524-44-44-44-44i−4i−4i4i0000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ534-44-44-44-4−4i4i4i−4i00000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ544-44-44-44-4−4i4i4i−4i0000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ554-4-4-444-4444-4-4000000000000000000000000000000000002i−2i2i−2i00000000
χ564-4-4-444-4444-4-400000000000000000000000000000000000−2i2i−2i2i00000000
χ574-4-4-444-44-4-444000000000000000000000000000000000002-2-2200000000
χ584-4-4-444-44-4-44400000000000000000000000000000000000-222-200000000
χ598-8-88-8-888000000000000000000000000000000000000000000000000000

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