Finite Group Databasebeta

← Group #97802

Character table — Group #97802

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444422444444442244444448888888822444444888888888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1111-1-111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-11-1-1-1-11-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-11-1-1-1-111111111-11-1-11-111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-11111111-1-1iiii−i−i−i−i1-1-1-11-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-11111111-1-1−i−i−i−iiiii1-1-1-11-11-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-111-1-111111iiii−i−i−i−i-11-1-1-11-11ii−i−i−i−iii−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-111-1-111111−i−i−i−iiiii-11-1-1-11-11−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1iiii−i−i−i−i1111-1-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1−i−i−i−iiiii1111-1-1-11ii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111iiii−i−i−i−i-1-111111-1−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111−i−i−i−iiiii-1-111111-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-2-2-2220022-2002200000000-20000-200000000000000
χ1822222222222222-2-2-2-2-2-22200-2-2-200-2-20000000020000200000000000000
χ19222222222222-2-22222-2-2-2-22200-2-2-2000000000000-220000000000000000
χ20222222222222-2-22222-2-2-2-2-2-200-2220000000000002-20000000000000000
χ21222222222222-2-2-2-2-2-222-2-2000020000000000000200-202-2000000000000
χ22222222222222-2-2-2-2-2-222-2-2000020000000000000-20020-22000000000000
χ2322222222-2-2-2-222-2-22222-2-20022-200-2-200000000-20000200000000000000
χ2422222222-2-2-2-222-2-22222-2-200-2-2-200220000000020000-200000000000000
χ2522222222-2-2-2-2-2-222-2-222222200-2-2-20000000000002-20000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-200-222000000000000-220000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200002000000000000020020-2-2000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-222000020000000000000-200-2022000000000000
χ29222-2-2-22-22i−2i2i−2i2-20000002i−2i002i−2i0002-21+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000001−i−1+i1+i−1−i0000
χ30222-2-2-22-22i−2i2i−2i2-20000002i−2i002i−2i0002-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000−1+i1−i−1−i1+i0000
χ31222-2-2-22-22i−2i2i−2i2-20000002i−2i00−2i2i000-221+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000−1+i1−i−1−i1+i0000
χ32222-2-2-22-22i−2i2i−2i2-20000002i−2i00−2i2i000-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000001−i−1+i1+i−1−i0000
χ33222-2-2-22-2−2i2i−2i2i2-2000000−2i2i002i−2i000-221−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000−1−i1+i−1+i1−i0000
χ34222-2-2-22-2−2i2i−2i2i2-2000000−2i2i002i−2i000-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000001+i−1−i1−i−1+i0000
χ35222-2-2-22-2−2i2i−2i2i2-2000000−2i2i00−2i2i0002-21−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000001+i−1−i1−i−1+i0000
χ36222-2-2-22-2−2i2i−2i2i2-2000000−2i2i00−2i2i0002-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000−1−i1+i−1+i1−i0000
χ37444-4-4-44-44i−4i4i−4i-44000000−4i4i0000000000000000000000000000000000000
χ38444-4-4-44-4−4i4i−4i4i-440000004i−4i0000000000000000000000000000000000000
χ3944-44-4-4-44000000004i−4i00000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ4044-44-4-4-44000000004i−4i0000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ4144-44-4-4-4400000000−4i4i00000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ4244-44-4-4-4400000000−4i4i0000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ4344-4-444-4-400000000004i−4i000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ4444-4-444-4-400000000004i−4i00000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ4544-4-444-4-40000000000−4i4i000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ4644-4-444-4-40000000000−4i4i00000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ474-4444-4-4-44i−4i−4i4i00000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ484-4444-4-4-44i−4i−4i4i0000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ494-4444-4-4-4−4i4i4i−4i00000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ504-4444-4-4-4−4i4i4i−4i0000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ514-44-4-44-4444-4-4000000000000000000000000000000000002i−2i2i−2i00000000
χ524-44-4-44-4444-4-400000000000000000000000000000000000−2i2i−2i2i00000000
χ534-44-4-44-44-4-444000000000000000000000000000000000002-2-2200000000
χ544-44-4-44-44-4-44400000000000000000000000000000000000-222-200000000
χ554-4-4-44-4440000004-4000000000004-4000000000000000000000000000000
χ564-4-4-44-4440000004-400000000000-44000000000000000000000000000000
χ574-4-4-44-444000000-440000004-400000000000000000000000000000000000
χ584-4-4-44-444000000-44000000-4400000000000000000000000000000000000
χ598-8-88-888-8000000000000000000000000000000000000000000000000000

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