Finite Group Databasebeta

← Group #97813

Character table — Group #97813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444422444444444444444448888888844444444888888888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111-1-11-1-1-11-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-111111111
χ51111111111111111111111-1-11-1-11111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-11-1-1-1-1-1-111111111-11-1-111-11-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-11111111-1-1iiii−i−i−i−i-1-1-111-1-11ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-11111111-1-1−i−i−i−iiiii-1-1-111-1-11−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-111111-1-111iiii−i−i−i−i11-1-1-11-1-1ii−i−i−i−iii−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-111111-1-111−i−i−i−iiiii11-1-1-11-1-1−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1iiii−i−i−i−i-1111-111-1−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1−i−i−i−iiiii-1111-111-1ii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111iiii−i−i−i−i1-11-11-111−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111−i−i−i−iiiii1-11-11-111ii−i−iii−i−i−i−iii
χ1722222222222222-2-222-2-2-2-200-200222200000000-200-20000000000000000
χ1822222222222222-2-222-2-2-2-200-200-2-2-2-20000000020020000000000000000
χ19222222222222-2-222-2-222-2-222-2-2-2000000000000002000-20000000000000
χ20222222222222-2-222-2-222-2-2-2-2-22200000000000000-200020000000000000
χ21222222222222-2-2-2-2-2-2-2-2220020000000000000002002-20-2000000000000
χ22222222222222-2-2-2-2-2-2-2-222002000000000000000-200-2202000000000000
χ2322222222-2-2-2-222-2-2-2-2222200-20022-2-200000000200-20000000000000000
χ2422222222-2-2-2-222-2-2-2-2222200-200-2-22200000000-20020000000000000000
χ2522222222-2-2-2-2-2-22222-2-22222-2-2-200000000000000-200020000000000000
χ2622222222-2-2-2-2-2-22222-2-222-2-2-222000000000000002000-20000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2002000000000000000200-2-202000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2002000000000000000-200220-2000000000000
χ2922-2-2-22-222i−2i2i−2i2-2002i−2i0000000002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000001−i−1+i1+i−1−i0000
χ3022-2-2-22-222i−2i2i−2i2-2002i−2i0000000002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000−1+i1−i−1−i1+i0000
χ3122-2-2-22-222i−2i2i−2i2-2002i−2i000000000−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000−1+i1−i−1−i1+i0000
χ3222-2-2-22-222i−2i2i−2i2-2002i−2i000000000−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000001−i−1+i1+i−1−i0000
χ3322-2-2-22-22−2i2i−2i2i2-200−2i2i0000000002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000−1−i1+i−1+i1−i0000
χ3422-2-2-22-22−2i2i−2i2i2-200−2i2i0000000002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000001+i−1−i1−i−1+i0000
χ3522-2-2-22-22−2i2i−2i2i2-200−2i2i000000000−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000001+i−1−i1−i−1+i0000
χ3622-2-2-22-22−2i2i−2i2i2-200−2i2i000000000−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000−1−i1+i−1+i1−i0000
χ374444-4-4-4-40000004-40000000004-400000000000000000000000000000000
χ384444-4-4-4-40000004-4000000000-4400000000000000000000000000000000
χ394444-4-4-4-4000000-440000004-400000000000000000000000000000000000
χ404444-4-4-4-4000000-44000000-4400000000000000000000000000000000000
χ4144-4-4-44-444i−4i4i−4i-4400−4i4i00000000000000000000000000000000000000000
χ4244-4-4-44-44−4i4i−4i4i-44004i−4i00000000000000000000000000000000000000000
χ434-44-44-4-444i−4i−4i4i00000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ444-44-44-4-444i−4i−4i4i0000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ454-44-44-4-44−4i4i4i−4i00000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ464-44-44-4-44−4i4i4i−4i0000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ474-44-4-444-40000000000004i−4i0000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ484-44-4-444-40000000000004i−4i000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ494-44-4-444-4000000000000−4i4i0000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ504-44-4-444-4000000000000−4i4i000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ514-4-4444-4-400000000004i−4i000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ524-4-4444-4-400000000004i−4i00000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ534-4-4444-4-40000000000−4i4i000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ544-4-4444-4-40000000000−4i4i00000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ554-4-44-4-44444-4-4000000000000000000000000000000000002i−2i2i−2i00000000
χ564-4-44-4-44444-4-400000000000000000000000000000000000−2i2i−2i2i00000000
χ574-4-44-4-444-4-444000000000000000000000000000000000002-2-2200000000
χ584-4-44-4-444-4-44400000000000000000000000000000000000-222-200000000
χ5988-8-88-88-8000000000000000000000000000000000000000000000000000

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