Finite Group Databasebeta

← Group #101830

Character table — Group #101830

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444488888888888888884488888888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ51111111111111111111111-1-11-1-11111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1
χ61111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ71111111111111111111111-1-11-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1
χ81111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ911111111-1-1-1-11111-11-1-1-1111-1-1-1ii−i−iii−i−i1111-1-1-1-11-1i−ii−iii−i−iii−i−i1-1
χ1011111111-1-1-1-11111-11-1-1-1111-1-1-1ii−i−iii−i−i-1-1-1-111111-1i−ii−i−i−iii−i−iii-11
χ1111111111-1-1-1-11111-11-1-1-1111-1-1-1−i−iii−i−iii1111-1-1-1-11-1−ii−ii−i−iii−i−iii1-1
χ1211111111-1-1-1-11111-11-1-1-1111-1-1-1−i−iii−i−iii-1-1-1-111111-1−ii−iiii−i−iii−i−i-11
χ1311111111-1-1-1-11111-11-1-1-11-1-1-111ii−i−i−i−iii1111-1-1-1-1-11i−i−iiii−i−i−i−iii-11
χ1411111111-1-1-1-11111-11-1-1-11-1-1-111ii−i−i−i−iii-1-1-1-11111-11i−i−ii−i−iiiii−i−i1-1
χ1511111111-1-1-1-11111-11-1-1-11-1-1-111−i−iiiii−i−i1111-1-1-1-1-11−iii−i−i−iiiii−i−i-11
χ1611111111-1-1-1-11111-11-1-1-11-1-1-111−i−iiiii−i−i-1-1-1-11111-11−iii−iii−i−i−i−iii1-1
χ1722222222222222-2-22-2-2-22-200-200222200000000000000-2-2000000000000
χ1822222222222222-2-22-2-2-22-200-200-2-2-2-20000000000000022000000000000
χ19222222222222-2-222-2-222-2-200-20000002222000000000000-2-20000000000
χ20222222222222-2-222-2-222-2-200-2000000-2-2-2-2000000000000220000000000
χ21222222222222-2-2-2-2-22-2-2-22222220000000000000000-2-200000000000000
χ22222222222222-2-2-2-2-22-2-2-22-2-22-2-200000000000000002200000000000000
χ2322222222-2-2-2-222-2-2-2-222-2-2002002i2i−2i−2i00000000000000−2i2i000000000000
χ2422222222-2-2-2-222-2-2-2-222-2-200200−2i−2i2i2i000000000000002i−2i000000000000
χ2522222222-2-2-2-2-2-2222-2-2-22-20020000002i2i−2i−2i000000000000−2i2i0000000000
χ2622222222-2-2-2-2-2-2222-2-2-22-2002000000−2i−2i2i2i0000000000002i−2i0000000000
χ2722222222-2-2-2-2-2-2-2-222222222-2-2-20000000000000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-2222222-2-2-22200000000000000002-200000000000000
χ292222-2-2-2-222-2-22-2002000-20000002-22-2000022−2−222−2−20000002−22−2000000
χ302222-2-2-2-222-2-22-2002000-20000002-22-20000−2−222−2−222000000−22−22000000
χ312222-2-2-2-222-2-22-2002000-2000000-22-22000022−2−222−2−2000000−22−22000000
χ322222-2-2-2-222-2-22-2002000-2000000-22-220000−2−222−2−2220000002−22−2000000
χ332222-2-2-2-2-2-2222-200-200020000002i−2i−2i2i000022−2−2−2−222000000i2−i2−i2i2000000
χ342222-2-2-2-2-2-2222-200-200020000002i−2i−2i2i0000−2−22222−2−2000000−i2i2i2−i2000000
χ352222-2-2-2-2-2-2222-200-20002000000−2i2i2i−2i000022−2−2−2−222000000−i2i2i2−i2000000
χ362222-2-2-2-2-2-2222-200-20002000000−2i2i2i−2i0000−2−22222−2−2000000i2−i2−i2i2000000
χ3722-2-22-2-222i−2i2i−2i002-2002i−2i000000000002ζ3−2ζ32ζ−2ζ2−22−2i2−i2i2−i200000000001−i−1+i1+i−1−i00
χ3822-2-22-2-222i−2i2i−2i002-2002i−2i000000000002ζ3−2ζ32ζ−2ζ−22−22−i2i2−i2i20000000000−1+i1−i−1−i1+i00
χ3922-2-22-2-222i−2i2i−2i002-2002i−2i00000000000−2ζ32ζ3−2ζ2ζ2−22−2i2−i2i2−i20000000000−1+i1−i−1−i1+i00
χ4022-2-22-2-222i−2i2i−2i002-2002i−2i00000000000−2ζ32ζ3−2ζ2ζ−22−22−i2i2−i2i200000000001−i−1+i1+i−1−i00
χ4122-2-22-2-22−2i2i−2i2i002-200−2i2i000000000002ζ−2ζ2ζ3−2ζ32−22−2−i2i2−i2i20000000000−1−i1+i−1+i1−i00
χ4222-2-22-2-22−2i2i−2i2i002-200−2i2i000000000002ζ−2ζ2ζ3−2ζ3−22−22i2−i2i2−i200000000001+i−1−i1−i−1+i00
χ4322-2-22-2-22−2i2i−2i2i002-200−2i2i00000000000−2ζ2ζ−2ζ32ζ32−22−2−i2i2−i2i200000000001+i−1−i1−i−1+i00
χ4422-2-22-2-22−2i2i−2i2i002-200−2i2i00000000000−2ζ2ζ−2ζ32ζ3−22−22i2−i2i2−i20000000000−1−i1+i−1+i1−i00
χ454444-4-4-4-444-4-4-4400-4000400000000000000000000000000000000000000
χ464444-4-4-4-4-4-444-44004000-400000000000000000000000000000000000000
χ4744-4-44-4-444i−4i4i−4i00-4400−4i4i000000000000000000000000000000000000000
χ4844-4-44-4-44−4i4i−4i4i00-44004i−4i000000000000000000000000000000000000000
χ4944-4-4-444-44i−4i−4i4i000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ5044-4-4-444-44i−4i−4i4i00000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ5144-4-4-444-4−4i4i4i−4i000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ5244-4-4-444-4−4i4i4i−4i00000000000000000000000-222-22i−2i−2i2i0000000000000000
χ534-44-444-4-40000000004000-44-400000000000000000000000000000000000
χ544-44-444-4-40000000004000-4-4400000000000000000000000000000000000
χ554-44-444-4-4000000000-400040004i−4i00000000000000000000000000000000
χ564-44-444-4-4000000000-40004000−4i4i00000000000000000000000000000000
χ578-88-8-8-888000000000000000000000000000000000000000000000000000
χ588-8-888-88-8000000000000000000000000000000000000000000000000000
χ598-8-88-88-88000000000000000000000000000000000000000000000000000

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