Finite Group Databasebeta

← Group #100711

Character table — Group #100711

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444442244488888888888888884488888888888824
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-11-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ71111111111111111111111-1-11-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-111-1-11-1-1-1-11111-1-1ii−i−iii−i−iiiii−i−i−i−i1-1i−ii−iii−i−i11-1-11-1
χ1011111111-1-1-1-111-1-11-1-1-1-11111-1-1ii−i−iii−i−i−i−i−i−iiiii1-1i−ii−i−i−iii-1-111-11
χ1111111111-1-1-1-111-1-11-1-1-1-11111-1-1−i−iii−i−iiiiiii−i−i−i−i1-1−ii−iiii−i−i-1-111-11
χ1211111111-1-1-1-111-1-11-1-1-1-11111-1-1−i−iii−i−iii−i−i−i−iiiii1-1−ii−ii−i−iii11-1-11-1
χ1311111111-1-1-1-111-1-11-1-1-1-11-1-1111ii−i−i−i−iiiiiii−i−i−i−i-11i−i−ii−i−iii11-1-1-11
χ1411111111-1-1-1-111-1-11-1-1-1-11-1-1111ii−i−i−i−iii−i−i−i−iiiii-11i−i−iiii−i−i-1-1111-1
χ1511111111-1-1-1-111-1-11-1-1-1-11-1-1111−i−iiiii−i−iiiii−i−i−i−i-11−iii−i−i−iii-1-1111-1
χ1611111111-1-1-1-111-1-11-1-1-1-11-1-1111−i−iiiii−i−i−i−i−i−iiiii-11−iii−iii−i−i11-1-1-11
χ1722222222222222-2-2-222-2-2-200-200222200000000000000-2-2000000000000
χ1822222222222222-2-2-222-2-2-200-200-2-2-2-20000000000000022000000000000
χ19222222222222-2-2222-2-2-2-2222-2220000000000000000-2-200000000000000
χ20222222222222-2-2222-2-2-2-22-2-2-2-2-200000000000000002200000000000000
χ21222222222222-2-2-2-2-2-2-222-20020000002222000000000000-2-20000000000
χ22222222222222-2-2-2-2-2-2-222-2002000000-2-2-2-2000000000000220000000000
χ2322222222-2-2-2-22222-2-2-222-200-2002i2i−2i−2i00000000000000−2i2i000000000000
χ2422222222-2-2-2-22222-2-2-222-200-200−2i−2i2i2i000000000000002i−2i000000000000
χ2522222222-2-2-2-2-2-222-222-2-2-20020000002i2i−2i−2i000000000000−2i2i0000000000
χ2622222222-2-2-2-2-2-222-222-2-2-2002000000−2i−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
χ29222-22-2-2-22i−2i2i−2i2-20002i−2i000000002ζ−2ζ2ζ3−2ζ300001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000002−2i2−i200
χ30222-22-2-2-22i−2i2i−2i2-20002i−2i000000002ζ−2ζ2ζ3−2ζ30000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−22−i2i200
χ31222-22-2-2-22i−2i2i−2i2-20002i−2i00000000−2ζ2ζ−2ζ32ζ300001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−22−i2i200
χ32222-22-2-2-22i−2i2i−2i2-20002i−2i00000000−2ζ2ζ−2ζ32ζ30000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000002−2i2−i200
χ33222-22-2-2-2−2i2i−2i2i2-2000−2i2i000000002ζ3−2ζ32ζ−2ζ00001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−22i2−i200
χ34222-22-2-2-2−2i2i−2i2i2-2000−2i2i000000002ζ3−2ζ32ζ−2ζ0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000002−2−i2i200
χ35222-22-2-2-2−2i2i−2i2i2-2000−2i2i00000000−2ζ32ζ3−2ζ2ζ00001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000002−2−i2i200
χ36222-22-2-2-2−2i2i−2i2i2-2000−2i2i00000000−2ζ32ζ3−2ζ2ζ0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−22i2−i200
χ3722-2-2-22-2222-2-2002-2-2000022-202-200000000i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2000000
χ3822-2-2-22-2222-2-2002-2-2000022-202-200000000−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2000000
χ3922-2-2-22-2222-2-2002-2-200002-220-2200000000i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i2000000
χ4022-2-2-22-2222-2-2002-2-200002-220-2200000000−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i2000000
χ4122-2-2-22-22-2-22200-22-2000022-20-22000000002−22−2−22−220000002−2−22000000
χ4222-2-2-22-22-2-22200-22-2000022-20-2200000000−22−222−22−2000000−222−2000000
χ4322-2-2-22-22-2-22200-22-200002-2202-2000000002−22−2−22−22000000−222−2000000
χ4422-2-2-22-22-2-22200-22-200002-2202-200000000−22−222−22−20000002−2−22000000
χ45444-44-4-4-44i−4i4i−4i-44000−4i4i0000000000000000000000000000000000000000
χ46444-44-4-4-4−4i4i−4i4i-440004i−4i0000000000000000000000000000000000000000
χ4744-44-4-44-44i−4i−4i4i000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ4844-44-4-44-44i−4i−4i4i00000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ4944-44-4-44-4−4i4i4i−4i000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ5044-44-4-44-4−4i4i4i−4i00000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ5144-4-4-44-4444-4-400-4440000-40000000000000000000000000000000000000
χ5244-4-4-44-44-4-444004-440000-40000000000000000000000000000000000000
χ534-444-44-4-4000000000004i−4i00000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ544-444-44-4-4000000000004i−4i0000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ554-444-44-4-400000000000−4i4i00000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ564-444-44-4-400000000000−4i4i0000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ578-88-8-8-888000000000000000000000000000000000000000000000000000
χ588-8-888-8-88000000000000000000000000000000000000000000000000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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