Finite Group Databasebeta

← Group #101813

Character table — Group #101813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444444444488888888888888884444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ51111111111111111111111-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ71111111111111111111111-1-11-1-1-1-1-1-1111111111111-1-11111-1-111-1-1-1-1-1-1
χ81111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1111111-1-111-1-1-1ii−i−iii−i−i1111-1-1-1-11-1ii−i−ii−ii−iii−i−i1-1
χ1011111111-1-1-1-1-1-1111111-1-111-1-1-1ii−i−iii−i−i-1-1-1-111111-1−i−iiii−ii−i−i−iii-11
χ1111111111-1-1-1-1-1-1111111-1-111-1-1-1−i−iii−i−iii1111-1-1-1-11-1−i−iii−ii−ii−i−iii1-1
χ1211111111-1-1-1-1-1-1111111-1-111-1-1-1−i−iii−i−iii-1-1-1-111111-1ii−i−i−ii−iiii−i−i-11
χ1311111111-1-1-1-1-1-1111111-1-1-1-1-111ii−i−i−i−iii1111-1-1-1-1-11−i−iiii−i−iiii−i−i-11
χ1411111111-1-1-1-1-1-1111111-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111-11ii−i−ii−i−ii−i−iii1-1
χ1511111111-1-1-1-1-1-1111111-1-1-1-1-111−i−iiiii−i−i1111-1-1-1-1-11ii−i−i−iii−i−i−iii-11
χ1611111111-1-1-1-1-1-1111111-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111-11−i−iii−iii−iii−i−i1-1
χ172222222222222222-2-2-2-2-2-200-2002222000000000000000000-2-200000000
χ182222222222222222-2-2-2-2-2-200-200-2-2-2-20000000000000000002200000000
χ19222222222222-2-2-2-222-2-22200-200000022220000000000000000-2-2000000
χ20222222222222-2-2-2-222-2-22200-2000000-2-2-2-2000000000000000022000000
χ21222222222222-2-2-2-2-2-222-2-2222220000000000000000-2-200000000000000
χ22222222222222-2-2-2-2-2-222-2-2-2-22-2-200000000000000002200000000000000
χ2322222222-2-2-2-222-2-222-2-2-2-20020000002i2i−2i−2i0000000000000000−2i2i000000
χ2422222222-2-2-2-222-2-222-2-2-2-2002000000−2i−2i2i2i00000000000000002i−2i000000
χ2522222222-2-2-2-222-2-2-2-2222222-2-2-20000000000000000-2200000000000000
χ2622222222-2-2-2-222-2-2-2-22222-2-2-22200000000000000002-200000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-222002002i2i−2i−2i000000000000000000−2i2i00000000
χ2822222222-2-2-2-2-2-222-2-2-2-22200200−2i−2i2i2i0000000000000000002i−2i00000000
χ29222-22-2-2-222-2-22-22-2000000000002-22-2000022−2−222−2−200000000002−22−200
χ30222-22-2-2-222-2-22-22-2000000000002-22-20000−2−222−2−2220000000000−22−2200
χ31222-22-2-2-222-2-22-22-200000000000-22-22000022−2−222−2−20000000000−22−2200
χ32222-22-2-2-222-2-22-22-200000000000-22-220000−2−222−2−22200000000002−22−200
χ33222-22-2-2-2-2-222-222-2000000000002i−2i−2i2i000022−2−2−2−2220000000000i2−i2−i2i200
χ34222-22-2-2-2-2-222-222-2000000000002i−2i−2i2i0000−2−22222−2−20000000000−i2i2i2−i200
χ35222-22-2-2-2-2-222-222-200000000000−2i2i2i−2i000022−2−2−2−2220000000000−i2i2i2−i200
χ36222-22-2-2-2-2-222-222-200000000000−2i2i2i−2i0000−2−22222−2−20000000000i2−i2−i2i200
χ3722-22-2-2-222i−2i2i−2i00002-2002i−2i0000000002ζ3−2ζ32ζ−2ζ2−22−2i2−i2i2−i2001−i−1+i1+i−1−i0000000000
χ3822-22-2-2-222i−2i2i−2i00002-2002i−2i0000000002ζ3−2ζ32ζ−2ζ−22−22−i2i2−i2i200−1+i1−i−1−i1+i0000000000
χ3922-22-2-2-222i−2i2i−2i00002-2002i−2i000000000−2ζ32ζ3−2ζ2ζ2−22−2i2−i2i2−i200−1+i1−i−1−i1+i0000000000
χ4022-22-2-2-222i−2i2i−2i00002-2002i−2i000000000−2ζ32ζ3−2ζ2ζ−22−22−i2i2−i2i2001−i−1+i1+i−1−i0000000000
χ4122-22-2-2-22−2i2i−2i2i00002-200−2i2i0000000002ζ−2ζ2ζ3−2ζ32−22−2−i2i2−i2i200−1−i1+i−1+i1−i0000000000
χ4222-22-2-2-22−2i2i−2i2i00002-200−2i2i0000000002ζ−2ζ2ζ3−2ζ3−22−22i2−i2i2−i2001+i−1−i1−i−1+i0000000000
χ4322-22-2-2-22−2i2i−2i2i00002-200−2i2i000000000−2ζ2ζ−2ζ32ζ32−22−2−i2i2−i2i2001+i−1−i1−i−1+i0000000000
χ4422-22-2-2-22−2i2i−2i2i00002-200−2i2i000000000−2ζ2ζ−2ζ32ζ3−22−22i2−i2i2−i200−1−i1+i−1+i1−i0000000000
χ45444-44-4-4-444-4-4-44-440000000000000000000000000000000000000000000
χ46444-44-4-4-4-4-4444-4-440000000000000000000000000000000000000000000
χ4744-44-4-4-444i−4i4i−4i0000-4400−4i4i0000000000000000000000000000000000000
χ4844-44-4-4-44−4i4i−4i4i0000-44004i−4i0000000000000000000000000000000000000
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
χ534-4-4-44-44400000000004-4000004-400000000000000000000000000000000
χ544-4-4-44-44400000000004-400000-4400000000000000000000000000000000
χ554-4-4-44-4440000000000-44004-400000000000000000000000000000000000
χ564-4-4-44-4440000000000-4400-4400000000000000000000000000000000000
χ578-888-8-88-8000000000000000000000000000000000000000000000000000
χ588-88-8-88-88000000000000000000000000000000000000000000000000000
χ598-8-8888-8-8000000000000000000000000000000000000000000000000000

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