Finite Group Databasebeta

← Group #99413

Character table — Group #99413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111111111111144444444444488888888888888888888888888888888888816161616161616161616
order12222222444444444444444444442244888888888888888888888888888888884488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1-1i−ii−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii1-1i−ii−i−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1-1−ii−ii−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−i1-1−ii−iiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-11i−i−ii−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-11i−i−iiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-11−iii−iii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-11−iii−i−i−iii
χ17222222222222222222-2-2-2-222-2-2-2-20000000022220000000000000000000000000000-2-20000
χ18222222222222222222-2-2-2-222-2-2-2-200000000-2-2-2-20000000000000000000000000000220000
χ192222222222222222-2-222-2-2-2-222-2-200002222000000000000000000000000000000-2-2000000
χ202222222222222222-2-222-2-2-2-222-2-20000-2-2-2-200000000000000000000000000000022000000
χ212222222222222222-2-2-2-222-2-2-2-222222200000000000000000000000000000000-2-200000000
χ222222222222222222-2-2-2-222-2-2-2-222-2-2-2-2000000000000000000000000000000002200000000
χ2322222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-200000000000000000000000000000000-2200000000
χ2422222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222000000000000000000000000000000002-200000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222200002i2i−2i−2i000000000000000000000000000000−2i2i000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-2-2-222220000−2i−2i2i2i0000000000000000000000000000002i−2i000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222000000002i2i−2i−2i0000000000000000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-222-2-22200000000−2i−2i2i2i00000000000000000000000000002i−2i0000
χ29222-2-22-2-22i−2i2i2i−2i−2i2i−2i00002-200002i−2i2-22i−2i00000000i2i2−i2−i222−2−2i2i2−i2−i222−2−2000000000000000000
χ30222-2-22-2-22i−2i2i2i−2i−2i2i−2i00002-200002i−2i2-22i−2i00000000−i2−i2i2i2−2−222−i2−i2i2i2−2−222000000000000000000
χ31222-2-22-2-22i−2i2i2i−2i−2i2i−2i00002-200002i−2i-22−2i2i00000000i2i2−i2−i222−2−2−i2−i2i2i2−2−222000000000000000000
χ32222-2-22-2-22i−2i2i2i−2i−2i2i−2i00002-200002i−2i-22−2i2i00000000−i2−i2i2i2−2−222i2i2−i2−i222−2−2000000000000000000
χ33222-2-22-2-2−2i2i−2i−2i2i2i−2i2i00002-20000−2i2i2-2−2i2i00000000i2i2−i2−i2−2−222i2i2−i2−i2−2−222000000000000000000
χ34222-2-22-2-2−2i2i−2i−2i2i2i−2i2i00002-20000−2i2i2-2−2i2i00000000−i2−i2i2i222−2−2−i2−i2i2i222−2−2000000000000000000
χ35222-2-22-2-2−2i2i−2i−2i2i2i−2i2i00002-20000−2i2i-222i−2i00000000i2i2−i2−i2−2−222−i2−i2i2i222−2−2000000000000000000
χ36222-2-22-2-2−2i2i−2i−2i2i2i−2i2i00002-20000−2i2i-222i−2i00000000−i2−i2i2i222−2−2i2i2−i2−i2−2−222000000000000000000
χ3722-22-2-22-22i−2i2i−2i2i−2i−2i2i002i−2i00002-20000002ζ3−2ζ32ζ−2ζ0000i2−i2i2−i22−22−2000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000
χ3822-22-2-22-22i−2i2i−2i2i−2i−2i2i002i−2i00002-20000002ζ3−2ζ32ζ−2ζ0000−i2i2−i2i2−22−2200000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000
χ3922-22-2-22-22i−2i2i−2i2i−2i−2i2i002i−2i00002-2000000−2ζ32ζ3−2ζ2ζ0000i2−i2i2−i22−22−200000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000
χ4022-22-2-22-22i−2i2i−2i2i−2i−2i2i002i−2i00002-2000000−2ζ32ζ3−2ζ2ζ0000−i2i2−i2i2−22−22000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000
χ4122-22-2-22-2−2i2i−2i2i−2i2i2i−2i00−2i2i00002-20000002ζ−2ζ2ζ3−2ζ30000i2−i2i2−i2−22−22000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000
χ4222-22-2-22-2−2i2i−2i2i−2i2i2i−2i00−2i2i00002-20000002ζ−2ζ2ζ3−2ζ30000−i2i2−i2i22−22−200000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000
χ4322-22-2-22-2−2i2i−2i2i−2i2i2i−2i00−2i2i00002-2000000−2ζ2ζ−2ζ32ζ30000i2−i2i2−i2−22−2200000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000
χ4422-22-2-22-2−2i2i−2i2i−2i2i2i−2i00−2i2i00002-2000000−2ζ2ζ−2ζ32ζ30000−i2i2−i2i22−22−2000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000
χ452-22-22-22-22i−2i−2i2i−2i2i−2i2i2i−2i00002-20000000000002ζ3−2ζ32ζ−2ζ00000000i2−i2i2−i22−22−21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ462-22-22-22-22i−2i−2i2i−2i2i−2i2i2i−2i00002-20000000000002ζ3−2ζ32ζ−2ζ00000000−i2i2−i2i2−22−22−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ472-22-22-22-22i−2i−2i2i−2i2i−2i2i2i−2i00002-2000000000000−2ζ32ζ3−2ζ2ζ00000000i2−i2i2−i22−22−2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ482-22-22-22-22i−2i−2i2i−2i2i−2i2i2i−2i00002-2000000000000−2ζ32ζ3−2ζ2ζ00000000−i2i2−i2i2−22−221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ492-22-22-22-2−2i2i2i−2i2i−2i2i−2i−2i2i00002-20000000000002ζ−2ζ2ζ3−2ζ300000000i2−i2i2−i2−22−221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ502-22-22-22-2−2i2i2i−2i2i−2i2i−2i−2i2i00002-20000000000002ζ−2ζ2ζ3−2ζ300000000−i2i2−i2i22−22−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ512-22-22-22-2−2i2i2i−2i2i−2i2i−2i−2i2i00002-2000000000000−2ζ2ζ−2ζ32ζ300000000i2−i2i2−i2−22−22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ522-22-22-22-2−2i2i2i−2i2i−2i2i−2i−2i2i00002-2000000000000−2ζ2ζ−2ζ32ζ300000000−i2i2−i2i22−22−21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ53444-4-44-4-44i−4i4i4i−4i−4i4i−4i0000-440000−4i4i0000000000000000000000000000000000000000000000
χ54444-4-44-4-4−4i4i−4i−4i4i4i−4i4i0000-4400004i−4i0000000000000000000000000000000000000000000000
χ5544-44-4-44-44i−4i4i−4i4i−4i−4i4i00−4i4i0000-44000000000000000000000000000000000000000000000000
χ5644-44-4-44-4−4i4i−4i4i−4i4i4i−4i004i−4i0000-44000000000000000000000000000000000000000000000000
χ5744-4-44-4-44444-4-44-4-40000000000000000000000002-2-222-2-2200000000000000000000000000
χ5844-4-44-4-44444-4-44-4-4000000000000000000000000-222-2-222-200000000000000000000000000
χ5944-4-44-4-44-4-4-444-4440000000000000000000000002-2-22-222-200000000000000000000000000
χ6044-4-44-4-44-4-4-444-444000000000000000000000000-222-22-2-2200000000000000000000000000
χ614-444-4-4-4444-444-4-4-4000000000000000000000000000000002-2-222-2-22000000000000000000
χ624-444-4-4-4444-444-4-4-400000000000000000000000000000000-222-2-222-2000000000000000000
χ634-444-4-4-44-4-44-4-4444000000000000000000000000000000002-2-22-222-2000000000000000000
χ644-444-4-4-44-4-44-4-444400000000000000000000000000000000-222-22-2-22000000000000000000
χ654-44-44-44-44i−4i−4i4i−4i4i−4i4i−4i4i0000-4400000000000000000000000000000000000000000000000000
χ664-44-44-44-4−4i4i4i−4i4i−4i4i−4i4i−4i0000-4400000000000000000000000000000000000000000000000000
χ674-4-4444-4-44i−4i−4i−4i4i4i4i−4i0000000000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ684-4-4444-4-44i−4i−4i−4i4i4i4i−4i000000000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ694-4-4444-4-4−4i4i4i4i−4i−4i−4i4i0000000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ704-4-4444-4-4−4i4i4i4i−4i−4i−4i4i000000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ714-4-4-4-444444-4-4-4-44400000000000000000000000000000000000000002-2-222-2-220000000000
χ724-4-4-4-444444-4-4-4-4440000000000000000000000000000000000000000-222-2-222-20000000000
χ734-4-4-4-4444-4-44444-4-400000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ744-4-4-4-4444-4-44444-4-40000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000

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