Finite Group Databasebeta

← Group #99404

Character table — Group #99404

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111111111111144444444444488888888888888888888888888888888888816161616161616161616
order12222222444444442244444444442244444444448888888888888888888888884488888888
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
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-11-1ii−i−ii−ii−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−iii−i−iii-1-1-1-11111-1-1-1-111111-1ii−i−i−ii−ii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiii−i−iii−i−i-1-1-1-11111-1-1-1-111111-1−i−iiii−ii−i
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-11111-1-1-1-11-1−i−iii−ii−ii
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−iii−i−i−i−iii1111-1-1-1-1-1-1-1-11111-11−i−iiii−i−ii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−i−i−iiiii−i−i-1-1-1-111111111-1-1-1-1-11−i−iii−iii−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111−i−i−i−iiiiiii−i−i−i−iii-1-1-1-111111111-1-1-1-1-11ii−i−ii−i−ii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111−i−i−i−iiiii−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111-11ii−i−i−iii−i
χ17222222222222222222-2-2-2-222-2-2-2-2222200000000000000000000000000000000-2-200000000
χ18222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2000000000000000000000000000000002200000000
χ192222222222222222-2-222-2-2-2-222-2-200000000000000002222000000000000000000000000-2-2
χ202222222222222222-2-222-2-2-2-222-2-20000000000000000-2-2-2-200000000000000000000000022
χ212222222222222222-2-2-2-222-2-2-2-222000000000000222200000000000000000000000000-2-200
χ222222222222222222-2-2-2-222-2-2-2-222000000000000-2-2-2-2000000000000000000000000002200
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2220000000000002i2i−2i−2i00000000000000000000000000−2i2i00
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222000000000000−2i−2i2i2i000000000000000000000000002i−2i00
χ2522222222-2-2-2-2-2-2-2-222-2-222-2-222-2-200000000000000002i2i−2i−2i000000000000000000000000−2i2i
χ2622222222-2-2-2-2-2-2-2-222-2-222-2-222-2-20000000000000000−2i−2i2i2i0000000000000000000000002i−2i
χ2722222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222-2-200000000000000000000000000000000-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222000000000000000000000000000000002-200000000
χ29222-2-2-2-222222-2-2-2-2-2200002-200002-22-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000
χ30222-2-2-2-222222-2-2-2-2-2200002-200002-22-20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000
χ31222-2-2-2-222222-2-2-2-2-2200002-20000-22-220000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000
χ32222-2-2-2-222222-2-2-2-2-2200002-20000-22-220000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000
χ33222-2-2-2-22-2-2-2-222222-200002-200002-2-220000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000
χ34222-2-2-2-22-2-2-2-222222-200002-200002-2-220000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000
χ35222-2-2-2-22-2-2-2-222222-200002-20000-222-20000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000
χ36222-2-2-2-22-2-2-2-222222-200002-20000-222-20000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000
χ3722-222-2-2-22i−2i2i−2i2i2i−2i−2i00002i−2i00002-200001+i1+i−1−i−1−i1−i1−i−1+i−1+i2ζ−2ζ2ζ3−2ζ300002−22−2i2−i2i2−i2000000000000000000
χ3822-222-2-2-22i−2i2i−2i2i2i−2i−2i00002i−2i00002-200001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ2ζ−2ζ32ζ30000−22−22−i2i2−i2i2000000000000000000
χ3922-222-2-2-22i−2i2i−2i2i2i−2i−2i00002i−2i00002-20000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ−2ζ2ζ3−2ζ30000−22−22−i2i2−i2i2000000000000000000
χ4022-222-2-2-22i−2i2i−2i2i2i−2i−2i00002i−2i00002-20000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ2ζ−2ζ32ζ300002−22−2i2−i2i2−i2000000000000000000
χ4122-222-2-2-2−2i2i−2i2i−2i−2i2i2i0000−2i2i00002-200001−i1−i−1+i−1+i1+i1+i−1−i−1−i2ζ3−2ζ32ζ−2ζ0000−22−22i2−i2i2−i2000000000000000000
χ4222-222-2-2-2−2i2i−2i2i−2i−2i2i2i0000−2i2i00002-200001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2ζ32ζ3−2ζ2ζ00002−22−2−i2i2−i2i2000000000000000000
χ4322-222-2-2-2−2i2i−2i2i−2i−2i2i2i0000−2i2i00002-20000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2ζ3−2ζ32ζ−2ζ00002−22−2−i2i2−i2i2000000000000000000
χ4422-222-2-2-2−2i2i−2i2i−2i−2i2i2i0000−2i2i00002-20000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2ζ32ζ3−2ζ2ζ0000−22−22i2−i2i2−i2000000000000000000
χ452-222-22-2-22i−2i−2i2i2i−2i2i−2i002i−2i00002-20000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002ζ−2ζ2ζ3−2ζ300000000i2−i2i2−i22−22−20000000000
χ462-222-22-2-22i−2i−2i2i2i−2i2i−2i002i−2i00002-20000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−2ζ2ζ−2ζ32ζ300000000−i2i2−i2i2−22−220000000000
χ472-222-22-2-22i−2i−2i2i2i−2i2i−2i002i−2i00002-2000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002ζ−2ζ2ζ3−2ζ300000000−i2i2−i2i2−22−220000000000
χ482-222-22-2-22i−2i−2i2i2i−2i2i−2i002i−2i00002-2000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−2ζ2ζ−2ζ32ζ300000000i2−i2i2−i22−22−20000000000
χ492-222-22-2-2−2i2i2i−2i−2i2i−2i2i00−2i2i00002-20000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002ζ3−2ζ32ζ−2ζ00000000i2−i2i2−i2−22−220000000000
χ502-222-22-2-2−2i2i2i−2i−2i2i−2i2i00−2i2i00002-20000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−2ζ32ζ3−2ζ2ζ00000000−i2i2−i2i22−22−20000000000
χ512-222-22-2-2−2i2i2i−2i−2i2i−2i2i00−2i2i00002-2000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002ζ3−2ζ32ζ−2ζ00000000−i2i2−i2i22−22−20000000000
χ522-222-22-2-2−2i2i2i−2i−2i2i−2i2i00−2i2i00002-2000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−2ζ32ζ3−2ζ2ζ00000000i2−i2i2−i2−22−220000000000
χ53444-4-4-4-444444-4-4-4-44-40000-4400000000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4-4-4-44444-440000-4400000000000000000000000000000000000000000000000000
χ5544-444-4-4-44i−4i4i−4i4i4i−4i−4i0000−4i4i0000-440000000000000000000000000000000000000000000000
χ5644-444-4-4-4−4i4i−4i4i−4i−4i4i4i00004i−4i0000-440000000000000000000000000000000000000000000000
χ5744-4-4-444-44i−4i4i−4i−4i−4i4i4i000000000000000000000000000000002i−2i−2i2i-222-2000000000000000000
χ5844-4-4-444-44i−4i4i−4i−4i−4i4i4i00000000000000000000000000000000−2i2i2i−2i2-2-22000000000000000000
χ5944-4-4-444-4−4i4i−4i4i4i4i−4i−4i000000000000000000000000000000002i−2i−2i2i2-2-22000000000000000000
χ6044-4-4-444-4−4i4i−4i4i4i4i−4i−4i00000000000000000000000000000000−2i2i2i−2i-222-2000000000000000000
χ614-444-44-4-44i−4i−4i4i4i−4i4i−4i00−4i4i0000-44000000000000000000000000000000000000000000000000
χ624-444-44-4-4−4i4i4i−4i−4i4i−4i4i004i−4i0000-44000000000000000000000000000000000000000000000000
χ634-44-44-44-44i−4i−4i4i−4i4i−4i4i00000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ644-44-44-44-44i−4i−4i4i−4i4i−4i4i0000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ654-44-44-44-4−4i4i4i−4i4i−4i4i−4i00000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ664-44-44-44-4−4i4i4i−4i4i−4i4i−4i0000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ674-4-44-4-44444-4-44-4-4400000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000
χ684-4-44-4-44444-4-44-4-440000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000
χ694-4-44-4-444-4-444-444-400000000000000002-2-222-2-220000000000000000000000000000000000
χ704-4-44-4-444-4-444-444-40000000000000000-222-2-222-20000000000000000000000000000000000
χ714-4-4-444-4444-4-4-444-4000000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ724-4-4-444-4444-4-4-444-400000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ734-4-4-444-44-4-4444-4-44000000000000000000000000000000000000000000000000002-2-220000
χ744-4-4-444-44-4-4444-4-4400000000000000000000000000000000000000000000000000-222-20000

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