Finite Group Databasebeta

← Group #97521

Character table — Group #97521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111111111111144444444444488888888888888888888888888888888888816161616161616161616
order12222222444444442244444444442244444444444444444488888888888888884444448888
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
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111
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
χ911111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-1−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1-11−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1-11ii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11-11−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11-11ii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-111-1ii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-111-1−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-20000000022220000000000000000000000000000-2-20000
χ1822222222222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000220000
χ192222222222222222-2-2-2-222-2-222-2-2000022220000000000000000000000000000-2-200000000
χ202222222222222222-2-2-2-222-2-222-2-20000-2-2-2-200000000000000000000000000002200000000
χ212222222222222222-2-2-2-2-2-222-2-22222220000000000000000000000000000000000-2-2000000
χ222222222222222222-2-2-2-2-2-222-2-222-2-2-2-2000000000000000000000000000000000022000000
χ2322222222-2-2-2-2-2-2-2-222-2-222-2-2-2-222000022-2-20000000000000000000000000000-2200000000
χ2422222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2220000-2-22200000000000000000000000000002-200000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-222-2-20000000000000000000000000000000000-22000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22200000000000000000000000000000000002-2000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222220000000022-2-20000000000000000000000000000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2222200000000-2-22200000000000000000000000000002-20000
χ2922-22-2-22-22i2i2i−2i−2i−2i2i−2i0000002-2002i−2i2-22i−2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000
χ3022-22-2-22-22i2i2i−2i−2i−2i2i−2i0000002-2002i−2i2-22i−2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000
χ3122-22-2-22-22i2i2i−2i−2i−2i2i−2i0000002-2002i−2i-22−2i2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000
χ3222-22-2-22-22i2i2i−2i−2i−2i2i−2i0000002-2002i−2i-22−2i2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000
χ3322-22-2-22-2−2i−2i−2i2i2i2i−2i2i0000002-200−2i2i2-2−2i2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000
χ3422-22-2-22-2−2i−2i−2i2i2i2i−2i2i0000002-200−2i2i2-2−2i2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000
χ3522-22-2-22-2−2i−2i−2i2i2i2i−2i2i0000002-200−2i2i-222i−2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000
χ3622-22-2-22-2−2i−2i−2i2i2i2i−2i2i0000002-200−2i2i-222i−2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000
χ3722-2-22-2-222i2i−2i2i−2i−2i−2i2i00002-2002i−2i0000002i−2i2-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000
χ3822-2-22-2-222i2i−2i2i−2i−2i−2i2i00002-2002i−2i0000002i−2i2-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000
χ3922-2-22-2-222i2i−2i2i−2i−2i−2i2i00002-2002i−2i000000−2i2i-2200001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000
χ4022-2-22-2-222i2i−2i2i−2i−2i−2i2i00002-2002i−2i000000−2i2i-220000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000
χ4122-2-22-2-22−2i−2i2i−2i2i2i2i−2i00002-200−2i2i0000002i−2i-2200001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000
χ4222-2-22-2-22−2i−2i2i−2i2i2i2i−2i00002-200−2i2i0000002i−2i-220000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000
χ4322-2-22-2-22−2i−2i2i−2i2i2i2i−2i00002-200−2i2i000000−2i2i2-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000
χ4422-2-22-2-22−2i−2i2i−2i2i2i2i−2i00002-200−2i2i000000−2i2i2-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000
χ452-2-2222-2-22-2222-2-2-2-222-200000000000000002i−2i2i−2i000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000
χ462-2-2222-2-22-2222-2-2-2-222-200000000000000002i−2i2i−2i00000000−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000
χ472-2-2222-2-22-2222-2-2-2-222-20000000000000000−2i2i−2i2i000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000
χ482-2-2222-2-22-2222-2-2-2-222-20000000000000000−2i2i−2i2i00000000−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000
χ492-2-2222-2-2-22-2-2-22222-22-200000000000000002i−2i−2i2i00000000i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000
χ502-2-2222-2-2-22-2-2-22222-22-200000000000000002i−2i−2i2i00000000−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000
χ512-2-2222-2-2-22-2-2-22222-22-20000000000000000−2i2i2i−2i00000000i2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000
χ522-2-2222-2-2-22-2-2-22222-22-20000000000000000−2i2i2i−2i00000000−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000
χ53444-4-44-4-444-4-444-4-40000000000000000000000002-2-222-2-2200000000000000000000000000
χ54444-4-44-4-444-4-444-4-4000000000000000000000000-222-2-222-200000000000000000000000000
χ55444-4-44-4-4-4-444-4-4440000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ56444-4-44-4-4-4-444-4-444000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5744-44-4-44-44i4i4i−4i−4i−4i4i−4i000000-4400−4i4i0000000000000000000000000000000000000000000000
χ5844-44-4-44-4−4i−4i−4i4i4i4i−4i4i000000-44004i−4i0000000000000000000000000000000000000000000000
χ5944-4-44-4-444i4i−4i4i−4i−4i−4i4i0000-4400−4i4i000000000000000000000000000000000000000000000000
χ6044-4-44-4-44−4i−4i4i−4i4i4i4i−4i0000-44004i−4i000000000000000000000000000000000000000000000000
χ614-444-4-4-444i−4i4i−4i−4i4i−4i4i000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000
χ624-444-4-4-444i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000
χ634-444-4-4-44−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000
χ644-444-4-4-44−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000
χ654-44-44-44-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000
χ664-44-44-44-44i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000
χ674-44-44-44-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000
χ684-44-44-44-4−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000
χ694-4-4444-4-44-4444-4-4-44-4-44000000000000000000000000000000000000000000000000000000
χ704-4-4444-4-4-44-4-4-4444-44-44000000000000000000000000000000000000000000000000000000
χ714-4-4-4-44444-4-4-44-4440000000000000000000000000000000000000000000000000000002-22-2
χ724-4-4-4-44444-4-4-44-444000000000000000000000000000000000000000000000000000000-22-22
χ734-4-4-4-4444-4444-44-4-40000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ744-4-4-4-4444-4444-44-4-4000000000000000000000000000000000000000000000000000000−2i2i2i−2i

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