Finite Group Databasebeta

← Group #96949

Character table — Group #96949

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888822444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-1-1-1111-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i-1111-1-1-11−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−i−i−iiiii1-1-1-1111-1−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−i−i−iiiii-1111-1-1-11ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000022-2-2-2-222000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000-2-22222-2-2000000000000000000000000
χ2122222222-2-2-2-222-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000002002-20-200000000
χ2222222222-2-2-2-222-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000-200-220200000000
χ2322222222-2-2-2-222-2-2-2-22222-2-2-2-222-2-22200000000000000000000000000000000202-200-2000000000
χ2422222222-2-2-2-222-2-2-2-22222-2-2-2-222-2-22200000000000000000000000000000000-20-22002000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2220000000000000000000000000000000020-2200-2000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22200000000000000000000000000000000-202-2002000000000
χ2722222222-2-2-2-2-2-222-2-222-2-222-2-22222-2-2000000000000000000000000000000000200-220-200000000
χ2822222222-2-2-2-2-2-222-2-222-2-222-2-22222-2-2000000000000000000000000000000000-2002-20200000000
χ292222-2-2-2-222-2-222220000-2-2-2-2000000002222−2−2−2−22222−2−2−2−22-22-2000022−2−222−2−20000000000000000
χ302222-2-2-2-222-2-222220000-2-2-2-2000000002222−2−2−2−22222−2−2−2−2-22-220000−2−222−2−2220000000000000000
χ312222-2-2-2-222-2-222220000-2-2-2-200000000−2−2−2−22222−2−2−2−222222-22-20000−2−222−2−2220000000000000000
χ322222-2-2-2-222-2-222220000-2-2-2-200000000−2−2−2−22222−2−2−2−22222-22-22000022−2−222−2−20000000000000000
χ332222-2-2-2-222-2-2-2-2-2-20000222200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22-2-220000i2i2−i2−i2−i2−i2i2i20000000000000000
χ342222-2-2-2-222-2-2-2-2-2-20000222200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-222-20000−i2−i2i2i2i2i2−i2−i20000000000000000
χ352222-2-2-2-222-2-2-2-2-2-20000222200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22-2-220000−i2−i2i2i2i2i2−i2−i20000000000000000
χ362222-2-2-2-222-2-2-2-2-2-20000222200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-222-20000i2i2−i2−i2−i2−i2i2i20000000000000000
χ3722-2-22-2-222-22-22i−2i2i−2i00002i−2i2i−2i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00002i−2i2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ3822-2-22-2-222-22-22i−2i2i−2i00002i−2i2i−2i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000−2i2i-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3922-2-22-2-222-22-22i−2i2i−2i00002i−2i2i−2i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00002i−2i2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4022-2-22-2-222-22-22i−2i2i−2i00002i−2i2i−2i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000−2i2i-221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4122-2-22-2-222-22-2−2i2i−2i2i0000−2i2i−2i2i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00002i−2i-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4222-2-22-2-222-22-2−2i2i−2i2i0000−2i2i−2i2i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000−2i2i2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4322-2-22-2-222-22-2−2i2i−2i2i0000−2i2i−2i2i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00002i−2i-221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4422-2-22-2-222-22-2−2i2i−2i2i0000−2i2i−2i2i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000−2i2i2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4522-2-2-222-22-2-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2-22-20000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ4622-2-2-222-22-2-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2-22-2000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ4722-2-2-222-22-2-222i−2i2i−2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i-22-222ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ300000000000000000000000000000000
χ4822-2-2-222-22-2-222i−2i2i−2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i-22-22−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ300000000000000000000000000000000
χ4922-2-2-222-22-2-22−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i-22-222ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ00000000000000000000000000000000
χ5022-2-2-222-22-2-22−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i-22-22−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ00000000000000000000000000000000
χ5122-2-2-222-22-2-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2-22-20000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ5222-2-2-222-22-2-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2-22-2000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ5322-2-2-222-2-222-22i−2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i2-2-2200000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ5422-2-2-222-2-222-22i−2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i2-2-220000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ5522-2-2-222-2-222-22i−2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i-222-2000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ5622-2-2-222-2-222-22i−2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i-222-200000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ5722-2-2-222-2-222-2−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i-222-2000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ5822-2-2-222-2-222-2−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i-222-200000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ5922-2-2-222-2-222-2−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2-2-2200000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ6022-2-2-222-2-222-2−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2-2-220000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ614444-4-4-4-4-4-44444-4-40000-4-44400000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-444-4-444000044-4-400000000000000000000000000000000000000000000000000000000
χ6344-4-44-4-44-44-444i−4i−4i4i00004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6444-4-44-4-44-44-44−4i4i4i−4i0000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ654-44-444-4-400000000004i−4i000000−4i4i00002ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ664-44-444-4-400000000004i−4i000000−4i4i0000−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ674-44-444-4-40000000000−4i4i0000004i−4i00002ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ684-44-444-4-40000000000−4i4i0000004i−4i0000−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ694-44-4-4-4440000000044000000-4-40000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ704-44-4-4-4440000000044000000-4-4000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ714-44-4-4-44400000000-4-4000000440000002-22-2-22-22-22-222-22-200000000000000000000000000000000
χ724-44-4-4-44400000000-4-400000044000000-22-222-22-22-22-2-22-2200000000000000000000000000000000
χ734-4-444-44-4000000004i−4i000000−4i4i0000002ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ744-4-444-44-4000000004i−4i000000−4i4i000000−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ754-4-444-44-400000000−4i4i0000004i−4i0000002ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ764-4-444-44-400000000−4i4i0000004i−4i000000−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ774-4-44-44-44000000000044000000-4-400002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ784-4-44-44-44000000000044000000-4-40000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ794-4-44-44-440000000000-4-40000004400002-2-22-222-2-222-22-2-2200000000000000000000000000000000
χ804-4-44-44-440000000000-4-4000000440000-222-22-2-222-2-22-222-200000000000000000000000000000000

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