Finite Group Databasebeta

← Group #116335

Character table — Group #116335

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12224444444444442244444422444444444444444444444488888888888888888888888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111ii−i−i
χ17222222222222222222222222-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ18222222222222222222222222-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-22-22-2-22-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-22-22-2-22-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-22-222-22-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ222222222222222222-2-2-2-2-2-2-2-2-22-222-22-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2222-2-2000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2622222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2222-2-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-222-2-2-2220000000022-2-2-2-22200000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-222-2-2-22200000000-2-22222-2-200000000000000000000000000000000
χ292222-2-2-2-22222-2-2-2-222-2-2-2-2222222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ302222-2-2-2-22222-2-2-2-222-2-2-2-2222222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ312222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2-2-2222222-2-222-2-20000000000000000000000000000000000000000
χ322222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2-2-22222-2-222-2-2220000000000000000000000000000000000000000
χ332222-2-2-2-22222-2-2-2-2-2-22222-2-22-22-22-22-200000000000000000000000000000000000000002-22-20000
χ342222-2-2-2-22222-2-2-2-2-2-22222-2-22-22-22-22-20000000000000000000000000000000000000000-22-220000
χ352222-2-2-2-22222-2-2-2-2-2-22222-2-2-22-22-22-22000000000000000000000000000000000000000000002i−2i2i−2i
χ362222-2-2-2-22222-2-2-2-2-2-22222-2-2-22-22-22-2200000000000000000000000000000000000000000000−2i2i−2i2i
χ372222-2-2-2-2-2-2-2-2222222-2-222-2-222-2-22-2-2222-2-2-2-2220000000000000000000000000000000000000000
χ382222-2-2-2-2-2-2-2-2222222-2-222-2-222-2-22-2-22-2-22222-2-20000000000000000000000000000000000000000
χ392222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-222-222-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-222-222-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-2-2-2-2-2-22222-2-222-2-2222-2-22-2-222000000000000000000000000000000000000000000002-2-22
χ422222-2-2-2-2-2-2-2-22222-2-222-2-2222-2-22-2-22200000000000000000000000000000000000000000000-222-2
χ432222-2-2-2-2-2-2-2-22222-2-222-2-222-222-222-2-200000000000000000000000000000000000000002-2-220000
χ442222-2-2-2-2-2-2-2-22222-2-222-2-222-222-222-2-20000000000000000000000000000000000000000-222-20000
χ4522-2-222-2-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ−2ζ002ζ3−2ζ3000000002−22−2i2−i2i2−i200000000
χ4622-2-222-2-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ2ζ00−2ζ32ζ300000000−22−22−i2i2−i2i200000000
χ4722-2-222-2-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ−2ζ002ζ3−2ζ300000000−22−22−i2i2−i2i200000000
χ4822-2-222-2-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ2ζ00−2ζ32ζ3000000002−22−2i2−i2i2−i200000000
χ4922-2-222-2-22i2i−2i−2i2i2i−2i−2i-22-22−2i2i−2i2i00000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i2ζ−2ζ002ζ3−2ζ30000000000i2−i2−i2i2−222−200000000
χ5022-2-222-2-22i2i−2i−2i2i2i−2i−2i-22-22−2i2i−2i2i00000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−2ζ2ζ00−2ζ32ζ30000000000−i2i2i2−i22−2−2200000000
χ5122-2-222-2-22i2i−2i−2i2i2i−2i−2i-22-22−2i2i−2i2i0000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i2ζ−2ζ002ζ3−2ζ30000000000−i2i2i2−i22−2−2200000000
χ5222-2-222-2-22i2i−2i−2i2i2i−2i−2i-22-22−2i2i−2i2i0000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−2ζ2ζ00−2ζ32ζ30000000000i2−i2−i2i2−222−200000000
χ5322-2-222-2-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ3−2ζ3002ζ−2ζ00000000−22−22i2−i2i2−i200000000
χ5422-2-222-2-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ32ζ300−2ζ2ζ000000002−22−2−i2i2−i2i200000000
χ5522-2-222-2-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ3−2ζ3002ζ−2ζ000000002−22−2−i2i2−i2i200000000
χ5622-2-222-2-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ32ζ300−2ζ2ζ00000000−22−22i2−i2i2−i200000000
χ5722-2-222-2-2−2i−2i2i2i−2i−2i2i2i-22-222i−2i2i−2i00000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i2ζ3−2ζ3002ζ−2ζ0000000000i2−i2−i2i22−2−2200000000
χ5822-2-222-2-2−2i−2i2i2i−2i−2i2i2i-22-222i−2i2i−2i00000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−2ζ32ζ300−2ζ2ζ0000000000−i2i2i2−i2−222−200000000
χ5922-2-222-2-2−2i−2i2i2i−2i−2i2i2i-22-222i−2i2i−2i0000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i2ζ3−2ζ3002ζ−2ζ0000000000−i2i2i2−i2−222−200000000
χ6022-2-222-2-2−2i−2i2i2i−2i−2i2i2i-22-222i−2i2i−2i0000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2ζ32ζ300−2ζ2ζ0000000000i2−i2−i2i22−2−2200000000
χ6144-4-4-4-4444i4i−4i−4i−4i−4i4i4i4-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ6244-4-4-4-4444i4i−4i−4i−4i−4i4i4i-444-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6344-4-4-4-444−4i−4i4i4i4i4i−4i−4i4-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6444-4-4-4-444−4i−4i4i4i4i4i−4i−4i-444-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i4-44-44i−4i4i−4i00000000000000002-22i−2i2-22i−2i0000000000000000000000000000000000000000
χ664-44-44i−4i4i−4i4-44-44i−4i4i−4i0000000000000000-22−2i2i-22−2i2i0000000000000000000000000000000000000000
χ674-44-44i−4i4i−4i-44-44−4i4i−4i4i00000000000000002-22i−2i-22−2i2i0000000000000000000000000000000000000000
χ684-44-44i−4i4i−4i-44-44−4i4i−4i4i0000000000000000-22−2i2i2-22i−2i0000000000000000000000000000000000000000
χ694-44-4−4i4i−4i4i4-44-4−4i4i−4i4i00000000000000002-2−2i2i2-2−2i2i0000000000000000000000000000000000000000
χ704-44-4−4i4i−4i4i4-44-4−4i4i−4i4i0000000000000000-222i−2i-222i−2i0000000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i-44-444i−4i4i−4i00000000000000002-2−2i2i-222i−2i0000000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i-44-444i−4i4i−4i0000000000000000-222i−2i2-2−2i2i0000000000000000000000000000000000000000
χ734-4-444i−4i−4i4i4i−4i−4i4i-444-400000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ0000000000000000
χ744-4-444i−4i−4i4i4i−4i−4i4i-444-40000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ0000000000000000
χ754-4-444i−4i−4i4i−4i4i4i−4i4-4-4400000000000000000000000000000000000000002ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ30000000000000000
χ764-4-444i−4i−4i4i−4i4i4i−4i4-4-440000000000000000000000000000000000000000−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ30000000000000000
χ774-4-44−4i4i4i−4i4i−4i−4i4i4-4-4400000000000000000000000000000000000000002ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ0000000000000000
χ784-4-44−4i4i4i−4i4i−4i−4i4i4-4-440000000000000000000000000000000000000000−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ0000000000000000
χ794-4-44−4i4i4i−4i−4i4i4i−4i-444-400000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ30000000000000000
χ804-4-44−4i4i4i−4i−4i4i4i−4i-444-40000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ30000000000000000

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