Finite Group Databasebeta

← Group #112976

Character table — Group #112976

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444422224444444444448888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ5111111111111111111111111111111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ91-1-1-1-111111-1-1111111-1-1-1-1-1-111-1-1-1111-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i
χ101-1-1-1-111111-1-1111111-1-1-1-1-1-111-1-1-1111-1-1iiii−i−i−i−i11-1-1−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i−i−iii
χ111-1-1-1-111111-1-1111111-1-1-1-1-1-111-1-1-1111-1-1−i−i−i−iiiii11-1-1iiii−i−i−i−i-1-1-1-11111-1-111−i−iiiii−i−i
χ121-1-1-1-111111-1-1111111-1-1-1-1-1-111-1-1-1111-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii
χ131-1-1-1-111111-1-1111111-1-1-1-1-1-111-1-1-11-1-111iiii−i−i−i−i-1-111iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii−i−iii
χ141-1-1-1-111111-1-1111111-1-1-1-1-1-111-1-1-11-1-111iiii−i−i−i−i-1-111−i−i−i−iiiii-1-1-1-1111111-1-1−i−iiiii−i−i
χ151-1-1-1-111111-1-1111111-1-1-1-1-1-111-1-1-11-1-111−i−i−i−iiiii-1-111iiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i−i−iii
χ161-1-1-1-111111-1-1111111-1-1-1-1-1-111-1-1-11-1-111−i−i−i−iiiii-1-111−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−iii−i−i
χ172222222222222222-2-2222-2-22-2-2-2-2-2-2000022-2-222-2-200000000000000000000000000000000
χ182222222222222222-2-2222-2-22-2-2-2-2-2-20000-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-222-2-2-222-22-22-2-2-20000000000000000000000000000000000002-22-20000
χ20222222222222-2-2-2-222-2-2-222-22-22-2-2-2000000000000000000000000000000000000-22-220000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-2222222200000000-2-2-2-20000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-2222-2-2-2-20000000022220000000000000000000000000000
χ2322222222-2-2-2-222-2-22222-222-2-2-2-22-2200000000000000000000000022-2-222-2-2000000000000
χ2422222222-2-2-2-222-2-22222-222-2-2-2-22-22000000000000000000000000-2-222-2-222000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-2-2-2222-22-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2-2-2222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2722222222-2-2-2-2-2-22222-2-22222-22-2-22-200000000000000000000000000000000000000002-22-2
χ2822222222-2-2-2-2-2-22222-2-22222-22-2-22-20000000000000000000000000000000000000000-22-22
χ2922222222-2-2-2-2-2-222-2-2-2-22-2-222-222-22000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-2-2-222-2-2-2-22-2-222-222-2200000000000000000000000000000000-22-2200000000
χ3122-22-22-2-22-22-22-22-2002-2-20020000000000002i−2i002i−2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ3222-22-22-2-22-22-22-22-2002-2-20020000000000002i−2i002i−2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ3322-22-22-2-22-22-22-22-2002-2-2002000000000000−2i2i00−2i2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ3422-22-22-2-22-22-22-22-2002-2-2002000000000000−2i2i00−2i2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ3522-22-22-2-2-22-222-2-22002-2200-200000000002-2002-2000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ3622-22-22-2-2-22-222-2-22002-2200-200000000002-2002-2000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ3722-22-22-2-2-22-222-2-22002-2200-20000000000-2200-22000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ3822-22-22-2-2-22-222-2-22002-2200-20000000000-2200-22000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ392-22-222-2-22-2-222-22-200-22200-20000000000002-200-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ402-22-222-2-22-2-222-22-200-22200-20000000000002-200-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ412-22-222-2-22-2-222-22-200-22200-2000000000000-22002-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ422-22-222-2-22-2-222-22-200-22200-2000000000000-22002-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ432-22-222-2-2-222-22-2-2200-22-200200000000002i−2i00−2i2i0000002−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ442-22-222-2-2-222-22-2-2200-22-200200000000002i−2i00−2i2i000000−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ452-22-222-2-2-222-22-2-2200-22-20020000000000−2i2i002i−2i0000002−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ462-22-222-2-2-222-22-2-2200-22-20020000000000−2i2i002i−2i000000−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ472-2-2-2-222222-2-22222-2-2-2-2-222-2-2-2222-200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ482-2-2-2-222222-2-22222-2-2-2-2-222-2-2-2222-20000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ492-2-2-2-222222-2-2-2-2-2-222222-2-222-2-222-20000000000000000000000000000000000002i−2i−2i2i0000
χ502-2-2-2-222222-2-2-2-2-2-222222-2-222-2-222-2000000000000000000000000000000000000−2i2i2i−2i0000
χ512-2-2-2-222222-2-2-2-2-2-2-2-2222222-222-2-2222-2-200000000-2-2220000000000000000000000000000
χ522-2-2-2-222222-2-2-2-2-2-2-2-2222222-222-2-22-2-2220000000022-2-20000000000000000000000000000
χ532-2-2-2-2222-2-22222-2-222-2-22-2-22-2-22-22200000000000000000000000022-2-2-2-222000000000000
χ542-2-2-2-2222-2-22222-2-222-2-22-2-22-2-22-222000000000000000000000000-2-22222-2-2000000000000
χ552-2-2-2-2222-2-22222-2-2-2-2-2-2222222-22-2-2000000000000000022-2-2-2-22200000000000000000000
χ562-2-2-2-2222-2-22222-2-2-2-2-2-2222222-22-2-20000000000000000-2-22222-2-200000000000000000000
χ572-2-2-2-2222-2-222-2-2222222-2-2-2-2-2222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ582-2-2-2-2222-2-222-2-2222222-2-2-2-2-2222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ592-2-2-2-2222-2-222-2-222-2-222-222-22-2-2-222000000000000000000000000000000002-2-2200000000
χ602-2-2-2-2222-2-222-2-222-2-222-222-22-2-2-22200000000000000000000000000000000-222-200000000
χ6144-44-44-4-44-44-4-44-4400-44400-400000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-44-44-444-400-44-400400000000000000000000000000000000000000000000000000
χ6344-4-44-44-4000000004i−4i0004i−4i00000002-22-2000000002i−2i2i−2i0000000000000000000000000000
χ6444-4-44-44-4000000004i−4i0004i−4i0000000-22-2200000000−2i2i−2i2i0000000000000000000000000000
χ6544-4-44-44-400000000−4i4i000−4i4i00000002-22-200000000−2i2i−2i2i0000000000000000000000000000
χ6644-4-44-44-400000000−4i4i000−4i4i0000000-22-22000000002i−2i2i−2i0000000000000000000000000000
χ674-444-4-44-4000000004i−4i000−4i4i00000002-2-22000000002i−2i−2i2i0000000000000000000000000000
χ684-444-4-44-4000000004i−4i000−4i4i0000000-222-200000000−2i2i2i−2i0000000000000000000000000000
χ694-444-4-44-400000000−4i4i0004i−4i00000002-2-2200000000−2i2i2i−2i0000000000000000000000000000
χ704-444-4-44-400000000−4i4i0004i−4i0000000-222-2000000002i−2i−2i2i0000000000000000000000000000
χ714-44-444-4-44-4-44-44-44004-4-400400000000000000000000000000000000000000000000000000
χ724-44-444-4-4-444-4-444-4004-4400-400000000000000000000000000000000000000000000000000
χ73888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).