Finite Group Databasebeta

← Group #116292

Character table — Group #116292

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888444444448888
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
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
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
χ91-11-1-111-11-1-111111-1-1-1-1-111-1111-1-1-1ii−i−iii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i
χ101-11-1-111-11-1-111111-1-1-1-1-111-1111-1-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−i−iii
χ111-11-1-111-11-1-111111-1-1-1-1-111-1111-1-1-1ii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−iii
χ121-11-1-111-11-1-111111-1-1-1-1-111-1111-1-1-1ii−i−i−i−iiiii−i−i−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1-1-111ii−i−i
χ131-11-1-111-11-1-111111-1-1-1-1-111-1111-1-1-1−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiii-1-111-1-111ii−i−i
χ141-11-1-111-11-1-111111-1-1-1-1-111-1111-1-1-1−i−iiiii−i−i−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1-1-111−i−iii
χ151-11-1-111-11-1-111111-1-1-1-1-111-1111-1-1-1−i−iii−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii
χ161-11-1-111-11-1-111111-1-1-1-1-111-1111-1-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-1-11111-1-1ii−i−i
χ172222222222222222222-2-2-2-22-2-2-2-2-2-222220000-2-2-2-200000000000000000000000000000000
χ182222222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-22222-22-2-22-2-20000000000000000000000000000000000002-22-20000
χ20222222222222-2-2-2-2-2-2-22222-22-2-22-2-2000000000000000000000000000000000000-22-220000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-222000022220000-2-2-2-20000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-2220000-2-2-2-2000022220000000000000000000000000000
χ2322222222-2-2-2-222-2-222-22222-2-22-2-2-2200000000000000000000000022-2-222-2-2000000000000
χ2422222222-2-2-2-222-2-222-22222-2-22-2-2-22000000000000000000000000-2-222-2-222000000000000
χ2522222222-2-2-2-222-2-222-2-2-2-2-2-22-2222-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-2-2-22-2222-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2722222222-2-2-2-2-2-222-2-2222222-2-22-22-200000000000000000000000000000000000000002-22-2
χ2822222222-2-2-2-2-2-222-2-2222222-2-22-22-20000000000000000000000000000000000000000-22-22
χ2922222222-2-2-2-2-2-222-2-22-2-2-2-2222-22-22000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-2-2-222-2-22-2-2-2-2222-22-2200000000000000000000000000000000-22-2200000000
χ312222-2-2-2-222-2-22-22-22-220000-20000002-22-20000000000002−22−22−22−22−22−22−22−2000000000000
χ322222-2-2-2-222-2-22-22-22-220000-20000002-22-2000000000000−22−22−22−22−22−22−22−22000000000000
χ332222-2-2-2-222-2-22-22-22-220000-2000000-22-220000000000002−22−22−22−2−22−22−22−22000000000000
χ342222-2-2-2-222-2-22-22-22-220000-2000000-22-22000000000000−22−22−22−222−22−22−22−2000000000000
χ352222-2-2-2-2-2-2222-2-222-2-200002000000000000002i−2i2i−2i0000i2−i2−i2i2i2−i2−i2i22−2−222−2−22000000000000
χ362222-2-2-2-2-2-2222-2-222-2-200002000000000000002i−2i2i−2i0000−i2i2i2−i2−i2i2i2−i2−222−2−222−2000000000000
χ372222-2-2-2-2-2-2222-2-222-2-20000200000000000000−2i2i−2i2i0000i2−i2−i2i2i2−i2−i2i2−222−2−222−2000000000000
χ382222-2-2-2-2-2-2222-2-222-2-20000200000000000000−2i2i−2i2i0000−i2i2i2−i2−i2i2i2−i22−2−222−2−22000000000000
χ392-22-22-2-222-22-22-22-2-22-2000020000002i−2i−2i2i0000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ402-22-22-2-222-22-22-22-2-22-2000020000002i−2i−2i2i000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ412-22-22-2-222-22-22-22-2-22-200002000000−2i2i2i−2i0000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ422-22-22-2-222-22-22-22-2-22-200002000000−2i2i2i−2i000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ432-22-22-2-22-22-222-2-22-2220000-2000000000000002-2-220000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ442-22-22-2-22-22-222-2-22-2220000-2000000000000002-2-220000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ452-22-22-2-22-22-222-2-22-2220000-200000000000000-222-20000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ462-22-22-2-22-22-222-2-22-2220000-200000000000000-222-20000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ472-22-2-222-22-2-222222-2-2-222-2-2-2-2-2-22222i2i−2i−2i0000−2i−2i2i2i00000000000000000000000000000000
χ482-22-2-222-22-2-222222-2-2-222-2-2-2-2-2-2222−2i−2i2i2i00002i2i−2i−2i00000000000000000000000000000000
χ492-22-2-222-22-2-22-2-2-2-222222-2-22-2222-2-200002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000
χ502-22-2-222-22-2-22-2-2-2-222222-2-22-2222-2-20000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000
χ512-22-2-222-22-2-22-2-2-2-2222-2-22222-2-2-2220000000000000000000000000000000000002-2-220000
χ522-22-2-222-22-2-22-2-2-2-2222-2-22222-2-2-222000000000000000000000000000000000000-222-20000
χ532-22-2-222-2-222-222-2-2-2-2222-2-222-22-2-2200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ542-22-2-222-2-222-222-2-2-2-2222-2-222-22-2-220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ552-22-2-222-2-222-222-2-2-2-22-2-2222-22-222-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ562-22-2-222-2-222-222-2-2-2-22-2-2222-22-222-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ572-22-2-222-2-222-2-2-22222-222-2-2-222-2-22-2000000000000000000000000000000002-2-2200000000
χ582-22-2-222-2-222-2-2-22222-222-2-2-222-2-22-200000000000000000000000000000000-222-200000000
χ592-22-2-222-2-222-2-2-22222-2-2-222-2-2-222-2200000000000000000000000000000000000000002i−2i−2i2i
χ602-22-2-222-2-222-2-2-22222-2-2-222-2-2-222-220000000000000000000000000000000000000000−2i2i2i−2i
χ614444-4-4-4-444-4-4-44-44-44-40000400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-444-444-4-4440000-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-44000000000004i−4i4i−4i000000000002i−2i2i−2i00002-22-20000000000000000000000000000
χ6444-4-4-44-44000000000004i−4i4i−4i00000000000−2i2i−2i2i0000-22-220000000000000000000000000000
χ6544-4-4-44-4400000000000−4i4i−4i4i000000000002i−2i2i−2i0000-22-220000000000000000000000000000
χ6644-4-4-44-4400000000000−4i4i−4i4i00000000000−2i2i−2i2i00002-22-20000000000000000000000000000
χ674-44-44-4-444-44-4-44-444-440000-400000000000000000000000000000000000000000000000000
χ684-44-44-4-44-44-44-444-44-4-40000400000000000000000000000000000000000000000000000000
χ694-4-4444-4-4000000000004i−4i−4i4i000000000002-2-2200002i−2i−2i2i0000000000000000000000000000
χ704-4-4444-4-4000000000004i−4i−4i4i00000000000-222-20000−2i2i2i−2i0000000000000000000000000000
χ714-4-4444-4-400000000000−4i4i4i−4i000000000002-2-220000−2i2i2i−2i0000000000000000000000000000
χ724-4-4444-4-400000000000−4i4i4i−4i00000000000-222-200002i−2i−2i2i0000000000000000000000000000
χ7388-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000

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