Finite Group Databasebeta

← Group #111846

Character table — Group #111846

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444422224444444444448888888888888888224444448888
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
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
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
χ91-1-11-1-11111-1-111111-1-1-1-1-1-1111-11-1-111-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−i11-1-1
χ101-1-11-1-11111-1-111111-1-1-1-1-1-1111-11-1-111-1-1iiii−i−i−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11ii−i−i-1-111
χ111-1-11-1-11111-1-111111-1-1-1-1-1-1111-11-1-111-1-1−i−i−i−iiiii11-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−i−iii-1-111
χ121-1-11-1-11111-1-111111-1-1-1-1-1-1111-11-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii11-1-1
χ131-1-11-1-11111-1-111111-1-1-1-1-1-1111-11-1-1-1-111iiii−i−i−i−i-1-111iiii−i−i−i−i−i−i−i−iiiii-11-11−i−iii11-1-1
χ141-1-11-1-11111-1-111111-1-1-1-1-1-1111-11-1-1-1-111iiii−i−i−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i1-11-1−i−iii-1-111
χ151-1-11-1-11111-1-111111-1-1-1-1-1-1111-11-1-1-1-111−i−i−i−iiiii-1-111iiii−i−i−i−i−i−i−i−iiiii1-11-1ii−i−i-1-111
χ161-1-11-1-11111-1-111111-1-1-1-1-1-1111-11-1-1-1-111−i−i−i−iiiii-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-11ii−i−i11-1-1
χ17222222222222222-2-22222-2-22-2-2-2-2-2-2222200000000-2-2-2-20000000000000000000000000000
χ18222222222222222-2-22222-2-22-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000
χ19222222222222-2-2-222-2-2-2-222-2-2-2-222-20000000000000000000000000000000000002-22-20000
χ20222222222222-2-2-222-2-2-2-222-2-2-2-222-2000000000000000000000000000000000000-22-220000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-22000022-2-222-2-200000000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-220000-2-222-2-22200000000000000000000000000000000
χ2322222222-2-2-2-222-22222-2-222-22-2-2-2-2200000000000000000000000022-2-222-2-2000000000000
χ2422222222-2-2-2-222-22222-2-222-22-2-2-2-22000000000000000000000000-2-222-2-222000000000000
χ2522222222-2-2-2-222-2-2-222-2-2-2-2-2-22222-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622222222-2-2-2-222-2-2-222-2-2-2-2-2-22222-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2722222222-2-2-2-2-2-2222-2-222222-222-2-2-200000000000000000000000000000000000000002-22-2
χ2822222222-2-2-2-2-2-2222-2-222222-222-2-2-20000000000000000000000000000000000000000-22-22
χ2922222222-2-2-2-2-2-22-2-2-2-222-2-222-2-22220000000000000000000000000000000022-2-200000000
χ3022222222-2-2-2-2-2-22-2-2-2-222-2-222-2-222200000000000000000000000000000000-2-22200000000
χ31222-2-2-22-22-22-22-2-2002-22-20020000002-22-2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ32222-2-2-22-22-22-22-2-2002-22-20020000002-22-2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ33222-2-2-22-22-22-22-2-2002-22-2002000000-22-22000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ34222-2-2-22-22-22-22-2-2002-22-2002000000-22-22000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ35222-2-2-22-2-22-222-22002-2-2200-20000000000000000002i−2i2i−2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ36222-2-2-22-2-22-222-22002-2-2200-20000000000000000002i−2i2i−2i−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ37222-2-2-22-2-22-222-22002-2-2200-2000000000000000000−2i2i−2i2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ38222-2-2-22-2-22-222-22002-2-2200-2000000000000000000−2i2i−2i2i−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ392-2-22-2-22222-2-2222-2-2-2-2-2-2222-2-22-22222-2-200000000-2-2220000000000000000000000000000
χ402-2-22-2-22222-2-2222-2-2-2-2-2-2222-2-22-222-2-2220000000022-2-20000000000000000000000000000
χ412-2-22-2-22222-2-2-2-2-2222222-2-2-2-2-222-220000000000000000000000000000000000002i−2i−2i2i0000
χ422-2-22-2-22222-2-2-2-2-2222222-2-2-2-2-222-22000000000000000000000000000000000000−2i2i2i−2i0000
χ432-2-22-2-22222-2-2-2-2-2-2-2222222-222-2-22-200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ442-2-22-2-22222-2-2-2-2-2-2-2222222-222-2-22-20000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ452-2-22-2-222-2-22222-222-2-222-2-2-22-22-22-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ462-2-22-2-222-2-22222-222-2-222-2-2-22-22-22-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ472-2-22-2-222-2-22222-2-2-2-2-22222-2-22-22-22000000000000000022-2-2-2-22200000000000000000000
χ482-2-22-2-222-2-22222-2-2-2-2-22222-2-22-22-220000000000000000-2-22222-2-200000000000000000000
χ492-2-22-2-222-2-222-2-222222-2-2-2-22-22-2-22200000000000000000000000000000000000000002-2-22
χ502-2-22-2-222-2-222-2-222222-2-2-2-22-22-2-2220000000000000000000000000000000000000000-222-2
χ512-2-22-2-222-2-222-2-22-2-222-2-22222-222-2-2000000000000000000000000000000002-2-2200000000
χ522-2-22-2-222-2-222-2-22-2-222-2-22222-222-2-200000000000000000000000000000000-222-200000000
χ532-2-2-2222-22-2-222-2-200-22-220020000002-2-220000000000002−22−2−22−222−22−2−22−22000000000000
χ542-2-2-2222-22-2-222-2-200-22-220020000002-2-22000000000000−22−222−22−2−22−222−22−2000000000000
χ552-2-2-2222-22-2-222-2-200-22-22002000000-222-20000000000002−22−2−22−22−22−222−22−2000000000000
χ562-2-2-2222-22-2-222-2-200-22-22002000000-222-2000000000000−22−222−22−22−22−2−22−22000000000000
χ572-2-2-2222-2-222-22-2200-222-200-20000000000000000002i−2i−2i2ii2−i2−i2i2−i2i2i2−i2−222−22−2−22000000000000
χ582-2-2-2222-2-222-22-2200-222-200-20000000000000000002i−2i−2i2i−i2i2i2−i2i2−i2−i2i22−2−22−222−2000000000000
χ592-2-2-2222-2-222-22-2200-222-200-2000000000000000000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i22−2−22−222−2000000000000
χ602-2-2-2222-2-222-22-2200-222-200-2000000000000000000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i2−222−22−2−22000000000000
χ61444-4-4-44-44-44-4-44400-44-4400-400000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-44-44-44-400-444-400400000000000000000000000000000000000000000000000000
χ6344-444-4-4-400000004i−4i00004i−4i000000000002-22i−2i2-22i−2i00000000000000000000000000000000
χ6444-444-4-4-400000004i−4i00004i−4i00000000000-22−2i2i-22−2i2i00000000000000000000000000000000
χ6544-444-4-4-40000000−4i4i0000−4i4i000000000002-2−2i2i2-2−2i2i00000000000000000000000000000000
χ6644-444-4-4-40000000−4i4i0000−4i4i00000000000-222i−2i-222i−2i00000000000000000000000000000000
χ674-444-44-4-400000004i−4i0000−4i4i000000000002i−2i-22−2i2i2-200000000000000000000000000000000
χ684-444-44-4-400000004i−4i0000−4i4i00000000000−2i2i2-22i−2i-2200000000000000000000000000000000
χ694-444-44-4-40000000−4i4i00004i−4i000000000002i−2i2-2−2i2i-2200000000000000000000000000000000
χ704-444-44-4-40000000−4i4i00004i−4i00000000000−2i2i-222i−2i2-200000000000000000000000000000000
χ714-4-4-4444-44-4-44-444004-44-400-400000000000000000000000000000000000000000000000000
χ724-4-4-4444-4-444-4-44-4004-4-4400400000000000000000000000000000000000000000000000000
χ7388-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ748-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000

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