Finite Group Databasebeta

← Group #10826077

Character table — Group #10826077

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12442223444666888888881212121266121224242424242424244444448888881212121212121212121212122424242424242424242424242244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ611111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111
χ711111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-11-1-1-11111-1-1-1-111
χ811111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1111-1-1-1-11111-1-1
χ911111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-111-1-111
χ1011111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-111-1-1
χ1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111-1-11111-1-1
χ1211111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-111-1-1-1-111
χ1311111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ1411111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ1511111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1611111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ172222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1111111110000000000000000
χ192222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-222-2-21111-1-1-1-111111111-1-1-1-111110000000000000000
χ202222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-22211111111-1-1-1-111111111-1-1-1-10000000000000000
χ212222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000
χ222222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-10000000000000000
χ232222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222-2-222-2-2221111-1-1-1-11111-1-1-1-11111-1-1-1-10000000000000000
χ242222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2-2-2222222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ2522222-2-222-2-22222222-2-2-2-22222-2-2-2-22222-2-2-2-22-200002-2000022-2-20000000022-2-2000000000000000000000000
χ2622222-2-222-2-22222222-2-2-2-22222-2-2-2-22222-2-2-2-2-220000-220000-2-22200000000-2-222000000000000000000000000
χ2722222-2-222-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-222222-20000-22000022-2-200000000-2-222000000000000000000000000
χ2822222-2-222-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2200002-20000-2-2220000000022-2-2000000000000000000000000
χ2922222-2-2-12-2-2-1-1-12222-2-2-2-2-1-1-1-11111-1-1-1-111112-200002-20000-1-111−i3−i3i3i3−i3−i3i3i3-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222-2-2-12-2-2-1-1-12222-2-2-2-2-1-1-1-11111-1-1-1-111112-200002-20000-1-111i3i3−i3−i3i3i3−i3−i3-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222-2-2-12-2-2-1-1-12222-2-2-2-2-1-1-1-11111-1-1-1-11111-220000-22000011-1-1−i3−i3i3i3i3i3−i3−i311-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ3222222-2-2-12-2-2-1-1-12222-2-2-2-2-1-1-1-11111-1-1-1-11111-220000-22000011-1-1i3i3−i3−i3−i3−i3i3i311-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ3322222-2-2-12-2-2-1-1-1-2-2-2-22222-1-1-1-111111111-1-1-1-12-20000-220000-1-111−i3−i3i3i3−i3−i3i3i311-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ3422222-2-2-12-2-2-1-1-1-2-2-2-22222-1-1-1-111111111-1-1-1-12-20000-220000-1-111i3i3−i3−i3i3i3−i3−i311-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ3522222-2-2-12-2-2-1-1-1-2-2-2-22222-1-1-1-111111111-1-1-1-1-2200002-2000011-1-1−i3−i3i3i3i3i3−i3−i3-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222-2-2-12-2-2-1-1-1-2-2-2-22222-1-1-1-111111111-1-1-1-1-2200002-2000011-1-1i3i3−i3−i3−i3−i3i3i3-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ372222-22-22-22-22-2-222-2-222-2-222-2-22-22-222-2-222-2-20000000000000000000000000000000000000000002i−2i0000002i−2i
χ382222-22-22-22-22-2-222-2-222-2-222-2-22-22-222-2-222-2-2000000000000000000000000000000000000000000−2i2i000000−2i2i
χ392222-22-22-22-22-2-2-2-222-2-22222-2-22-22-2-2-222-2-2220000000000000000000000000000000000000000002i−2i000000−2i2i
χ402222-22-22-22-22-2-2-2-222-2-22222-2-22-22-2-2-222-2-222000000000000000000000000000000000000000000−2i2i0000002i−2i
χ412222-2-222-2-222-2-222-2-2-2-22222-2-2-22-2222-2-2-2-22200000000000000000000000000000000000000002i−2i0000002i−2i00
χ422222-2-222-2-222-2-222-2-2-2-22222-2-2-22-2222-2-2-2-2220000000000000000000000000000000000000000−2i2i000000−2i2i00
χ432222-2-222-2-222-2-2-2-22222-2-222-2-2-22-22-2-22222-2-200000000000000000000000000000000000000002i−2i000000−2i2i00
χ442222-2-222-2-222-2-2-2-22222-2-222-2-2-22-22-2-22222-2-20000000000000000000000000000000000000000−2i2i0000002i−2i00
χ4522-2-22222-2-2-22222i−2i2i−2i2i−2i2i−2i-2-2-2-222-2-22i−2i2i−2i2i−2i2i−2i002-200002i−2i0000002-22-2000000002i−2i2i−2i00000000000000000000
χ4622-2-22222-2-2-22222i−2i2i−2i2i−2i2i−2i-2-2-2-222-2-22i−2i2i−2i2i−2i2i−2i00-220000−2i2i000000-22-2200000000−2i2i−2i2i00000000000000000000
χ4722-2-22222-2-2-2222−2i2i−2i2i−2i2i−2i2i-2-2-2-222-2-2−2i2i−2i2i−2i2i−2i2i002-20000−2i2i0000002-22-200000000−2i2i−2i2i00000000000000000000
χ4822-2-22222-2-2-2222−2i2i−2i2i−2i2i−2i2i-2-2-2-222-2-2−2i2i−2i2i−2i2i−2i2i00-2200002i−2i000000-22-22000000002i−2i2i−2i00000000000000000000
χ4922-2-2222-1-2-2-2-1-1-12i−2i2i−2i2i−2i2i−2i1111-1-111−ii−ii−ii−ii002-200002i−2i00−i3i3−i3i3-11-11−i3i3−i3i33−33−3−ii−ii3−33−30000000000000000
χ5022-2-2222-1-2-2-2-1-1-12i−2i2i−2i2i−2i2i−2i1111-1-111−ii−ii−ii−ii002-200002i−2i00i3−i3i3−i3-11-11i3−i3i3−i3−33−33−ii−ii−33−330000000000000000
χ5122-2-2222-1-2-2-2-1-1-12i−2i2i−2i2i−2i2i−2i1111-1-111−ii−ii−ii−ii00-220000−2i2i00−i3i3−i3i31-11-1i3−i3i3−i33−33−3i−ii−i−33−330000000000000000
χ5222-2-2222-1-2-2-2-1-1-12i−2i2i−2i2i−2i2i−2i1111-1-111−ii−ii−ii−ii00-220000−2i2i00i3−i3i3−i31-11-1−i3i3−i3i3−33−33i−ii−i3−33−30000000000000000
χ5322-2-2222-1-2-2-2-1-1-1−2i2i−2i2i−2i2i−2i2i1111-1-111i−ii−ii−ii−i002-20000−2i2i00−i3i3−i3i3-11-11−i3i3−i3i3−33−33i−ii−i−33−330000000000000000
χ5422-2-2222-1-2-2-2-1-1-1−2i2i−2i2i−2i2i−2i2i1111-1-111i−ii−ii−ii−i002-20000−2i2i00i3−i3i3−i3-11-11i3−i3i3−i33−33−3i−ii−i3−33−30000000000000000
χ5522-2-2222-1-2-2-2-1-1-1−2i2i−2i2i−2i2i−2i2i1111-1-111i−ii−ii−ii−i00-2200002i−2i00−i3i3−i3i31-11-1i3−i3i3−i3−33−33−ii−ii3−33−30000000000000000
χ5622-2-2222-1-2-2-2-1-1-1−2i2i−2i2i−2i2i−2i2i1111-1-111i−ii−ii−ii−i00-2200002i−2i00i3−i3i3−i31-11-1−i3i3−i3i33−33−3−ii−ii−33−330000000000000000
χ5722-2-22-2-22-2222222i−2i2i−2i−2i2i−2i2i-2-2-2-2-2-2222i−2i2i−2i−2i2i−2i2i00002-200002i−2i000000002-2-22000000002i−2i−2i2i0000000000000000
χ5822-2-22-2-22-2222222i−2i2i−2i−2i2i−2i2i-2-2-2-2-2-2222i−2i2i−2i−2i2i−2i2i0000-220000−2i2i00000000-222-200000000−2i2i2i−2i0000000000000000
χ5922-2-22-2-22-222222−2i2i−2i2i2i−2i2i−2i-2-2-2-2-2-222−2i2i−2i2i2i−2i2i−2i00002-20000−2i2i000000002-2-2200000000−2i2i2i−2i0000000000000000
χ6022-2-22-2-22-222222−2i2i−2i2i2i−2i2i−2i-2-2-2-2-2-222−2i2i−2i2i2i−2i2i−2i0000-2200002i−2i00000000-222-2000000002i−2i−2i2i0000000000000000
χ6122-2-22-2-2-1-222-1-1-12i−2i2i−2i−2i2i−2i2i111111-1-1−ii−iii−ii−i00002-200002i−2i−i3i3i3−i3−i3i3i3−i3-111-13−3−333−3−33−iii−i0000000000000000
χ6222-2-22-2-2-1-222-1-1-12i−2i2i−2i−2i2i−2i2i111111-1-1−ii−iii−ii−i00002-200002i−2ii3−i3−i3i3i3−i3−i3i3-111-1−333−3−333−3−iii−i0000000000000000
χ6322-2-22-2-2-1-222-1-1-12i−2i2i−2i−2i2i−2i2i111111-1-1−ii−iii−ii−i0000-220000−2i2i−i3i3i3−i3i3−i3−i3i31-1-113−3−33−333−3i−i−ii0000000000000000
χ6422-2-22-2-2-1-222-1-1-12i−2i2i−2i−2i2i−2i2i111111-1-1−ii−iii−ii−i0000-220000−2i2ii3−i3−i3i3−i3i3i3−i31-1-11−333−33−3−33i−i−ii0000000000000000
χ6522-2-22-2-2-1-222-1-1-1−2i2i−2i2i2i−2i2i−2i111111-1-1i−ii−i−ii−ii00002-20000−2i2i−i3i3i3−i3−i3i3i3−i3-111-1−333−3−333−3i−i−ii0000000000000000
χ6622-2-22-2-2-1-222-1-1-1−2i2i−2i2i2i−2i2i−2i111111-1-1i−ii−i−ii−ii00002-20000−2i2ii3−i3−i3i3i3−i3−i3i3-111-13−3−333−3−33i−i−ii0000000000000000
χ6722-2-22-2-2-1-222-1-1-1−2i2i−2i2i2i−2i2i−2i111111-1-1i−ii−i−ii−ii0000-2200002i−2i−i3i3i3−i3i3−i3−i3i31-1-11−333−33−3−33−iii−i0000000000000000
χ6822-2-22-2-2-1-222-1-1-1−2i2i−2i2i2i−2i2i−2i111111-1-1i−ii−i−ii−ii0000-2200002i−2ii3−i3−i3i3−i3i3i3−i31-1-113−3−33−333−3−iii−i0000000000000000
χ6922-2-2-22-222-222-2-22i−2i−2i2i2i−2i−2i2i-2-2222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000020-20000002i−2i0000
χ7022-2-2-22-222-222-2-22i−2i−2i2i2i−2i−2i2i-2-2222-2-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000-202000000−2i2i0000
χ7122-2-2-22-222-222-2-2−2i2i2i−2i−2i2i2i−2i-2-2222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000020-2000000−2i2i0000
χ7222-2-2-22-222-222-2-2−2i2i2i−2i−2i2i2i−2i-2-2222-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000-2020000002i−2i0000
χ7322-2-2-2-22222-22-2-22i−2i−2i2i−2i2i2i−2i-2-222-222-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000020-2000002i−2i000000
χ7422-2-2-2-22222-22-2-22i−2i−2i2i−2i2i2i−2i-2-222-222-22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000-20200000−2i2i000000
χ7522-2-2-2-22222-22-2-2−2i2i2i−2i2i−2i−2i2i-2-222-222-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000020-200000−2i2i000000
χ7622-2-2-2-22222-22-2-2−2i2i2i−2i2i−2i−2i2i-2-222-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000-202000002i−2i000000
χ774444-44-4-2-44-4-22244-4-444-4-4-2-222-22-22-2-222-2-2220000000000000000000000000000000000000000000000000000
χ784444-44-4-2-44-4-222-4-444-4-444-2-222-22-2222-2-222-2-20000000000000000000000000000000000000000000000000000
χ794444-4-44-2-4-44-22244-4-4-4-444-2-2222-22-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-44-2-4-44-222-4-44444-4-4-2-2222-22-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ8144-4-4-44-4-24-44-2224i−4i−4i4i4i−4i−4i4i22-2-2-222-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ8244-4-4-44-4-24-44-222−4i4i4i−4i−4i4i4i−4i22-2-2-222-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8344-4-4-4-44-244-4-2224i−4i−4i4i−4i4i4i−4i22-2-22-2-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8444-4-4-4-44-244-4-222−4i4i4i−4i4i−4i−4i4i22-2-22-2-222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ858-88i−8i0008000-800000000008i−8i000000000000000000000000000000000000000000000000000000000000000000
χ868-88i−8i000-40004−4i34i300000000−4i4i43−430000000000000000000000000000000000000000000000000000000000000000
χ878-88i−8i000-400044i3−4i300000000−4i4i−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8−8i8i0008000-80000000000−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ898-8−8i8i000-40004−4i34i3000000004i−4i−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8−8i8i000-400044i3−4i3000000004i−4i43−430000000000000000000000000000000000000000000000000000000000000000

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