Finite Group Databasebeta

← Group #10829370

Character table — Group #10829370

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order1222222222344446664444446666661212121212121212121212122224444444666666121212121212121212121212121212122222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-111-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ6111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-111-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-111
χ8111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ911111111111-1-1-1-111111-1-1111111111111-1-1-1-11111-11-1-11-11-11-1-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-111-1-11-11-1
χ1011111111111-1-1-1-111111-1-1111111111111-1-1-1-11111-11-1-11-11-11-1-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-111-11-11
χ1111111111111-1-1-1-111111-1-1111111111111-1-1-1-11111-1-11-1-11-11-11-1-1-1-111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-1-11-11
χ1211111111111-1-1-1-111111-1-1111111111111-1-1-1-11111-1-11-1-11-11-11-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1111-11-1
χ1311111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ1411111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-111-1
χ1511111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-111-11-111-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-111-1
χ1611111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-111-11-111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-11-1-11
χ172222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-22-2-2-2-2-2-2-1-11111-1-111111111-1-111110000000000000000
χ192222222222-12222-1-1-1-2-222-2-2-1-1-1-1-1-11111-1-1-1-11111-222-222-2-2-2-211-1-1-1-111-1-1-1-11111-1-111110000000000000000
χ202222222222-12222-1-1-1-2-222-2-2-1-1-1-1-1-11111-1-1-1-11111-2-2-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-10000000000000000
χ212222222222-1-2-2-2-2-1-1-122-2-222-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-22-2-22-22-22-211-1-11111-1-111-1-11111-1-1110000000000000000
χ222222222222-1-2-2-2-2-1-1-122-2-222-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-2-22-2-22-22-221111-1-11111-1-111-1-11111-1-10000000000000000
χ232222222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111122-222-2-22-22-1-1-1-111-1-1-1-11111-1-11111-1-10000000000000000
χ242222222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1-1-11111111111112-222-222-22-2-1-111-1-1-1-111-1-1-1-11111-1-1110000000000000000
χ2522222-2-2-22-2222-2-2222002-20022-2-2-2-2000022-2-2000000000022-2-200000000000022222-2-2-2-2-20000000000000000
χ2622222-2-2-22-2222-2-2222002-20022-2-2-2-2000022-2-20000000000-2-222000000000000-2-2-2-22-222220000000000000000
χ2722222-2-2-22-22-2-22222200-220022-2-2-2-20000-2-22200000000002-2-2200000000000022-2-2-22-2-2220000000000000000
χ2822222-2-2-22-22-2-22222200-220022-2-2-2-20000-2-2220000000000-222-2000000000000-2-222-2222-2-20000000000000000
χ2922222-2-2-22-2-122-2-2-1-1-1002-200-1-11111−i3−i3i3i3-1-111−i3−i3i3i300000022-2-2−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3-1-1-1-1-1111110000000000000000
χ3022222-2-2-22-2-122-2-2-1-1-1002-200-1-11111−i3−i3i3i3-1-111−i3−i3i3i3000000-2-222−i3i3i3−i3i3−i3−i3i3i3−i3i3−i31111-11-1-1-1-10000000000000000
χ3122222-2-2-22-2-122-2-2-1-1-1002-200-1-11111i3i3−i3−i3-1-111i3i3−i3−i300000022-2-2i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3-1-1-1-1-1111110000000000000000
χ3222222-2-2-22-2-122-2-2-1-1-1002-200-1-11111i3i3−i3−i3-1-111i3i3−i3−i3000000-2-222i3−i3−i3i3−i3i3i3−i3−i3i3−i3i31111-11-1-1-1-10000000000000000
χ3322222-2-2-22-2-1-2-222-1-1-100-2200-1-11111−i3−i3i3i311-1-1−i3−i3i3i30000002-2-22i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3-1-1111-111-1-10000000000000000
χ3422222-2-2-22-2-1-2-222-1-1-100-2200-1-11111−i3−i3i3i311-1-1−i3−i3i3i3000000-222-2i3−i3i3−i3−i3i3i3−i3i3−i3−i3i311-1-11-1-1-1110000000000000000
χ3522222-2-2-22-2-1-2-222-1-1-100-2200-1-11111i3i3−i3−i311-1-1i3i3−i3−i30000002-2-22−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3-1-1111-111-1-10000000000000000
χ3622222-2-2-22-2-1-2-222-1-1-100-2200-1-11111i3i3−i3−i311-1-1i3i3−i3−i3000000-222-2−i3i3−i3i3i3−i3−i3i3−i3i3i3−i311-1-11-1-1-1110000000000000000
χ372222-22-2-2-22222-2-222200-2200-2-222-2-2000022-2-200000220-2-2000000222200-2-2-2-20000-2200000000000000000000
χ382222-22-2-2-22222-2-222200-2200-2-222-2-2000022-2-200000-2-2022000000-2-2-2-20022220000-2200000000000000000000
χ392222-22-2-2-222-2-222222002-200-2-222-2-20000-2-222000002-20-2200000022-2-200-2-22200002-200000000000000000000
χ402222-22-2-2-222-2-222222002-200-2-222-2-20000-2-22200000-2202-2000000-2-2220022-2-200002-200000000000000000000
χ412222-22-2-2-22-122-2-2-1-1-100-220011-1-111−i3−i3i3i3-1-111i3i3−i3−i30220-2-20000i3−i3-1-1-1-1−i3i31111−i3i3−i3i31-1−i3i3−i3i30000000000000000
χ422222-22-2-2-22-122-2-2-1-1-100-220011-1-111−i3−i3i3i3-1-111i3i3−i3−i30-2-20220000i3−i31111−i3i3-1-1-1-1i3−i3i3−i31-1i3−i3i3−i30000000000000000
χ432222-22-2-2-22-122-2-2-1-1-100-220011-1-111i3i3−i3−i3-1-111−i3−i3i3i30220-2-20000−i3i3-1-1-1-1i3−i31111i3−i3i3−i31-1i3−i3i3−i30000000000000000
χ442222-22-2-2-22-122-2-2-1-1-100-220011-1-111i3i3−i3−i3-1-111−i3−i3i3i30-2-20220000−i3i31111i3−i3-1-1-1-1−i3i3−i3i31-1−i3i3−i3i30000000000000000
χ452222-22-2-2-22-1-2-222-1-1-1002-20011-1-111−i3−i3i3i311-1-1i3i3−i3−i302-20-220000−i3i3-1-111i3−i311-1-1−i3i3i3−i3-11−i3i3i3−i30000000000000000
χ462222-22-2-2-22-1-2-222-1-1-1002-20011-1-111−i3−i3i3i311-1-1i3i3−i3−i30-2202-20000−i3i311-1-1i3−i3-1-111i3−i3−i3i3-11i3−i3−i3i30000000000000000
χ472222-22-2-2-22-1-2-222-1-1-1002-20011-1-111i3i3−i3−i311-1-1−i3−i3i3i302-20-220000i3−i3-1-111−i3i311-1-1i3−i3−i3i3-11i3−i3−i3i30000000000000000
χ482222-22-2-2-22-1-2-222-1-1-1002-20011-1-111i3i3−i3−i311-1-1−i3−i3i3i30-2202-20000i3−i311-1-1−i3i3-1-111−i3i3i3−i3-11−i3i3i3−i30000000000000000
χ492222-2-222-2-22222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2002000000-2-200002200000000-2-200000000000000000000
χ502222-2-222-2-222222222-2-2-2-222-2-2-2-222-2-2-2-222222222200-2000000220000-2-200000000-2-200000000000000000000
χ512222-2-222-2-22-2-2-2-22222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2200-2000000220000-2-2000000002200000000000000000000
χ522222-2-222-2-22-2-2-2-2222-2-22222-2-2-2-222-2-2-2-2-2-2-2-22222-2002000000-2-2000022000000002200000000000000000000
χ532222-2-222-2-2-12222-1-1-122-2-2-2-21111-1-1-1-1-1-1-1-1-1-11111-200200000011−i3i3−i3i3-1-1i3−i3i3−i3−i3i3−i3i311i3−i3i3−i30000000000000000
χ542222-2-222-2-2-12222-1-1-122-2-2-2-21111-1-1-1-1-1-1-1-1-1-11111-200200000011i3−i3i3−i3-1-1−i3i3−i3i3i3−i3i3−i311−i3i3−i3i30000000000000000
χ552222-2-222-2-2-12222-1-1-1-2-2-2-2221111-1-11111-1-1-1-1-1-1-1-1200-2000000-1-1−i3i3−i3i311i3−i3i3−i3i3−i3i3−i311−i3i3−i3i30000000000000000
χ562222-2-222-2-2-12222-1-1-1-2-2-2-2221111-1-11111-1-1-1-1-1-1-1-1200-2000000-1-1i3−i3i3−i311−i3i3−i3i3−i3i3−i3i311i3−i3i3−i30000000000000000
χ572222-2-222-2-2-1-2-2-2-2-1-1-12222-2-21111-1-1-1-1-1-111111111200-2000000-1-1−i3i3i3−i311i3−i3−i3i3−i3i3i3−i3-1-1i3−i3−i3i30000000000000000
χ582222-2-222-2-2-1-2-2-2-2-1-1-12222-2-21111-1-1-1-1-1-111111111200-2000000-1-1i3−i3−i3i311−i3i3i3−i3i3−i3−i3i3-1-1−i3i3i3−i30000000000000000
χ592222-2-222-2-2-1-2-2-2-2-1-1-1-2-222221111-1-111111111-1-1-1-1-200200000011−i3i3i3−i3-1-1i3−i3−i3i3i3−i3−i3i3-1-1−i3i3i3−i30000000000000000
χ602222-2-222-2-2-1-2-2-2-2-1-1-1-2-222221111-1-111111111-1-1-1-1-200200000011i3−i3−i3i3-1-1−i3i3i3−i3−i3i3i3−i3-1-1i3−i3−i3i30000000000000000
χ6122-2-22-22-2-22200002-2-22i−2i002i−2i2-22-22-22i−2i2i−2i00002i−2i2i−2i0000000000000000000000000000000022-2-200002i−2i000000
χ6222-2-22-22-2-22200002-2-22i−2i002i−2i2-22-22-22i−2i2i−2i00002i−2i2i−2i00000000000000000000000000000000-2-2220000−2i2i000000
χ6322-2-22-22-2-22200002-2-2−2i2i00−2i2i2-22-22-2−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000000000000022-2-20000−2i2i000000
χ6422-2-22-22-2-22200002-2-2−2i2i00−2i2i2-22-22-2−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000000000-2-22200002i−2i000000
χ6522-2-2-222-22-2200002-2-22i−2i00−2i2i-22-222-22i−2i2i−2i0000−2i2i−2i2i0000000000000000000000000000000000002i2i−2i−2i002-20000
χ6622-2-2-222-22-2200002-2-22i−2i00−2i2i-22-222-22i−2i2i−2i0000−2i2i−2i2i000000000000000000000000000000000000−2i−2i2i2i00-220000
χ6722-2-2-222-22-2200002-2-2−2i2i002i−2i-22-222-2−2i2i−2i2i00002i−2i2i−2i0000000000000000000000000000000000002i2i−2i−2i00-220000
χ6822-2-2-222-22-2200002-2-2−2i2i002i−2i-22-222-2−2i2i−2i2i00002i−2i2i−2i000000000000000000000000000000000000−2i−2i2i2i002-20000
χ6944-4-444-44-4-4400004-4-40000004-4-44-44000000000000000000000000000000000000000000000000000000000000
χ7044-4-444-44-4-4-20000-222000000-222-22-223−23−2323000023−23−2323000000000000000000000000000000000000000000000000
χ7144-4-444-44-4-4-20000-222000000-222-22-2−232323−230000−232323−23000000000000000000000000000000000000000000000000
χ7244-4-44-44-4-44-20000-2224i−4i004i−4i-22-22-22−2i2i−2i2i0000−2i2i−2i2i000000000000000000000000000000000000000000000000
χ7344-4-44-44-4-44-20000-222−4i4i00−4i4i-22-22-222i−2i2i−2i00002i−2i2i−2i000000000000000000000000000000000000000000000000
χ7444-4-4-444-44-4-20000-2224i−4i00−4i4i2-22-2-22−2i2i−2i2i00002i−2i2i−2i000000000000000000000000000000000000000000000000
χ7544-4-4-444-44-4-20000-222−4i4i004i−4i2-22-2-222i−2i2i−2i0000−2i2i−2i2i000000000000000000000000000000000000000000000000
χ7644-4-4-4-4-4444400004-4-4000000-444-4-44000000000000000000000000000000000000000000000000000000000000
χ7744-4-4-4-4-4444-20000-2220000002-2-222-223−23−23230000−232323−23000000000000000000000000000000000000000000000000
χ7844-4-4-4-4-4444-20000-2220000002-2-222-2−232323−23000023−23−2323000000000000000000000000000000000000000000000000
χ794-44-40000004004i−4i-44-40000000000000000004i−4i0000000000000000000000000000000000002-22-22i−2i2i−2i00000000
χ804-44-40000004004i−4i-44-40000000000000000004i−4i000000000000000000000000000000000000-22-22−2i2i−2i2i00000000
χ814-44-4000000400−4i4i-44-4000000000000000000−4i4i0000000000000000000000000000000000002-22-2−2i2i−2i2i00000000
χ824-44-4000000400−4i4i-44-4000000000000000000−4i4i000000000000000000000000000000000000-22-222i−2i2i−2i00000000
χ834-4-4400000044-400-4-4400000000000000004-4000000000000000000000000000000000000002-2-222-2-2200000000
χ844-4-4400000044-400-4-4400000000000000004-400000000000000000000000000000000000000-222-2-222-200000000
χ854-4-440000004-4400-4-440000000000000000-44000000000000000000000000000000000000002-2-22-222-200000000
χ864-4-440000004-4400-4-440000000000000000-4400000000000000000000000000000000000000-222-22-2-2200000000
χ878-88-8000000-4008i−8i4-44000000000000000000−4i4i0000000000000000000000000000000000000000000000000000
χ888-88-8000000-400−8i8i4-440000000000000000004i−4i0000000000000000000000000000000000000000000000000000
χ898-8-88000000-48-80044-40000000000000000-44000000000000000000000000000000000000000000000000000000
χ908-8-88000000-4-880044-400000000000000004-4000000000000000000000000000000000000000000000000000000

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