Finite Group Databasebeta

← Group #10827630

Character table — Group #10827630

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order122222222222223666224444666666666612121212121212122244444444666666121212121212121212121212121212122222222244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ911111-1-1-1-1111111111-1-11111111111-1-1-1-1111111111-11-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-11-1
χ1011111-1-1-1-1111111111-1-11111111111-1-1-1-1111111111-11-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-11
χ1111111-1-1-1-1111111111-1-11111111111-1-1-1-111111111-11-11-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-11-11
χ1211111-1-1-1-1111111111-1-11111111111-1-1-1-111111111-11-11-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-11-1
χ1311111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11
χ1411111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1
χ1511111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-111-1
χ1611111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-11-1-11
χ1722222222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-111111111-1-1-1-1111111110000000000000000
χ1922222222222222-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111112-22-2-2-222-2-2-1-1-1-111-1-1111111-1-1-1-111110000000000000000
χ2022222222222222-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-22-22-2-2-2-222-1-111-1-111-1-111111111-1-1-1-10000000000000000
χ21222222222-2-2-2-222222-2-222-2-222-2-2-2-222222222-2-2-2-200002-20000-2-20000000022-2-2000000000000000000000000
χ22222222222-2-2-2-222222-2-2-2-22222-2-2-2-22222-2-2-2-222220000-220000-2-200000000-2-222000000000000000000000000
χ23222222222-2-2-2-22-1-1-1-1-2-222-2-2-1-11111-1-1-1-1-1-1-1-1111100002-2000011−i3i3−i3i3−i3i3−i3i3-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ24222222222-2-2-2-22-1-1-1-1-2-222-2-2-1-11111-1-1-1-1-1-1-1-1111100002-2000011i3−i3i3−i3i3−i3i3−i3-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ25222222222-2-2-2-22-1-1-1-1-2-2-2-222-1-11111-1-1-1-11111-1-1-1-10000-22000011−i3i3i3−i3−i3i3i3−i311-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ26222222222-2-2-2-22-1-1-1-1-2-2-2-222-1-11111-1-1-1-11111-1-1-1-10000-22000011i3−i3−i3i3i3−i3−i3i311-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ2722222-2-2-2-222222-1-1-1-1-2-22222-1-1-1-1-1-11111-1-1-1-1-1-1-1-12-22-2-2-2-2-22211-1-111-1-11111111111-1-1-1-10000000000000000
χ2822222-2-2-2-222222-1-1-1-1-2-22222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-22-22-2-222-2-21111-1-111-1-11111-1-1-1-111110000000000000000
χ2922222-2-2-2-222222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1111111111111222222-2-2-2-211-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000
χ3022222-2-2-2-222222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1111111111111-2-2-2-22222221111111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ3122222-2-2-2-2-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-20000-2200002200000000-2-222000000000000000000000000
χ3222222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200002-20000220000000022-2-2000000000000000000000000
χ3322222-2-2-2-2-2-2-2-22-1-1-1-12222-2-2-1-111111111-1-1-1-111110000-220000-1-1−i3i3i3−i3−i3i3i3−i311-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ3422222-2-2-2-2-2-2-2-22-1-1-1-12222-2-2-1-111111111-1-1-1-111110000-220000-1-1i3−i3−i3i3i3−i3−i3i311-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ3522222-2-2-2-2-2-2-2-22-1-1-1-122-2-222-1-1111111111111-1-1-1-100002-20000-1-1−i3i3−i3i3−i3i3−i3i3-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ3622222-2-2-2-2-2-2-2-22-1-1-1-122-2-222-1-1111111111111-1-1-1-100002-20000-1-1i3−i3i3−i3i3−i3i3−i3-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ372222-222-2-222-2-2-222222-20000-2-222-2-222-2-200000000020-200002-22-2002200-2-2000000002-22-20000000000000000
χ382222-222-2-222-2-2-222222-20000-2-222-2-222-2-2000000000-2020000-222-200-2-2002200000000-22-220000000000000000
χ392222-222-2-222-2-2-2-1-1-1-12-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i3020-200002-2-11−i3i3-1-1i3−i311−i3i3−i3i3−i3i3−i3i3-11-110000000000000000
χ402222-222-2-222-2-2-2-1-1-1-12-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i30-2020000-22-11i3−i311−i3i3-1-1−i3i3−i3i3i3−i3i3−i31-11-10000000000000000
χ412222-222-2-222-2-2-2-1-1-1-12-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i3020-200002-2-11i3−i3-1-1−i3i311i3−i3i3−i3i3−i3i3−i3-11-110000000000000000
χ422222-222-2-222-2-2-2-1-1-1-12-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i30-2020000-22-11−i3i311i3−i3-1-1i3−i3i3−i3−i3i3−i3i31-11-10000000000000000
χ432222-222-2-2-2-222-22222-220000-2-2-2-22222-2-20000000020-20002-200-222200-2-20000002-2-2200000000000000000000
χ442222-222-2-2-2-222-22222-220000-2-2-2-22222-2-200000000-202000-2200-22-2-20022000000-222-200000000000000000000
χ452222-222-2-2-2-222-2-1-1-1-1-2200001111-1-1-1-111−i3−i3i3i3i3i3−i3−i320-20002-2001-1-1-1−i3i311i3−i3−i3i3i3−i3-111-1−i3i3i3−i30000000000000000
χ462222-222-2-2-2-222-2-1-1-1-1-2200001111-1-1-1-111−i3−i3i3i3i3i3−i3−i3-202000-22001-111i3−i3-1-1−i3i3−i3i3i3−i31-1-11i3−i3−i3i30000000000000000
χ472222-222-2-2-2-222-2-1-1-1-1-2200001111-1-1-1-111i3i3−i3−i3−i3−i3i3i320-20002-2001-1-1-1i3−i311−i3i3i3−i3−i3i3-111-1i3−i3−i3i30000000000000000
χ482222-222-2-2-2-222-2-1-1-1-1-2200001111-1-1-1-111i3i3−i3−i3−i3−i3i3i3-202000-22001-111−i3i3-1-1i3−i3i3−i3−i3i31-1-11−i3i3i3−i30000000000000000
χ492222-2-2-22222-2-2-22222-220000-2-222-2-2-2-22200000000020-20000-22-22002200-2-200000000-22-220000000000000000
χ502222-2-2-22222-2-2-22222-220000-2-222-2-2-2-222000000000-20200002-2-2200-2-20022000000002-22-20000000000000000
χ512222-2-2-22222-2-2-2-1-1-1-1-22000011-1-11111-1-1−i3−i3i3i3−i3−i3i3i3020-20000-221-1i3−i3-1-1−i3i311i3−i3i3−i3−i3i3−i3i31-11-10000000000000000
χ522222-2-2-22222-2-2-2-1-1-1-1-22000011-1-11111-1-1−i3−i3i3i3−i3−i3i3i30-20200002-21-1−i3i311i3−i3-1-1i3−i3i3−i3i3−i3i3−i3-11-110000000000000000
χ532222-2-2-22222-2-2-2-1-1-1-1-22000011-1-11111-1-1i3i3−i3−i3i3i3−i3−i3020-20000-221-1−i3i3-1-1i3−i311−i3i3−i3i3i3−i3i3−i31-11-10000000000000000
χ542222-2-2-22222-2-2-2-1-1-1-1-22000011-1-11111-1-1i3i3−i3−i3i3i3−i3−i30-20200002-21-1i3−i311−i3i3-1-1−i3i3−i3i3−i3i3−i3i3-11-110000000000000000
χ552222-2-2-222-2-222-222222-20000-2-2-2-222-2-2220000000020-2000-22002-22200-2-2000000-222-200000000000000000000
χ562222-2-2-222-2-222-222222-20000-2-2-2-222-2-22200000000-2020002-2002-2-2-200220000002-2-2200000000000000000000
χ572222-2-2-222-2-222-2-1-1-1-12-200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i320-2000-2200-11-1-1i3−i311−i3i3i3−i3−i3i31-1-11−i3i3i3−i30000000000000000
χ582222-2-2-222-2-222-2-1-1-1-12-200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i3-2020002-200-1111−i3i3-1-1i3−i3i3−i3−i3i3-111-1i3−i3−i3i30000000000000000
χ592222-2-2-222-2-222-2-1-1-1-12-200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i320-2000-2200-11-1-1−i3i311i3−i3−i3i3i3−i31-1-11i3−i3−i3i30000000000000000
χ602222-2-2-222-2-222-2-1-1-1-12-200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i3-2020002-200-1111i3−i3-1-1−i3i3−i3i3i3−i3-111-1−i3i3i3−i30000000000000000
χ6122-2-2200002-22-2-222-2-2002i−2i2i−2i2-22-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000022-2-2002i−2i0000
χ6222-2-2200002-22-2-222-2-2002i−2i2i−2i2-22-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000-2-22200−2i2i0000
χ6322-2-2200002-22-2-222-2-200−2i2i−2i2i2-22-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000022-2-200−2i2i0000
χ6422-2-2200002-22-2-222-2-200−2i2i−2i2i2-22-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000-2-222002i−2i0000
χ6522-2-220000-22-22-222-2-2002i−2i−2i2i2-2-22-2200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000022-2-200002i−2i000000
χ6622-2-220000-22-22-222-2-2002i−2i−2i2i2-2-22-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000-2-2220000−2i2i000000
χ6722-2-220000-22-22-222-2-200−2i2i2i−2i2-2-22-220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000022-2-20000−2i2i000000
χ6822-2-220000-22-22-222-2-200−2i2i2i−2i2-2-22-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000-2-22200002i−2i000000
χ6944-4-4400004-44-4-4-2-222004i−4i4i−4i-22-22-220000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ7044-4-4400004-44-4-4-2-22200−4i4i−4i4i-22-22-2200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ7144-4-440000-44-44-4-2-222004i−4i−4i4i-222-22-20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ7244-4-440000-44-44-4-2-22200−4i4i4i−4i-222-22-200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ7344-4-4-400004-4-44444-4-4000000-444-4-44000000000000000000000000000000000000000000000000000000000000
χ7444-4-4-400004-4-444-2-2220000002-2-222-2000023−23−232323−23−2323000000000000000000000000000000000000000000000000
χ7544-4-4-400004-4-444-2-2220000002-2-222-20000−232323−23−232323−23000000000000000000000000000000000000000000000000
χ7644-4-4-40000-444-4444-4-4000000-44-444-4000000000000000000000000000000000000000000000000000000000000
χ7744-4-4-40000-444-44-2-2220000002-22-2-22000023−23−2323−232323−23000000000000000000000000000000000000000000000000
χ7844-4-4-40000-444-44-2-2220000002-22-2-220000−232323−2323−23−2323000000000000000000000000000000000000000000000000
χ794-44-40004-4000004-44-4000000000000004-400000000000000000000000000000000000000002-22-22-22-200000000
χ804-44-40004-4000004-44-4000000000000004-40000000000000000000000000000000000000000-22-22-22-2200000000
χ814-44-4000-44000004-44-400000000000000-4400000000000000000000000000000000000000002-22-2-22-2200000000
χ824-44-4000-44000004-44-400000000000000-440000000000000000000000000000000000000000-22-222-22-200000000
χ834-4-4404-400000004-4-440000000000004-40000000000000000000000000000000000000000002-2-222-2-2200000000
χ844-4-4404-400000004-4-440000000000004-4000000000000000000000000000000000000000000-222-2-222-200000000
χ854-4-440-4400000004-4-44000000000000-440000000000000000000000000000000000000000002-2-22-222-200000000
χ864-4-440-4400000004-4-44000000000000-44000000000000000000000000000000000000000000-222-22-2-2200000000
χ878-88-80008-800000-44-4400000000000000-4400000000000000000000000000000000000000000000000000000000
χ888-88-8000-8800000-44-44000000000000004-400000000000000000000000000000000000000000000000000000000
χ898-8-8808-80000000-444-4000000000000-440000000000000000000000000000000000000000000000000000000000
χ908-8-880-880000000-444-40000000000004-40000000000000000000000000000000000000000000000000000000000

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