Finite Group Databasebeta

← Group #10690713

Character table — Group #10690713

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222223444444444444666666612121212121212121212121222224444444466666666121212121212121212121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii
χ172222222-2-2-2-222-2-2-2-2222222222-2-2-2-22222-2-2-2-22-2002-200000022-2-200000000000022-2-200000000000000000000
χ182222222-2-2-2-222-2-2-2-2222222222-2-2-2-22222-2-2-2-2-2200-22000000-2-222000000000000-2-22200000000000000000000
χ192222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-222222-200-2200000022-2-2000000000000-2-22200000000000000000000
χ202222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-22222-22002-2000000-2-22200000000000022-2-200000000000000000000
χ21222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-1111111111111-1-1-1-111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-21111-1-1-1-1111111111111-1-1-1-10000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ25222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000
χ26222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ27222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-22222-2-2-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ28222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2222222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-10000000000000000
χ29222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-111112-2002-2000000-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-111−i3−i3i3i30000000000000000
χ30222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-111112-2002-2000000-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-111i3i3−i3−i30000000000000000
χ31222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111-2200-2200000011-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-1−i3−i3i3i30000000000000000
χ32222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111-2200-2200000011-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-1i3i3−i3−i30000000000000000
χ33222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-12-200-22000000-1-111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311-1-1i3i3−i3−i30000000000000000
χ34222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-12-200-22000000-1-111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311-1-1−i3−i3i3i30000000000000000
χ35222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-1-22002-200000011-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-111i3i3−i3−i30000000000000000
χ36222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-1-22002-200000011-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-111−i3−i3i3i30000000000000000
χ372222-2-2222-2-22222-2-2-2-22-2-2-2-22222-2-222-2-222-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ382222-2-2222-2-22222-2-2-2-22-2-2-2-22222-2-222-2-222-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ392222-2-2222-2-2-2-2-2-222222-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000000000000000000000002-2-22
χ402222-2-2222-2-2-2-2-2-222222-2-2-2-22222-2-2-2-222-2-222000000000000000000000000000000000000000000000000-222-2
χ412222-2-22-2-22222-2-222-2-22-2-2-2-222-2-22222-2-2-2-222000000000000000000000000000000000000000000002i−2i2i−2i0000
χ422222-2-22-2-22222-2-222-2-22-2-2-2-222-2-22222-2-2-2-22200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ432222-2-22-2-222-2-222-2-2222-2-2-2-222-2-222-2-22222-2-2000000000000000000000000000000000000000000002-2-220000
χ442222-2-22-2-222-2-222-2-2222-2-2-2-222-2-222-2-22222-2-200000000000000000000000000000000000000000000-222-20000
χ4522-2-22-222-22-22i−2i2i−2i2i−2i2i−2i222-2-2-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ4622-2-22-222-22-22i−2i2i−2i2i−2i2i−2i222-2-2-2-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ4722-2-22-222-22-2−2i2i−2i2i−2i2i−2i2i222-2-2-2-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ4822-2-22-222-22-2−2i2i−2i2i−2i2i−2i2i222-2-2-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ4922-2-22-22-22-222i−2i−2i2i−2i2i2i−2i222-2-2-2-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ5022-2-22-22-22-222i−2i−2i2i−2i2i2i−2i222-2-2-2-2-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ5122-2-22-22-22-22−2i2i2i−2i2i−2i−2i2i222-2-2-2-2-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ5222-2-22-22-22-22−2i2i2i−2i2i−2i−2i2i222-2-2-2-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ5322-2-2-2222-2-222i−2i2i−2i−2i2i−2i2i2-2-222-2-22-2-222i−2i−2i2i2i−2i−2i2i002-2002i−2i000000002-22-20000000000002i−2i2i−2i0000000000000000
χ5422-2-2-2222-2-222i−2i2i−2i−2i2i−2i2i2-2-222-2-22-2-222i−2i−2i2i2i−2i−2i2i00-2200−2i2i00000000-22-22000000000000−2i2i−2i2i0000000000000000
χ5522-2-2-2222-2-22−2i2i−2i2i2i−2i2i−2i2-2-222-2-22-2-22−2i2i2i−2i−2i2i2i−2i002-200−2i2i000000002-22-2000000000000−2i2i−2i2i0000000000000000
χ5622-2-2-2222-2-22−2i2i−2i2i2i−2i2i−2i2-2-222-2-22-2-22−2i2i2i−2i−2i2i2i−2i00-22002i−2i00000000-22-220000000000002i−2i2i−2i0000000000000000
χ5722-2-2-222-222-22i−2i−2i2i2i−2i−2i2i2-2-222-2-2-222-22i−2i−2i2i−2i2i2i−2i000000002-22i−2i000000002-22-22i−2i2i−2i000000000000000000000000
χ5822-2-2-222-222-22i−2i−2i2i2i−2i−2i2i2-2-222-2-2-222-22i−2i−2i2i−2i2i2i−2i00000000-22−2i2i00000000-22-22−2i2i−2i2i000000000000000000000000
χ5922-2-2-222-222-2−2i2i2i−2i−2i2i2i−2i2-2-222-2-2-222-2−2i2i2i−2i2i−2i−2i2i000000002-2−2i2i000000002-22-2−2i2i−2i2i000000000000000000000000
χ6022-2-2-222-222-2−2i2i2i−2i−2i2i2i−2i2-2-222-2-2-222-2−2i2i2i−2i2i−2i−2i2i00000000-222i−2i00000000-22-222i−2i2i−2i000000000000000000000000
χ6122-2-2-22-12-2-222i−2i2i−2i−2i2i−2i2i-111-1-111-111-1−iii−i−iii−i002-2002i−2i0000−i3i3−i3i3-11-11−i3i3i3−i33−3−333−33−3−ii−ii0000000000000000
χ6222-2-2-22-12-2-222i−2i2i−2i−2i2i−2i2i-111-1-111-111-1−iii−i−iii−i002-2002i−2i0000i3−i3i3−i3-11-11i3−i3−i3i3−333−3−33−33−ii−ii0000000000000000
χ6322-2-2-22-12-2-222i−2i2i−2i−2i2i−2i2i-111-1-111-111-1−iii−i−iii−i00-2200−2i2i0000−i3i3−i3i31-11-1i3−i3−i3i3−333−33−33−3i−ii−i0000000000000000
χ6422-2-2-22-12-2-222i−2i2i−2i−2i2i−2i2i-111-1-111-111-1−iii−i−iii−i00-2200−2i2i0000i3−i3i3−i31-11-1−i3i3i3−i33−3−33−33−33i−ii−i0000000000000000
χ6522-2-2-22-12-2-22−2i2i−2i2i2i−2i2i−2i-111-1-111-111-1i−i−iii−i−ii002-200−2i2i0000−i3i3−i3i3-11-11−i3i3i3−i3−333−3−33−33i−ii−i0000000000000000
χ6622-2-2-22-12-2-22−2i2i−2i2i2i−2i2i−2i-111-1-111-111-1i−i−iii−i−ii002-200−2i2i0000i3−i3i3−i3-11-11i3−i3−i3i33−3−333−33−3i−ii−i0000000000000000
χ6722-2-2-22-12-2-22−2i2i−2i2i2i−2i2i−2i-111-1-111-111-1i−i−iii−i−ii00-22002i−2i0000−i3i3−i3i31-11-1i3−i3−i3i33−3−33−33−33−ii−ii0000000000000000
χ6822-2-2-22-12-2-22−2i2i−2i2i2i−2i2i−2i-111-1-111-111-1i−i−iii−i−ii00-22002i−2i0000i3−i3i3−i31-11-1−i3i3i3−i3−333−33−33−3−ii−ii0000000000000000
χ6922-2-2-22-1-222-22i−2i−2i2i2i−2i−2i2i-111-1-1111-1-11−iii−ii−i−ii000000002-22i−2i−i3i3i3−i3−i3i3i3−i3-11-11−ii−ii3−3−333−3−330000000000000000
χ7022-2-2-22-1-222-22i−2i−2i2i2i−2i−2i2i-111-1-1111-1-11−iii−ii−i−ii000000002-22i−2ii3−i3−i3i3i3−i3−i3i3-11-11−ii−ii−333−3−333−30000000000000000
χ7122-2-2-22-1-222-22i−2i−2i2i2i−2i−2i2i-111-1-1111-1-11−iii−ii−i−ii00000000-22−2i2i−i3i3i3−i3i3−i3−i3i31-11-1i−ii−i3−3−33−333−30000000000000000
χ7222-2-2-22-1-222-22i−2i−2i2i2i−2i−2i2i-111-1-1111-1-11−iii−ii−i−ii00000000-22−2i2ii3−i3−i3i3−i3i3i3−i31-11-1i−ii−i−333−33−3−330000000000000000
χ7322-2-2-22-1-222-2−2i2i2i−2i−2i2i2i−2i-111-1-1111-1-11i−i−ii−iii−i000000002-2−2i2i−i3i3i3−i3−i3i3i3−i3-11-11i−ii−i−333−3−333−30000000000000000
χ7422-2-2-22-1-222-2−2i2i2i−2i−2i2i2i−2i-111-1-1111-1-11i−i−ii−iii−i000000002-2−2i2ii3−i3−i3i3i3−i3−i3i3-11-11i−ii−i3−3−333−3−330000000000000000
χ7522-2-2-22-1-222-2−2i2i2i−2i−2i2i2i−2i-111-1-1111-1-11i−i−ii−iii−i00000000-222i−2i−i3i3i3−i3i3−i3−i3i31-11-1−ii−ii−333−33−3−330000000000000000
χ7622-2-2-22-1-222-2−2i2i2i−2i−2i2i2i−2i-111-1-1111-1-11i−i−ii−iii−i00000000-222i−2ii3−i3−i3i3−i3i3i3−i31-11-1−ii−ii3−3−33−333−30000000000000000
χ774444-4-4-244-4-44444-4-4-4-4-22222-2-2-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ784444-4-4-244-4-4-4-4-4-44444-22222-2-2-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000
χ794444-4-4-2-4-44444-4-444-4-4-22222-2-222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-4-2-4-444-4-444-4-444-22222-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ8144-4-44-4-24-44-44i−4i4i−4i4i−4i4i−4i-2-2-22222-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ8244-4-44-4-24-44-4−4i4i−4i4i−4i4i−4i4i-2-2-22222-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ8344-4-44-4-2-44-444i−4i−4i4i−4i4i4i−4i-2-2-222222-22-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ8444-4-44-4-2-44-44−4i4i4i−4i4i−4i−4i4i-2-2-222222-22-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ858-88-8008000000000000-800008-80000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-40000000000004−4i34i3−4i34i3-440000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-400000000000044i3−4i34i3−4i3-440000000000000000000000000000000000000000000000000000000000000000
χ888-8-88008000000000000-80000-880000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800-40000000000004−4i34i34i3−4i34-40000000000000000000000000000000000000000000000000000000000000000
χ908-8-8800-400000000000044i3−4i3−4i34i34-40000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.