Finite Group Databasebeta

← Group #10691047

Character table — Group #10691047

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888121212121616161616161616161616162424242424242424242424242424
order122222344444466644444446612121212121212122466121212121212121288884488121212122424242488888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111-1-11-1-111111111111-1-1-1-11-1-1-1-11-1-1111111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111-1-11-1-111111111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ711111111111111111-1-11-1-111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111
χ811111111111111111-1-11-1-111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1
χ91111-1-111-11-1-1-11111111-1-1-1-1-1111-1-1-1-111-111-111-1-11-1-1ii−i−i1-11-111-1-111-1-1i−iii−i−iii−i−iii−i−i
χ101111-1-111-11-1-1-11111111-1-1-1-1-1111-1-1-1-111-111-111-1-11-1-1ii−i−i-11-11-1-111-1-111i−iii−i−i−i−iii−i−iii
χ111111-1-111-11-1-1-11111111-1-1-1-1-1111-1-1-1-111-111-111-1-11-1-1−i−iii1-11-111-1-111-1-1−ii−i−iii−i−iii−i−iii
χ121111-1-111-11-1-1-11111111-1-1-1-1-1111-1-1-1-111-111-111-1-11-1-1−i−iii-11-11-1-111-1-111−ii−i−iiiii−i−iii−i−i
χ131111-1-111-11-1-1-11111-1-1111-1-1-1111-1-1-1-11-11-1-1-1-1-111111ii−i−i1-1-1111-1-1-1-111i−i−i−iiiii−i−i−i−iii
χ141111-1-111-11-1-1-11111-1-1111-1-1-1111-1-1-1-11-11-1-1-1-1-111111ii−i−i-111-1-1-11111-1-1i−i−i−iii−i−iiiii−i−i
χ151111-1-111-11-1-1-11111-1-1111-1-1-1111-1-1-1-11-11-1-1-1-1-111111−i−iii1-1-1111-1-1-1-111−iiii−i−i−i−iiiii−i−i
χ161111-1-111-11-1-1-11111-1-1111-1-1-1111-1-1-1-11-11-1-1-1-1-111111−i−iii-111-1-1-11111-1-1−iiii−i−iii−i−i−i−iii
χ1722222222-2222-2222-222-222-2222-2-222-2-22-2-2-2-2-222-2-2-222000000000000000000000000000000
χ1822222222-2222-2222-2-2-2-2-2-2-2222-2-222-2-222222-2-2-222-2-2-2000000000000000000000000000000
χ192222222-22-2-2-22222-200200-222-2-2-2-2-222-20000-200002000000000000000000002i−2i2i−2i00000000
χ202222222-22-2-2-22222-200200-222-2-2-2-2-222-20000-20000200000000000000000000−2i2i−2i2i00000000
χ212222222-2-2-2-2-2-2222200-200222-222-2-2-2-2-2000020000-2002i2i−2i−2i000000000000−2i2i000000000000
χ222222222-2-2-2-2-2-2222200-200222-222-2-2-2-2-2000020000-200−2i−2i2i2i0000000000002i−2i000000000000
χ23222222-1222222-1-1-12222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-100000000000000
χ24222222-1222222-1-1-12222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-21111111100000000000000
χ25222222-1222222-1-1-12-2-22-2-22-1-1-1-1-1-1-1-1-1-1-2-211-11111-111000022-2-2-1-1-1-1111100000000000000
χ26222222-1222222-1-1-12-2-22-2-22-1-1-1-1-1-1-1-1-1-1-2-211-11111-1110000-2-2221111-1-1-1-100000000000000
χ27222222-12-2222-2-1-1-1-222-222-2-1-1-111-1-111-1-2-2111-1-1111-1-100000000−i3i3−i3i3−i3i3−i3i300000000000000
χ28222222-12-2222-2-1-1-1-222-222-2-1-1-111-1-111-1-2-2111-1-1111-1-100000000i3−i3i3−i3i3−i3i3−i300000000000000
χ29222222-12-2222-2-1-1-1-2-2-2-2-2-2-2-1-1-111-1-111-122-1-1111-1-111100000000−i3i3−i3i3i3−i3i3−i300000000000000
χ30222222-12-2222-2-1-1-1-2-2-2-2-2-2-2-1-1-111-1-111-122-1-1111-1-111100000000i3−i3i3−i3−i3i3−i3i300000000000000
χ312222-2-22222-2-22222-222-2-2-22-2-22-2-2-2-2222-22-2-222222-2-2-2000000000000000000000000000000
χ322222-2-22222-2-22222-2-2-2-2222-2-22-2-2-2-22222-2222-2-2-2-2-222000000000000000000000000000000
χ332222-2-22-22-2222222200-200-2-2-2-2222222-20000-20000-2002222000000000000-2-2000000000000
χ342222-2-22-22-2222222200-200-2-2-2-2222222-20000-20000-200-2-2-2-200000000000022000000000000
χ352222-2-22-2-2-222-2222-2002002-2-2-2-2-222-2-2-20000200002000000000000000000002-2-2200000000
χ362222-2-22-2-2-222-2222-2002002-2-2-2-2-222-2-2-2000020000200000000000000000000-222-200000000
χ372222-2-2-1222-2-22-1-1-1-222-2-2-2211-11111-1-1-1-2211-1-1-1-1-111100000000−i3i3i3−i3−i3i3i3−i300000000000000
χ382222-2-2-1222-2-22-1-1-1-222-2-2-2211-11111-1-1-1-2211-1-1-1-1-111100000000i3−i3−i3i3i3−i3−i3i300000000000000
χ392222-2-2-1222-2-22-1-1-1-2-2-2-222211-11111-1-1-12-2-1-1-111111-1-100000000−i3i3i3−i3i3−i3−i3i300000000000000
χ402222-2-2-1222-2-22-1-1-1-2-2-2-222211-11111-1-1-12-2-1-1-111111-1-100000000i3−i3−i3i3−i3i3i3−i300000000000000
χ412222-2-2-12-22-2-2-2-1-1-12222-2-2-211-1-1-11111-12-2-1-11-1-111-11100002-22-2-1-111-1-11100000000000000
χ422222-2-2-12-22-2-2-2-1-1-12222-2-2-211-1-1-11111-12-2-1-11-1-111-1110000-22-2211-1-111-1-100000000000000
χ432222-2-2-12-22-2-2-2-1-1-12-2-2222-211-1-1-11111-1-2211111-1-1-1-1-100002-2-22-1-11111-1-100000000000000
χ442222-2-2-12-22-2-2-2-1-1-12-2-2222-211-1-1-11111-1-2211111-1-1-1-1-10000-222-211-1-1-1-11100000000000000
χ4522-2-22-22-2022-202-2-202i−2i02i−2i02-2-2002-2002000002i−2i0002i−2i0000000000000000000000−i2i2−i2i22−22−2
χ4622-2-22-22-2022-202-2-202i−2i02i−2i02-2-2002-2002000002i−2i0002i−2i0000000000000000000000i2−i2i2−i2−22−22
χ4722-2-22-22-2022-202-2-20−2i2i0−2i2i02-2-2002-200200000−2i2i000−2i2i0000000000000000000000−i2i2−i2i2−22−22
χ4822-2-22-22-2022-202-2-20−2i2i0−2i2i02-2-2002-200200000−2i2i000−2i2i0000000000000000000000i2−i2i2−i22−22−2
χ4922-2-2-222-202-2202-2-202i−2i0−2i2i0-22-200-22002000002i−2i000−2i2i00000000000000000000002−2−22i2−i2−i2i2
χ5022-2-2-222-202-2202-2-202i−2i0−2i2i0-22-200-22002000002i−2i000−2i2i0000000000000000000000−222−2−i2i2i2−i2
χ5122-2-2-222-202-2202-2-20−2i2i02i−2i0-22-200-2200200000−2i2i0002i−2i00000000000000000000002−2−22−i2i2i2−i2
χ5222-2-2-222-202-2202-2-20−2i2i02i−2i0-22-200-2200200000−2i2i0002i−2i0000000000000000000000−222−2i2−i2−i2i2
χ53444444-2-44-4-4-44-2-2-2-400400-4-2-222222-2-22000020000-200000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2400-4004-2-22-2-2222220000-20000200000000000000000000000000000000
χ554444-4-4-2-44-4444-2-2-2400-400-4222-2-2-2-2-2-22000020000200000000000000000000000000000000
χ564444-4-4-2-4-4-444-4-2-2-2-400400422222-2-22220000-20000-200000000000000000000000000000000
χ5744-4-44-4440-4-4404-4-400000004-4400-4400-4000000000000000000000000000000000000000000
χ5844-4-44-4-240-4-440-2220000000-22-2002-200200−2i32i3000−2i32i3000000000000000000000000000000000
χ5944-4-44-4-240-4-440-2220000000-22-2002-2002002i3−2i30002i3−2i3000000000000000000000000000000000
χ6044-4-44-4-2-4044-40-22204i−4i04i−4i0-22200-2200-200000−2i2i000−2i2i000000000000000000000000000000
χ6144-4-44-4-2-4044-40-2220−4i4i0−4i4i0-22200-2200-2000002i−2i0002i−2i000000000000000000000000000000
χ6244-4-4-44440-44-404-4-40000000-444004-400-4000000000000000000000000000000000000000000
χ6344-4-4-44-240-44-40-22200000002-2-200-2200200−2i32i30002i3−2i3000000000000000000000000000000000
χ6444-4-4-44-240-44-40-22200000002-2-200-22002002i3−2i3000−2i32i3000000000000000000000000000000000
χ6544-4-4-44-2-404-440-22204i−4i0−4i4i02-22002-200-200000−2i2i0002i−2i000000000000000000000000000000
χ6644-4-4-44-2-404-440-2220−4i4i04i−4i02-22002-200-2000002i−2i000−2i2i000000000000000000000000000000
χ674-4-4400404000-4-4-44000000000000004-40000000000000−2i22i2−2i22i200000000000000000000000000
χ684-4-4400404000-4-4-44000000000000004-400000000000002i2−2i22i2−2i200000000000000000000000000
χ694-4-440040-40004-4-4400000000000000-44000000000000022−22−222200000000000000000000000000
χ704-4-440040-40004-4-4400000000000000-440000000000000−222222−2200000000000000000000000000
χ718-88-8008000000-88-800000000000000000000000000000000000000000000000000000000000
χ728-88-800-40000004-440000000000−4i34i300000000000000000000000000000000000000000000000
χ738-88-800-40000004-4400000000004i3−4i300000000000000000000000000000000000000000000000
χ748-8-8800-408000-844-400000000000000-440000000000000000000000000000000000000000000
χ758-8-8800-40-8000844-4000000000000004-40000000000000000000000000000000000000000000

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