Finite Group Databasebeta

← Group #10694689

Character table — Group #10694689

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order1222223444444446664466121212121212121288881212242424242424242488888888226666882424242488882288
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111-1-11-1-1-111-1-1-111111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i1111-1-1-1-11-111-1-1i−iii−i−iii−i−i1-1i−i
χ101111-1-11-1-1-111-1-1-111111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i1111-1-1-1-1-11-1-111−ii−i−iiiii−i−i-11−ii
χ111111-1-11-1-1-111-1-1-111111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-1-1-1-111111-111-1-1i−iii−i−i−i−iii-11−ii
χ121111-1-11-1-1-111-1-1-111111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-1-1-1-11111-11-1-111−ii−i−iii−i−iii1-1i−i
χ131111-1-11-1-1-111-1-1-111111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii1111-1-1-1-11-111-1-1−ii−i−iii−i−iii1-1−ii
χ141111-1-11-1-1-111-1-1-111111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii1111-1-1-1-1-11-1-111i−iii−i−i−i−iii-11i−i
χ151111-1-11-1-1-111-1-1-111111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-1-1-1-111111-111-1-1−ii−i−iiiii−i−i-11i−i
χ161111-1-11-1-1-111-1-1-111111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-1-1-1-11111-11-1-111i−iii−i−iii−i−i1-1−ii
χ17222222222-2-2-2-2-2-22222-222-2-2-2-2-222-200002-200000000000000000000000000002i−2i2i−2i0000
χ18222222222-2-2-2-2-2-22222-222-2-2-2-2-222-200002-20000000000000000000000000000−2i2i−2i2i0000
χ192222222-2-2222-2-22222-2-222222-2-2-2-220000-2-20000000022-2-222-2-200000000000000000000
χ202222222-2-2222-2-22222-2-222222-2-2-2-220000-2-200000000-2-222-2-22200000000000000000000
χ212222222-2-2-2-2-222-2222-2222-2-2-222-2-2-22i−2i2i−2i-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ222222222-2-2-2-2-222-2222-2222-2-2-222-2-2-2−2i2i−2i2i-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-122-1-1-1-100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-21111-2-2111100000000
χ25222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-1-1-1-1-2-2111100000000
χ26222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2111122-1-1-1-100000000
χ27222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-11112i−2i2i−2i1-1−i−iii−i−iii0000000000−i3i3−i3i3003−33−300000000
χ28222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-11112i−2i2i−2i1-1−i−iii−i−iii0000000000i3−i3i3−i300−33−3300000000
χ29222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-1111−2i2i−2i2i1-1ii−i−iii−i−i0000000000−i3i3−i3i300−33−3300000000
χ30222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-1111−2i2i−2i2i1-1ii−i−iii−i−i0000000000i3−i3i3−i3003−33−300000000
χ312222-2-22222-2-2-2-22222-22-2-2-2-22-2-22222-2-22-2222-2-2-2-2220000000000000000000000000000
χ322222-2-22222-2-2-2-22222-22-2-2-2-22-2-2222-222-2-22-2-22222-2-20000000000000000000000000000
χ332222-2-2222-22222-2222-2-2-2-222-22222-20000-2-20000000022-2-2-2-22200000000000000000000
χ342222-2-2222-22222-2222-2-2-2-222-22222-20000-2-200000000-2-22222-2-200000000000000000000
χ352222-2-22-2-22-2-22222222-2-2-2-2-2222-2-2200002-200000000000000000000000000002-2-220000
χ362222-2-22-2-22-2-22222222-2-2-2-2-2222-2-2200002-20000000000000000000000000000-222-20000
χ372222-2-2-1222-2-2-2-22-1-1-1-221111-111-1-1-12-2-221-1-1-11111-1-10000000000−i3i3i3−i300−i3i3i3−i300000000
χ382222-2-2-1222-2-2-2-22-1-1-1-221111-111-1-1-12-2-221-1-1-11111-1-10000000000i3−i3−i3i300i3−i3−i3i300000000
χ392222-2-2-1222-2-2-2-22-1-1-1-221111-111-1-1-1-222-21-111-1-1-1-1110000000000−i3i3i3−i300i3−i3−i3i300000000
χ402222-2-2-1222-2-2-2-22-1-1-1-221111-111-1-1-1-222-21-111-1-1-1-1110000000000i3−i3−i3i300−i3i3i3−i300000000
χ412222-2-2-1-2-2-222-2-2-2-1-1-12211-1-11111112i2i−2i−2i-1-1−i−i−i−iiiii000000002-2-1-1112i−2i−i−iii00000000
χ422222-2-2-1-2-2-222-2-2-2-1-1-12211-1-11111112i2i−2i−2i-1-1−i−i−i−iiiii00000000-2211-1-1−2i2iii−i−i00000000
χ432222-2-2-1-2-2-222-2-2-2-1-1-12211-1-1111111−2i−2i2i2i-1-1iiii−i−i−i−i000000002-2-1-111−2i2iii−i−i00000000
χ442222-2-2-1-2-2-222-2-2-2-1-1-12211-1-1111111−2i−2i2i2i-1-1iiii−i−i−i−i00000000-2211-1-12i−2i−i−iii00000000
χ45444444-244-4-4-4-4-4-4-2-2-24-4-2-222222-2-220000-22000000000000000000000000000000000000
χ46444444-2-4-4444-4-44-2-2-2-4-4-2-2-2-2-22222-2000022000000000000000000000000000000000000
χ474444-4-4-244-44444-4-2-2-2-4-422-2-22-2-2-2-22000022000000000000000000000000000000000000
χ484444-4-4-2-4-44-4-4444-2-2-24-42222-2-2-222-20000-22000000000000000000000000000000000000
χ4944-4-4004000004-404-4-400000004-4000000000000000000022−2222−220000000000000000000000
χ5044-4-4004000004-404-4-400000004-40000000000000000000−2222−22220000000000000000000000
χ5144-4-400400000-4404-4-40000000-44000000000000000000022−22−22220000000000000000000000
χ5244-4-400400000-4404-4-40000000-440000000000000000000−222222−220000000000000000000000
χ534-44-40044-4000000-44-40000000004-400000000000000022−22000022−2200000000000000000000
χ544-44-40044-4000000-44-40000000004-4000000000000000−22220000−222200000000000000000000
χ554-44-4004-44000000-44-4000000000-4400000000000000022−220000−222200000000000000000000
χ564-44-4004-44000000-44-4000000000-44000000000000000−2222000022−2200000000000000000000
χ574-4-444-440044-400-4-4-44004-44-4-400004000000000000000000000000000000000000000000
χ584-4-444-4400-4-44004-4-44004-4-4440000-4000000000000000000000000000000000000000000
χ594-4-444-4-20044-400-422-200-22-2220000-2000000i6−i6i6−i6i6−i6i6−i60000000000000000000000000000
χ604-4-444-4-20044-400-422-200-22-2220000-2000000−i6i6−i6i6−i6i6−i6i60000000000000000000000000000
χ614-4-444-4-200-4-4400422-200-222-2-2000020000006−6−666−6−660000000000000000000000000000
χ624-4-444-4-200-4-4400422-200-222-2-200002000000−666−6−666−60000000000000000000000000000
χ634-4-44-444004-4400-4-4-4400-44-44-400004000000000000000000000000000000000000000000
χ644-4-44-44400-44-4004-4-4400-444-440000-4000000000000000000000000000000000000000000
χ654-4-44-44-2004-4400-422-2002-22-220000-2000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ664-4-44-44-2004-4400-422-2002-22-220000-2000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ674-4-44-44-200-44-400422-2002-2-22-2000020000006−66−6−66−660000000000000000000000000000
χ684-4-44-44-200-44-400422-2002-2-22-200002000000−66−666−66−60000000000000000000000000000
χ6988-8-800-4000008-80-4440000000-44000000000000000000000000000000000000000000000
χ7088-8-800-400000-880-44400000004-4000000000000000000000000000000000000000000000
χ718-88-800-48-80000004-44000000000-440000000000000000000000000000000000000000000
χ728-88-800-4-880000004-440000000004-40000000000000000000000000000000000000000000

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