Finite Group Databasebeta

← Group #10694882

Character table — Group #10694882

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order1222223444444446664466121212121212121288881212242424242424242488888888226666882424242488884488
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
χ91111111-1-1-111-1-1-11111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i1111-1-1-1-11-111-1-1i−iii−i−iii−i−i1-1i−i
χ101111111-1-1-111-1-1-11111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i1111-1-1-1-1-11-1-111−ii−i−iiiii−i−i-11−ii
χ111111111-1-1-111-1-1-11111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i-1-1-1-111111-111-1-1i−iii−i−i−i−iii-11−ii
χ121111111-1-1-111-1-1-11111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i-1-1-1-11111-11-1-111−ii−i−iii−i−iii1-1i−i
χ131111111-1-1-111-1-1-11111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii1111-1-1-1-11-111-1-1−ii−i−iii−i−iii1-1−ii
χ141111111-1-1-111-1-1-11111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii1111-1-1-1-1-11-1-111i−iii−i−i−i−iii-11i−i
χ151111111-1-1-111-1-1-11111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii-1-1-1-111111-111-1-1−ii−i−iiiii−i−i-11i−i
χ161111111-1-1-111-1-1-11111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii-1-1-1-11111-11-1-111i−iii−i−iii−i−i1-1−ii
χ1722222222-2-2-2-2222222-2-222-2-2222-2-220000-2-200000000000000000000000000002-22-20000
χ1822222222-2-2-2-2222222-2-222-2-2222-2-220000-2-20000000000000000000000000000-22-220000
χ192222222-222-2-2-2-2-2222-2222-2-2-2-2-222-20000-2200000000000000000000000000002i−2i−2i2i0000
χ202222222-222-2-2-2-2-2222-2222-2-2-2-2-222-20000-220000000000000000000000000000−2i2i2i−2i0000
χ21222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-122-1-1-1-100000000
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-21111-2-2111100000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-1-1-1-1-2-2111100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2111122-1-1-1-100000000
χ25222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii000000002-2-1-1112i−2i−i−iii00000000
χ26222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii00000000-2211-1-1−2i2iii−i−i00000000
χ27222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i000000002-2-1-111−2i2iii−i−i00000000
χ28222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i00000000-2211-1-12i−2i−i−iii00000000
χ292222-2-22222-2-2-2-222222-2-2-2-2-22-2-22222-22-22-222-2-222-2-20000000000000000000000000000
χ302222-2-22222-2-2-2-222222-2-2-2-2-22-2-2222-22-222-2-2-222-2-2220000000000000000000000000000
χ312222-2-222-2-222-2-22222-22-2-2222-2-2-2-220000-220000000022-2-222-2-200000000000000000000
χ322222-2-222-2-222-2-22222-22-2-2222-2-2-2-220000-2200000000-2-222-2-22200000000000000000000
χ332222-2-22-2222222-2222-2-2-2-222-22222-20000-2-20000000022-2-2-2-22200000000000000000000
χ342222-2-22-2222222-2222-2-2-2-222-22222-20000-2-200000000-2-22222-2-200000000000000000000
χ352222-2-22-2-2-2-2-222-222222-2-2-2-2-222-2-2-22i−2i−2i2i222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ362222-2-22-2-2-2-2-222-222222-2-2-2-2-222-2-2-2−2i2i2i−2i22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ372222-2-2-1222-2-2-2-22-1-1-12-21111-111-1-1-12-22-2-11-1-111-1-1110000000000−i3i3−i3i300−i3i3−i3i300000000
χ382222-2-2-1222-2-2-2-22-1-1-12-21111-111-1-1-12-22-2-11-1-111-1-1110000000000i3−i3i3−i300i3−i3i3−i300000000
χ392222-2-2-1222-2-2-2-22-1-1-12-21111-111-1-1-1-22-22-1111-1-111-1-10000000000−i3i3−i3i300i3−i3i3−i300000000
χ402222-2-2-1222-2-2-2-22-1-1-12-21111-111-1-1-1-22-22-1111-1-111-1-10000000000i3−i3i3−i300−i3i3−i3i300000000
χ412222-2-2-1-2-2-2-2-222-2-1-1-12211111-1-11112i−2i−2i2i-1-1−i−iiiii−i−i0000000000−i3i3i3−i3003−3−3300000000
χ422222-2-2-1-2-2-2-2-222-2-1-1-12211111-1-11112i−2i−2i2i-1-1−i−iiiii−i−i0000000000i3−i3−i3i300−333−300000000
χ432222-2-2-1-2-2-2-2-222-2-1-1-12211111-1-1111−2i2i2i−2i-1-1ii−i−i−i−iii0000000000−i3i3i3−i300−333−300000000
χ442222-2-2-1-2-2-2-2-222-2-1-1-12211111-1-1111−2i2i2i−2i-1-1ii−i−i−i−iii0000000000i3−i3−i3i3003−3−3300000000
χ45444444-24-4-4-4-4444-2-2-2-4-4-2-222-2-2-222-2000022000000000000000000000000000000000000
χ46444444-2-444-4-4-4-4-4-2-2-2-44-2-222222-2-2200002-2000000000000000000000000000000000000
χ474444-4-4-24-4-444-4-44-2-2-2-4422-2-2-22222-200002-2000000000000000000000000000000000000
χ484444-4-4-2-4444444-4-2-2-2-4-422-2-22-2-2-2-22000022000000000000000000000000000000000000
χ4944-4-40040004-40004-4-400004-4000000000000000000000000004i−4i00000000000000000000
χ5044-4-40040004-40004-4-400004-400000000000000000000000000−4i4i00000000000000000000
χ5144-4-4004000-440004-4-40000-44000000000000000000004i−4i00000000000000000000000000
χ5244-4-4004000-440004-4-40000-4400000000000000000000−4i4i00000000000000000000000000
χ534-44-44-44400004-4-4-44-4004-40044-400-4000000000000000000000000000000000000000000
χ544-44-44-44-40000-444-44-4004-400-4-44004000000000000000000000000000000000000000000
χ554-44-44-4-2400004-4-42-2200-2200-2-220020000006−66−66−66−60000000000000000000000000000
χ564-44-44-4-2400004-4-42-2200-2200-2-22002000000−66−66−66−660000000000000000000000000000
χ574-44-44-4-2-40000-4442-2200-220022-200-2000000i6−i6i6−i6−i6i6−i6i60000000000000000000000000000
χ584-44-44-4-2-40000-4442-2200-220022-200-2000000−i6i6−i6i6i6−i6i6−i60000000000000000000000000000
χ594-44-4-44440000-44-4-44-400-44004-4400-4000000000000000000000000000000000000000000
χ604-44-4-444-400004-44-44-400-4400-44-4004000000000000000000000000000000000000000000
χ614-44-4-44-240000-44-42-22002-200-22-20020000006−6−666−6−660000000000000000000000000000
χ624-44-4-44-240000-44-42-22002-200-22-2002000000−666−6−666−60000000000000000000000000000
χ634-44-4-44-2-400004-442-22002-2002-2200-2000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ644-44-4-44-2-400004-442-22002-2002-2200-2000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ654-4-4400404-400000-4-440000000004-40000000000000000022−2222−220000000000000000000000
χ664-4-4400404-400000-4-440000000004-400000000000000000−2222−22220000000000000000000000
χ674-4-440040-4400000-4-44000000000-440000000000000000022−22−22220000000000000000000000
χ684-4-440040-4400000-4-44000000000-4400000000000000000−222222−220000000000000000000000
χ6988-8-800-40008-8000-4440000-44000000000000000000000000000000000000000000000000
χ7088-8-800-4000-88000-44400004-4000000000000000000000000000000000000000000000000
χ718-8-8800-408-80000044-4000000000-440000000000000000000000000000000000000000000
χ728-8-8800-40-880000044-40000000004-40000000000000000000000000000000000000000000

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