Finite Group Databasebeta

← Group #10692589

Character table — Group #10692589

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244488121212122424242422444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ91111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-11-111-1-1ii−i−ii−i
χ101111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i-11-11-1-111−i−iii−ii
χ111111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i-11−ii-1-111−i−iii1-11-1-1-111ii−i−i−ii
χ121111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11-1111-1-1−i−iiii−i
χ131111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-11-111-1-1−i−iii−ii
χ141111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii-11-11-1-111ii−i−ii−i
χ151111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii-11i−i-1-111ii−i−i1-11-1-1-111−i−iiii−i
χ161111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11-1111-1-1ii−i−i−ii
χ172222222222-2-22222-2-2-222-2-2222-2-220000-2-20000000000000000000022-2-20000000000
χ182222222222-2-22222-2-2-222-2-2222-2-220000-2-200000000000000000000-2-2220000000000
χ192222222-2-2-222-2222-2-2222-2-2-2-2-222-20000-22000000000000000000002-2-220000000000
χ202222222-2-2-222-2222-2-2222-2-2-2-2-222-20000-2200000000000000000000-222-20000000000
χ21222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ25222222-1-2-2-2-2-2-2-1-1-122-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii2-22i−2i-1-111−i−iii00000000000000
χ26222222-1-2-2-2-2-2-2-1-1-122-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii-22−2i2i11-1-1ii−i−i00000000000000
χ27222222-1-2-2-2-2-2-2-1-1-122-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i2-2−2i2i-1-111ii−i−i00000000000000
χ28222222-1-2-2-2-2-2-2-1-1-122-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i-222i−2i11-1-1−i−iii00000000000000
χ292222-2-222-2222-22222-2-2-2-2-2-22-2-22222-22-22-222-2-222-2-200000000000000000000000000
χ302222-2-222-2222-22222-2-2-2-2-2-22-2-2222-22-222-2-2-222-2-22200000000000000000000000000
χ312222-2-222-22-2-2-2222-222-2-2222-2-2-2-220000-2200000000000000000000000000002i−2i2i−2i00
χ322222-2-222-22-2-2-2222-222-2-2222-2-2-2-220000-220000000000000000000000000000−2i2i−2i2i00
χ332222-2-22-22-2222222-22-2-2-222-22222-20000-2-200000000000000000000000000002-2-2200
χ342222-2-22-22-2222222-22-2-2-222-22222-20000-2-20000000000000000000000000000-222-200
χ352222-2-22-22-2-2-222222-22-2-2-2-2-222-2-2-22i−2i−2i2i222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-22-2-2-222222-22-2-2-2-2-222-2-2-2−2i2i2i−2i22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-12-2222-2-1-1-12-2-21111-111-1-1-12-22-2-11-1-111-1-1110000−i3i3−i3i3−i3i3−i3i300000000000000
χ382222-2-2-12-2222-2-1-1-12-2-21111-111-1-1-12-22-2-11-1-111-1-1110000i3−i3i3−i3i3−i3i3−i300000000000000
χ392222-2-2-12-2222-2-1-1-12-2-21111-111-1-1-1-22-22-1111-1-111-1-10000−i3i3−i3i3i3−i3i3−i300000000000000
χ402222-2-2-12-2222-2-1-1-12-2-21111-111-1-1-1-22-22-1111-1-111-1-10000i3−i3i3−i3−i3i3−i3i300000000000000
χ412222-2-2-1-22-2-2-22-1-1-12-2211111-1-11112i−2i−2i2i-1-1−i−iiiii−i−i0000−i3i3i3−i33−3−3300000000000000
χ422222-2-2-1-22-2-2-22-1-1-12-2211111-1-11112i−2i−2i2i-1-1−i−iiiii−i−i0000i3−i3−i3i3−333−300000000000000
χ432222-2-2-1-22-2-2-22-1-1-12-2211111-1-1111−2i2i2i−2i-1-1ii−i−i−i−iii0000−i3i3i3−i3−333−300000000000000
χ442222-2-2-1-22-2-2-22-1-1-12-2211111-1-1111−2i2i2i−2i-1-1ii−i−i−i−iii0000i3−i3−i3i33−3−3300000000000000
χ45444444-2444-4-44-2-2-2-4-4-4-2-222-2-2-222-20000220000000000000000000000000000000000
χ46444444-2-4-4-444-4-2-2-2-4-44-2-222222-2-2200002-20000000000000000000000000000000000
χ474444-4-4-24-44-4-4-4-2-2-2-44422-2-2-22222-200002-20000000000000000000000000000000000
χ484444-4-4-2-44-4444-2-2-2-44-422-2-22-2-2-2-220000220000000000000000000000000000000000
χ494-44-44-4444-400-4-4-440004-40044-400-40000000000000000000000000000000000000000
χ504-44-44-44-4-44004-4-440004-400-4-440040000000000000000000000000000000000000000
χ514-44-44-4-244-400-422-2000-2200-2-220020000006−66−66−66−600000000000000000000000000
χ524-44-44-4-244-400-422-2000-2200-2-22002000000−66−66−66−6600000000000000000000000000
χ534-44-44-4-2-4-4400422-2000-220022-200-2000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ544-44-44-4-2-4-4400422-2000-220022-200-2000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ554-44-4-4444-4-4004-4-44000-44004-4400-40000000000000000000000000000000000000000
χ564-44-4-444-44400-4-4-44000-4400-44-40040000000000000000000000000000000000000000
χ574-44-4-44-24-4-400422-20002-200-22-20020000006−6−666−6−6600000000000000000000000000
χ584-44-4-44-24-4-400422-20002-200-22-2002000000−666−6−666−600000000000000000000000000
χ594-44-4-44-2-44400-422-20002-2002-2200-2000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ604-44-4-44-2-44400-422-20002-2002-2200-2000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ614-4-440040004-404-4-400000000004-400000000000000000000000000000002i−2i2i−2i000000
χ624-4-440040004-404-4-400000000004-40000000000000000000000000000000−2i2i−2i2i000000
χ634-4-44004000-4404-4-40000000000-4400000000000000000000000000000002i−2i−2i2i000000
χ644-4-44004000-4404-4-40000000000-440000000000000000000000000000000−2i2i2i−2i000000
χ6588-8-8008000000-88-800000000000000000000000000000000000000000000000000000
χ6688-8-800-40000004-4400000−4i34i30000000000000000000000000000000000000000000000
χ6788-8-800-40000004-44000004i3−4i30000000000000000000000000000000000000000000000
χ688-8-8800-40008-80-4440000000000-4400000000000000000000000000000000000000000
χ698-8-8800-4000-880-44400000000004-400000000000000000000000000000000000000000

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