Finite Group Databasebeta

← Group #10692579

Character table — Group #10692579

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
χ91111111-1-1-1-1-1-111111-111-1-1-111-1-1-1ii−i−i-11iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-11-111-1-1ii−i−ii−i
χ101111111-1-1-1-1-1-111111-111-1-1-111-1-1-1ii−i−i-11iiii−i−i−i−i1-1i−i11-1-1ii−i−i-11-11-1-111−i−iii−ii
χ111111111-1-1-1-1-1-111111-111-1-1-111-1-1-1ii−i−i-11iiii−i−i−i−i-11−ii-1-111−i−iii1-11-1-1-111ii−i−i−ii
χ121111111-1-1-1-1-1-111111-111-1-1-111-1-1-1ii−i−i-11iiii−i−i−i−i-11−ii-1-111−i−iii-11-1111-1-1−i−iiii−i
χ131111111-1-1-1-1-1-111111-111-1-1-111-1-1-1−i−iii-11−i−i−i−iiiii1-1−ii11-1-1−i−iii1-11-111-1-1−i−iii−ii
χ141111111-1-1-1-1-1-111111-111-1-1-111-1-1-1−i−iii-11−i−i−i−iiiii1-1−ii11-1-1−i−iii-11-11-1-111ii−i−ii−i
χ151111111-1-1-1-1-1-111111-111-1-1-111-1-1-1−i−iii-11−i−i−i−iiiii-11i−i-1-111ii−i−i1-11-1-1-111−i−iiii−i
χ161111111-1-1-1-1-1-111111-111-1-1-111-1-1-1−i−iii-11−i−i−i−iiiii-11i−i-1-111ii−i−i-11-1111-1-1ii−i−i−ii
χ172222222222-2-22222-2-2-222222-2-2-2-220000-2-20000000000000000000022-2-20000000000
χ182222222222-2-22222-2-2-222222-2-2-2-220000-2-200000000000000000000-2-2220000000000
χ192222222-2-2-222-2222-2-2222-2-2-2-2-222-200002-2000000000000000000002-2-220000000000
χ202222222-2-2-222-2222-2-2222-2-2-2-2-222-200002-200000000000000000000-222-20000000000
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
χ25222222-1-2-2-2-2-2-2-1-1-122-2-1-1111-1-11112i2i−2i−2i1-1−i−i−i−iiiii2-22i−2i-1-111−i−iii00000000000000
χ26222222-1-2-2-2-2-2-2-1-1-122-2-1-1111-1-11112i2i−2i−2i1-1−i−i−i−iiiii-22−2i2i11-1-1ii−i−i00000000000000
χ27222222-1-2-2-2-2-2-2-1-1-122-2-1-1111-1-1111−2i−2i2i2i1-1iiii−i−i−i−i2-2−2i2i-1-111ii−i−i00000000000000
χ28222222-1-2-2-2-2-2-2-1-1-122-2-1-1111-1-1111−2i−2i2i2i1-1iiii−i−i−i−i-222i−2i11-1-1−i−iii00000000000000
χ292222-2-222-2222-22222-2-2-2-22-2-2-2-22222-22-2-2222-2-222-2-200000000000000000000000000
χ302222-2-222-2222-22222-2-2-2-22-2-2-2-2222-22-22-22-2-222-2-22200000000000000000000000000
χ312222-2-222-22-2-2-2222-222-2-22-2-222-2-2200002-200000000000000000000000000002i−2i2i−2i00
χ322222-2-222-22-2-2-2222-222-2-22-2-222-2-2200002-20000000000000000000000000000−2i2i−2i2i00
χ332222-2-22-22-2222222-22-2-2-2-2222222-20000-2-200000000000000000000000000002-2-2200
χ342222-2-22-22-2222222-22-2-2-2-2222222-20000-2-20000000000000000000000000000-222-200
χ352222-2-22-22-2-2-222222-22-2-2-222-2-2-2-2-22i−2i−2i2i222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-22-2-2-222222-22-2-2-222-2-2-2-2-2−2i2i2i−2i22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-12-2222-2-1-1-12-2-211-11111-1-1-12-22-21-1-1-111-1-1110000−i3i3−i3i3−i3i3−i3i300000000000000
χ382222-2-2-12-2222-2-1-1-12-2-211-11111-1-1-12-22-21-1-1-111-1-1110000i3−i3i3−i3i3−i3i3−i300000000000000
χ392222-2-2-12-2222-2-1-1-12-2-211-11111-1-1-1-22-221-111-1-111-1-10000−i3i3−i3i3i3−i3i3−i300000000000000
χ402222-2-2-12-2222-2-1-1-12-2-211-11111-1-1-1-22-221-111-1-111-1-10000i3−i3i3−i3−i3i3−i3i300000000000000
χ412222-2-2-1-22-2-2-22-1-1-12-22111-1-1111112i−2i−2i2i-1-1−i−iiiii−i−i0000−i3i3i3−i33−3−3300000000000000
χ422222-2-2-1-22-2-2-22-1-1-12-22111-1-1111112i−2i−2i2i-1-1−i−iiiii−i−i0000i3−i3−i3i3−333−300000000000000
χ432222-2-2-1-22-2-2-22-1-1-12-22111-1-111111−2i2i2i−2i-1-1ii−i−i−i−iii0000−i3i3i3−i3−333−300000000000000
χ442222-2-2-1-22-2-2-22-1-1-12-22111-1-111111−2i2i2i−2i-1-1ii−i−i−i−iii0000i3−i3−i3i33−3−3300000000000000
χ45444444-2444-4-44-2-2-2-4-4-4-2-2-2-2-22222-20000220000000000000000000000000000000000
χ46444444-2-4-4-444-4-2-2-2-4-44-2-222222-2-220000-220000000000000000000000000000000000
χ474444-4-4-24-44-4-4-4-2-2-2-44422-222-2-222-20000-220000000000000000000000000000000000
χ484444-4-4-2-44-4444-2-2-2-44-4222-2-2-2-2-2-220000220000000000000000000000000000000000
χ4944-4-44-444-4-40044-4-40004-444-40000-40000000000000000000000000000000000000000
χ5044-4-44-44-44400-44-4-40004-4-4-44000040000000000000000000000000000000000000000
χ5144-4-44-4-24-4-4004-222000-22-2-2200002000000i6−i6i6−i6i6−i6i6−i600000000000000000000000000
χ5244-4-44-4-24-4-4004-222000-22-2-2200002000000−i6i6−i6i6−i6i6−i6i600000000000000000000000000
χ5344-4-44-4-2-44400-4-222000-2222-20000-20000006−66−6−66−6600000000000000000000000000
χ5444-4-44-4-2-44400-4-222000-2222-20000-2000000−66−666−66−600000000000000000000000000
χ5544-4-4-44444-400-44-4-4000-444-440000-40000000000000000000000000000000000000000
χ5644-4-4-444-4-440044-4-4000-44-44-4000040000000000000000000000000000000000000000
χ5744-4-4-44-244-400-4-2220002-2-22-200002000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ5844-4-4-44-244-400-4-2220002-2-22-200002000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ5944-4-4-44-2-4-44004-2220002-22-220000-20000006−6−66−666−600000000000000000000000000
χ6044-4-4-44-2-4-44004-2220002-22-220000-2000000−666−66−6−6600000000000000000000000000
χ614-4-440040004-40-44-400000000004-400000000000000000000000000000002i−2i2i−2i000000
χ624-4-440040004-40-44-400000000004-40000000000000000000000000000000−2i2i−2i2i000000
χ634-4-44004000-440-44-40000000000-4400000000000000000000000000000002i−2i−2i2i000000
χ644-4-44004000-440-44-40000000000-440000000000000000000000000000000−2i2i2i−2i000000
χ658-88-8008000000-8-8800000000000000000000000000000000000000000000000000000
χ668-88-800-400000044-400000000−4i34i30000000000000000000000000000000000000000000
χ678-88-800-400000044-4000000004i3−4i30000000000000000000000000000000000000000000
χ688-8-8800-40008-804-440000000000-4400000000000000000000000000000000000000000
χ698-8-8800-4000-8804-4400000000004-400000000000000000000000000000000000000000

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