Finite Group Databasebeta

← Group #10694875

Character table — Group #10694875

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
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
χ172222222222-2-2-2-22222-2-222-2-22-2-22222-22-2-2-222-2-222-2-20000000000000000000000000000
χ182222222222-2-2-2-22222-2-222-2-22-2-2222-22-22-2-2-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2-222-2222-2222-2-2-222-2-2-22i−2i−2i2i-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ202222222-2-2-2-2-222-2222-2222-2-2-222-2-2-2−2i2i2i−2i-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
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
χ25222222-1222-2-2-2-22-1-1-1-2-2-1-111-111-1-1-12-22-211-1-111-1-1110000000000−i3i3−i3i300−i3i3−i3i300000000
χ26222222-1222-2-2-2-22-1-1-1-2-2-1-111-111-1-1-12-22-211-1-111-1-1110000000000i3−i3i3−i300i3−i3i3−i300000000
χ27222222-1222-2-2-2-22-1-1-1-2-2-1-111-111-1-1-1-22-221111-1-111-1-10000000000−i3i3−i3i300i3−i3i3−i300000000
χ28222222-1222-2-2-2-22-1-1-1-2-2-1-111-111-1-1-1-22-221111-1-111-1-10000000000i3−i3i3−i300−i3i3−i3i300000000
χ29222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii000000002-2-1-1112i−2i−i−iii00000000
χ30222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii00000000-2211-1-1−2i2iii−i−i00000000
χ31222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i000000002-2-1-111−2i2iii−i−i00000000
χ32222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i00000000-2211-1-12i−2i−i−iii00000000
χ33222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-11112i−2i−2i2i1-1−i−iiiii−i−i0000000000−i3i3i3−i3003−3−3300000000
χ34222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-11112i−2i−2i2i1-1−i−iiiii−i−i0000000000i3−i3−i3i300−333−300000000
χ35222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-1111−2i2i2i−2i1-1ii−i−i−i−iii0000000000−i3i3i3−i300−333−300000000
χ36222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-1111−2i2i2i−2i1-1ii−i−i−i−iii0000000000i3−i3−i3i3003−3−3300000000
χ372222-2-2222-22222-2222-2-2-2-222-22222-20000-2-20000000022-2-222-2-200000000000000000000
χ382222-2-2222-22222-2222-2-2-2-222-22222-20000-2-200000000-2-222-2-22200000000000000000000
χ392222-2-2222-2-2-2-2-2-222222-2-2-2-2-2-2-222-200002200000000000000000000000000002i−2i2i−2i0000
χ402222-2-2222-2-2-2-2-2-222222-2-2-2-2-2-2-222-20000220000000000000000000000000000−2i2i−2i2i0000
χ412222-2-22-2-2222-2-22222-22-2-2222-2-2-2-220000-220000000022-2-2-2-22200000000000000000000
χ422222-2-22-2-2222-2-22222-22-2-2222-2-2-2-220000-2200000000-2-22222-2-200000000000000000000
χ432222-2-22-2-22-2-22222222-2-2-2-2-2222-2-2200002-200000000000000000000000000002-2-220000
χ442222-2-22-2-22-2-22222222-2-2-2-2-2222-2-2200002-20000000000000000000000000000-222-20000
χ454444-4-4-244-44444-4-2-2-2-4-422-2-22-2-2-2-22000022000000000000000000000000000000000000
χ464444-4-4-244-4-4-4-4-4-4-2-2-2442222222-2-220000-2-2000000000000000000000000000000000000
χ474444-4-4-2-4-4444-4-44-2-2-2-4422-2-2-22222-200002-2000000000000000000000000000000000000
χ484444-4-4-2-4-44-4-4444-2-2-24-42222-2-2-222-20000-22000000000000000000000000000000000000
χ4944-4-4004000004-404-4-400000004-4000000000000000000022−220022−2200000000000000000000
χ5044-4-4004000004-404-4-400000004-40000000000000000000−222200−222200000000000000000000
χ5144-4-400400000-4404-4-40000000-44000000000000000000022−2200−222200000000000000000000
χ5244-4-400400000-4404-4-40000000-440000000000000000000−22220022−2200000000000000000000
χ534-44-40040004-4000-44-400004-40000000000000000000000004-40000000000000000000000
χ544-44-40040004-4000-44-400004-4000000000000000000000000-440000000000000000000000
χ554-44-4004000-44000-44-40000-44000000000000000000004-400000000000000000000000000
χ564-44-4004000-44000-44-40000-4400000000000000000000-4400000000000000000000000000
χ574-4-444-444-440000-4-4-44004-400-4004-44000000000000000000000000000000000000000000
χ584-4-444-44-44-400004-4-44004-400400-44-4000000000000000000000000000000000000000000
χ594-4-444-4-24-440000-422-200-2200200-22-2000000−2i32i300−2i32i3000000000000000000000000000000
χ604-4-444-4-24-440000-422-200-2200200-22-20000002i3−2i3002i3−2i3000000000000000000000000000000
χ614-4-444-4-2-44-40000422-200-2200-2002-2200000023−2300−2323000000000000000000000000000000
χ624-4-444-4-2-44-40000422-200-2200-2002-22000000−23230023−23000000000000000000000000000000
χ634-4-44-4444-4-400004-4-4400-44004004-4-4000000000000000000000000000000000000000000
χ644-4-44-444-4440000-4-4-4400-4400-400-444000000000000000000000000000000000000000000
χ654-4-44-44-24-4-40000422-2002-200-200-2220000000023−230023−230000000000000000000000000000
χ664-4-44-44-24-4-40000422-2002-200-200-22200000000−232300−23230000000000000000000000000000
χ674-4-44-44-2-4440000-422-2002-2002002-2-200000000−2i32i3002i3−2i30000000000000000000000000000
χ684-4-44-44-2-4440000-422-2002-2002002-2-2000000002i3−2i300−2i32i30000000000000000000000000000
χ6988-8-800-4000008-80-4440000000-44000000000000000000000000000000000000000000000
χ7088-8-800-400000-880-44400000004-4000000000000000000000000000000000000000000000
χ718-88-800-40008-80004-440000-44000000000000000000000000000000000000000000000000
χ728-88-800-4000-880004-4400004-4000000000000000000000000000000000000000000000000

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