Finite Group Databasebeta

← Group #10694884

Character table — Group #10694884

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424888888884488121212122424242488882288
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ91111111-1-1-111-1-1-11111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i1111-1-1-1-11-1i−i11-1-1ii−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−ii-1-111−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-1-1-1-111111-1i−i11-1-1ii−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−ii-1-111−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−iiiii1111-1-1-1-11-1−ii11-1-1−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−iiiii1111-1-1-1-1-11i−i-1-111ii−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-1-1-1-111111-1−ii11-1-1−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-1-1-1-11111-11i−i-1-111ii−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
χ21222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ25222222-1222-2-2-2-22-1-1-1-2-2-1-111-111-1-1-12-22-211-1-111-1-111000000000000−i3i3−i3i3−i3i3−i3i300000000
χ26222222-1222-2-2-2-22-1-1-1-2-2-1-111-111-1-1-12-22-211-1-111-1-111000000000000i3−i3i3−i3i3−i3i3−i300000000
χ27222222-1222-2-2-2-22-1-1-1-2-2-1-111-111-1-1-1-22-221111-1-111-1-1000000000000−i3i3−i3i3i3−i3i3−i300000000
χ28222222-1222-2-2-2-22-1-1-1-2-2-1-111-111-1-1-1-22-221111-1-111-1-1000000000000i3−i3i3−i3−i3i3−i3i300000000
χ29222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii000000002-22i−2i-1-111−i−iii00000000
χ30222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii00000000-22−2i2i11-1-1ii−i−i00000000
χ31222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i000000002-2−2i2i-1-111ii−i−i00000000
χ32222222-1-2-2-222-2-2-2-1-1-12-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i00000000-222i−2i11-1-1−i−iii00000000
χ33222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-11112i−2i−2i2i1-1−i−iiiii−i−i000000000000−i3i3i3−i33−3−3300000000
χ34222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-11112i−2i−2i2i1-1−i−iiiii−i−i000000000000i3−i3−i3i3−333−300000000
χ35222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-1111−2i2i2i−2i1-1ii−i−i−i−iii000000000000−i3i3i3−i3−333−300000000
χ36222222-1-2-2-2-2-222-2-1-1-1-22-1-1111-1-1111−2i2i2i−2i1-1ii−i−i−i−iii000000000000i3−i3−i3i33−3−3300000000
χ372222-2-222-2-222-2-22222-22-2-2222-2-2-2-220000-220000000022-2-222-2-200000000000000000000
χ382222-2-222-2-222-2-22222-22-2-2222-2-2-2-220000-2200000000-2-222-2-22200000000000000000000
χ392222-2-222-2-2-2-22222222-2-2-2-2-2222-2-2200002-200000000000000000000000000002-22-20000
χ402222-2-222-2-2-2-22222222-2-2-2-2-2222-2-2200002-20000000000000000000000000000-22-220000
χ412222-2-22-2222222-2222-2-2-2-222-22222-20000-2-20000000022-2-2-2-22200000000000000000000
χ422222-2-22-2222222-2222-2-2-2-222-22222-20000-2-200000000-2-22222-2-200000000000000000000
χ432222-2-22-222-2-2-2-2-222222-2-2-2-2-2-2-222-200002200000000000000000000000000002i−2i−2i2i0000
χ442222-2-22-222-2-2-2-2-222222-2-2-2-2-2-2-222-20000220000000000000000000000000000−2i2i2i−2i0000
χ454444-4-4-24-4-444-4-44-2-2-2-4422-2-2-22222-200002-2000000000000000000000000000000000000
χ464444-4-4-24-4-4-4-4444-2-2-24-42222-2-2-222-20000-22000000000000000000000000000000000000
χ474444-4-4-2-4444444-4-2-2-2-4-422-2-22-2-2-2-22000022000000000000000000000000000000000000
χ484444-4-4-2-444-4-4-4-4-4-2-2-2442222222-2-220000-2-2000000000000000000000000000000000000
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
χ534-44-44-4444-40000-4-44-4004-4004004-4-4000000000000000000000000000000000000000000
χ544-44-44-44-4-4400004-44-4004-400-400-444000000000000000000000000000000000000000000
χ554-44-44-4-244-40000-42-2200-2200-200-222000000−2i32i300−2i32i3000000000000000000000000000000
χ564-44-44-4-244-40000-42-2200-2200-200-2220000002i3−2i3002i3−2i3000000000000000000000000000000
χ574-44-44-4-2-4-44000042-2200-22002002-2-200000023−2300−2323000000000000000000000000000000
χ584-44-44-4-2-4-44000042-2200-22002002-2-2000000−23230023−23000000000000000000000000000000
χ594-44-4-4444-440000-4-44-400-4400400-44-4000000000000000000000000000000000000000000
χ604-44-4-444-44-400004-44-400-4400-4004-44000000000000000000000000000000000000000000
χ614-44-4-44-24-440000-42-22002-200-2002-2200000000−2i32i300−2i32i30000000000000000000000000000
χ624-44-4-44-24-440000-42-22002-200-2002-22000000002i3−2i3002i3−2i30000000000000000000000000000
χ634-44-4-44-2-44-4000042-22002-200200-22-20000000023−2300−23230000000000000000000000000000
χ644-44-4-44-2-44-4000042-22002-200200-22-200000000−23230023−230000000000000000000000000000
χ654-4-44004000004-40-4-4400000004-4000000000000000000022−2222−220000000000000000000000
χ664-4-44004000004-40-4-4400000004-40000000000000000000−2222−22220000000000000000000000
χ674-4-4400400000-440-4-440000000-44000000000000000000022−22−22220000000000000000000000
χ684-4-4400400000-440-4-440000000-440000000000000000000−222222−220000000000000000000000
χ6988-8-800-40008-8000-4440000-44000000000000000000000000000000000000000000000000
χ7088-8-800-4000-88000-44400004-4000000000000000000000000000000000000000000000000
χ718-8-8800-4000008-8044-40000000-44000000000000000000000000000000000000000000000
χ728-8-8800-400000-88044-400000004-4000000000000000000000000000000000000000000000

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