Finite Group Databasebeta

← Group #10694726

Character table — Group #10694726

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order1222222222344446664466666612121212444412121212121212121212888888884444121212121212121288882444
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
χ9111111-1-1-1-111-1-111111-111-1-1-1-111-1-1ii−i−i1-1iiii−i−i−i−i1111-1-1-1-11-1i−i11-1-1ii−i−iii−i−i1-1i−i
χ10111111-1-1-1-111-1-111111-111-1-1-1-111-1-1ii−i−i1-1iiii−i−i−i−i1111-1-1-1-1-11−ii-1-111−i−iiiii−i−i-11−ii
χ11111111-1-1-1-111-1-111111-111-1-1-1-111-1-1ii−i−i1-1iiii−i−i−i−i-1-1-1-111111-1i−i11-1-1ii−i−i−i−iii-11−ii
χ12111111-1-1-1-111-1-111111-111-1-1-1-111-1-1ii−i−i1-1iiii−i−i−i−i-1-1-1-11111-11−ii-1-111−i−iii−i−iii1-1i−i
χ13111111-1-1-1-111-1-111111-111-1-1-1-111-1-1−i−iii1-1−i−i−i−iiiii1111-1-1-1-11-1−ii11-1-1−i−iii−i−iii1-1−ii
χ14111111-1-1-1-111-1-111111-111-1-1-1-111-1-1−i−iii1-1−i−i−i−iiiii1111-1-1-1-1-11i−i-1-111ii−i−i−i−iii-11i−i
χ15111111-1-1-1-111-1-111111-111-1-1-1-111-1-1−i−iii1-1−i−i−i−iiiii-1-1-1-111111-1−ii11-1-1−i−iiiii−i−i-11i−i
χ16111111-1-1-1-111-1-111111-111-1-1-1-111-1-1−i−iii1-1−i−i−i−iiiii-1-1-1-11111-11i−i-1-111ii−i−iii−i−i1-1−ii
χ1722222222222-2-2-2-2222-2-2222222-2-2-2-22-22-2-2-222-2-222-2-20000000000000000000000000000
χ1822222222222-2-2-2-2222-2-2222222-2-2-2-2-22-22-2-2-2-222-2-2220000000000000000000000000000
χ192222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ202222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ212222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ222222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ232222222222-1-2-2-2-2-1-1-1-2-2-1-1-1-1-1-111112-22-211-1-111-1-111000000000000−i3i3−i3i3−i3i3−i3i300000000
χ242222222222-1-2-2-2-2-1-1-1-2-2-1-1-1-1-1-111112-22-211-1-111-1-111000000000000i3−i3i3−i3i3−i3i3−i300000000
χ252222222222-1-2-2-2-2-1-1-1-2-2-1-1-1-1-1-11111-22-221111-1-111-1-1000000000000−i3i3−i3i3i3−i3i3−i300000000
χ262222222222-1-2-2-2-2-1-1-1-2-2-1-1-1-1-1-11111-22-221111-1-111-1-1000000000000i3−i3i3−i3−i3i3−i3i300000000
χ27222222-2-2-2-22-222-2222-2222-2-2-2-2-2-2222i−2i−2i2i-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ28222222-2-2-2-22-222-2222-2222-2-2-2-2-2-222−2i2i2i−2i-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ29222222-2-2-2-2-12-2-22-1-1-12-2-1-11111-1-1112i2i−2i−2i-11−i−i−i−iiiii000000002-22i−2i-1-111−i−iii00000000
χ30222222-2-2-2-2-12-2-22-1-1-12-2-1-11111-1-1112i2i−2i−2i-11−i−i−i−iiiii00000000-22−2i2i11-1-1ii−i−i00000000
χ31222222-2-2-2-2-12-2-22-1-1-12-2-1-11111-1-111−2i−2i2i2i-11iiii−i−i−i−i000000002-2−2i2i-1-111ii−i−i00000000
χ32222222-2-2-2-2-12-2-22-1-1-12-2-1-11111-1-111−2i−2i2i2i-11iiii−i−i−i−i00000000-222i−2i11-1-1−i−iii00000000
χ33222222-2-2-2-2-1-222-2-1-1-1-22-1-1111111-1-12i−2i−2i2i1-1−i−iiiii−i−i000000000000−i3i3i3−i33−3−3300000000
χ34222222-2-2-2-2-1-222-2-1-1-1-22-1-1111111-1-12i−2i−2i2i1-1−i−iiiii−i−i000000000000i3−i3−i3i3−333−300000000
χ35222222-2-2-2-2-1-222-2-1-1-1-22-1-1111111-1-1−2i2i2i−2i1-1ii−i−i−i−iii000000000000−i3i3i3−i3−333−300000000
χ36222222-2-2-2-2-1-222-2-1-1-1-22-1-1111111-1-1−2i2i2i−2i1-1ii−i−i−i−iii000000000000i3−i3−i3i33−3−3300000000
χ372222-2-22-2-2222-2-22222-22-2-22-2-2222-2-20000-220000000022-2-222-2-200000000000000000000
χ382222-2-22-2-2222-2-22222-22-2-22-2-2222-2-20000-2200000000-2-222-2-22200000000000000000000
χ392222-2-22-2-222-222-22222-2-2-22-2-22-2-22200002-200000000000000000000000000002-22-20000
χ402222-2-22-2-222-222-22222-2-2-22-2-22-2-22200002-20000000000000000000000000000-22-220000
χ412222-2-2-222-222222222-2-2-2-2-222-222220000-2-20000000022-2-2-2-22200000000000000000000
χ422222-2-2-222-222222222-2-2-2-2-222-222220000-2-200000000-2-22222-2-200000000000000000000
χ432222-2-2-222-22-2-2-2-222222-2-2-222-2-2-2-2-200002200000000000000000000000000002i−2i−2i2i0000
χ442222-2-2-222-22-2-2-2-222222-2-2-222-2-2-2-2-20000220000000000000000000000000000−2i2i2i−2i0000
χ454444-4-44-4-44-24-4-44-2-2-2-4422-222-2-2-22200002-2000000000000000000000000000000000000
χ464444-4-44-4-44-2-444-4-2-2-24-422-222-222-2-20000-22000000000000000000000000000000000000
χ474444-4-4-444-4-24444-2-2-2-4-4222-2-22-2-2-2-2000022000000000000000000000000000000000000
χ484444-4-4-444-4-2-4-4-4-4-2-2-244222-2-2222220000-2-2000000000000000000000000000000000000
χ4944-4-4000000404i−4i0-44-400000000004i−4i000000000000000022−22−2i22i20000000000000000000000
χ5044-4-4000000404i−4i0-44-400000000004i−4i0000000000000000−22222i2−2i20000000000000000000000
χ5144-4-400000040−4i4i0-44-40000000000−4i4i000000000000000022−222i2−2i20000000000000000000000
χ5244-4-400000040−4i4i0-44-40000000000−4i4i0000000000000000−2222−2i22i20000000000000000000000
χ534-44-40000004400-4-4-44000000004-400000000000000004i−4i00000000000000000000000000
χ544-44-40000004400-4-4-44000000004-40000000000000000−4i4i00000000000000000000000000
χ554-44-40000004-4004-4-4400000000-4400000000000000000000004-400000000000000000000
χ564-44-40000004-4004-4-4400000000-440000000000000000000000-4400000000000000000000
χ574-4-444-444-4-4400004-4-4004-444-4-40000000000000000000000000000000000000000000000
χ584-4-444-444-4-4-20000-22200-22-2-2220000000000−2i32i300−2i32i3000000000000000000000000000000
χ594-4-444-444-4-4-20000-22200-22-2-22200000000002i3−2i3002i3−2i3000000000000000000000000000000
χ604-4-444-4-4-444400004-4-4004-4-4-4440000000000000000000000000000000000000000000000
χ614-4-444-4-4-444-20000-22200-2222-2-2000000000023−2300−2323000000000000000000000000000000
χ624-4-444-4-4-444-20000-22200-2222-2-20000000000−23230023−23000000000000000000000000000000
χ634-4-44-444-44-4400004-4-400-444-44-40000000000000000000000000000000000000000000000
χ644-4-44-444-44-4-20000-222002-2-22-22000000000000−2i32i300−2i32i30000000000000000000000000000
χ654-4-44-444-44-4-20000-222002-2-22-220000000000002i3−2i3002i3−2i30000000000000000000000000000
χ664-4-44-44-44-44400004-4-400-44-44-440000000000000000000000000000000000000000000000
χ674-4-44-44-44-44-20000-222002-22-22-200000000000023−2300−23230000000000000000000000000000
χ684-4-44-44-44-44-20000-222002-22-22-2000000000000−23230023−230000000000000000000000000000
χ6988-8-8000000-408i−8i04-440000000000−4i4i000000000000000000000000000000000000000000
χ7088-8-8000000-40−8i8i04-4400000000004i−4i000000000000000000000000000000000000000000
χ718-88-8000000-4800-844-400000000-4400000000000000000000000000000000000000000000
χ728-88-8000000-4-800844-4000000004-400000000000000000000000000000000000000000000

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