Finite Group Databasebeta

← Group #10692049

Character table — Group #10692049

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12222234444446662244444444466121212121212121266121212121212121288888888888888882266668824242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-1111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111-1-1111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ71111111111111111-1-1111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1
χ81111111111111111-1-1111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111
χ91111-1-111-11-1-1-11111111-111-1-1-1-1-1-1111-1-1-1-11111-111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i1-111-1-11-111-1-1ii−i−ii−i
χ101111-1-111-11-1-1-11111111-111-1-1-1-1-1-1111-1-1-1-11111-111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-11-1-111-11-1-111−i−iii−ii
χ111111-1-111-11-1-1-11111111-111-1-1-1-1-1-1111-1-1-1-11111-111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii1-111-1-11-111-1-1−i−iii−ii
χ121111-1-111-11-1-1-11111111-111-1-1-1-1-1-1111-1-1-1-11111-111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-11-1-111-11-1-111ii−i−ii−i
χ131111-1-111-11-1-1-1111-1-111-1-1-11111-1-1111-1-1-1-11-1-11-1-1-11111ii−i−iii−i−i−i−i−i−iiiii1-111-1-1-11-1-111−i−iiii−i
χ141111-1-111-11-1-1-1111-1-111-1-1-11111-1-1111-1-1-1-11-1-11-1-1-11111ii−i−iii−i−i−i−i−i−iiiii-11-1-1111-111-1-1ii−i−i−ii
χ151111-1-111-11-1-1-1111-1-111-1-1-11111-1-1111-1-1-1-11-1-11-1-1-11111−i−iii−i−iiiiiii−i−i−i−i1-111-1-1-11-1-111ii−i−i−ii
χ161111-1-111-11-1-1-1111-1-111-1-1-11111-1-1111-1-1-1-11-1-11-1-1-11111−i−iii−i−iiiiiii−i−i−i−i-11-1-1111-111-1-1−i−iiii−i
χ172222222222-22-222222-2-2-2-2-222-2-2222-2-222-2-2222-2-2-2-222-2-20000000000000000000000000000000000
χ182222222222-22-2222-2-2-2-2-222-2-222222-2-222-2-22-2-2-2-222-2-2220000000000000000000000000000000000
χ192222222-2-2-22-22222002-2-200000022-2-2-2-2-222-2002-20000000000000022-2-222-2-2000000000000000000
χ202222222-2-2-22-22222002-2-200000022-2-2-2-2-222-2002-200000000000000-2-222-2-222000000000000000000
χ212222222-2-2-2-2-2-222200-22200000022-222-2-2-2-2-200-220000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ222222222-2-2-2-2-2-222200-22200000022-222-2-2-2-2-200-22000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ23222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-122-1-1-1-1000000
χ24222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-21111-2-21111000000
χ25222222-1222222-1-1-1-2-2222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111-1-1111111000000000000000022-1-1-1-1-2-21111000000
χ26222222-1222222-1-1-1-2-2222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111-1-11111110000000000000000-2-2111122-1-1-1-1000000
χ27222222-1222-22-2-1-1-122-2-2-2-2-222-2-2-1-1-111-1-111-1-1-11111-1-111000000000000000000−i3i3−i3i300−i3i3−i3i3000000
χ28222222-1222-22-2-1-1-122-2-2-2-2-222-2-2-1-1-111-1-111-1-1-11111-1-111000000000000000000i3−i3i3−i300i3−i3i3−i3000000
χ29222222-1222-22-2-1-1-1-2-2-2-2-222-2-222-1-1-111-1-111-11111-1-111-1-1000000000000000000−i3i3−i3i300i3−i3i3−i3000000
χ30222222-1222-22-2-1-1-1-2-2-2-2-222-2-222-1-1-111-1-111-11111-1-111-1-1000000000000000000i3−i3i3−i300−i3i3−i3i3000000
χ312222-2-222-222-2222222-2-22-2-2-2-222-2-22-2-2-2-222222-22-2-2-2-2220000000000000000000000000000000000
χ322222-2-222-222-22222-2-2-2-222222-2-2-2-22-2-2-2-2222-2-2-222222-2-20000000000000000000000000000000000
χ332222-2-22-22-222222200-22-2000000-2-2-2222222-200-2-20000002222-2-2-2-200000000000000000000000000
χ342222-2-22-22-222222200-22-2000000-2-2-2222222-200-2-2000000-2-2-2-2222200000000000000000000000000
χ352222-2-22-22-2-22-2222002-22000000-2-2-2-2-222-2-2-20022000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ362222-2-22-22-2-22-2222002-22000000-2-2-2-2-222-2-2-2002200000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ372222-2-2-12-222-22-1-1-122-2-22-2-2-2-22211-11111-1-1-1-1-11-11111-1-1000000000000000000−i3i3i3−i300−i3i3i3−i3000000
χ382222-2-2-12-222-22-1-1-122-2-22-2-2-2-22211-11111-1-1-1-1-11-11111-1-1000000000000000000i3−i3−i3i300i3−i3−i3i3000000
χ392222-2-2-12-222-22-1-1-1-2-2-2-222222-2-211-11111-1-1-1111-1-1-1-1-111000000000000000000−i3i3i3−i300i3−i3−i3i3000000
χ402222-2-2-12-222-22-1-1-1-2-2-2-222222-2-211-11111-1-1-1111-1-1-1-1-111000000000000000000i3−i3−i3i300−i3i3i3−i3000000
χ412222-2-2-12-22-2-2-2-1-1-12222-222-2-2-2-211-1-1-11111-1-1-1-11-1-1111100000000000000002-2-1-1112-2-1-111000000
χ422222-2-2-12-22-2-2-2-1-1-12222-222-2-2-2-211-1-1-11111-1-1-1-11-1-111110000000000000000-2211-1-1-2211-1-1000000
χ432222-2-2-12-22-2-2-2-1-1-1-2-222-2-2-2222211-1-1-11111-111-1111-1-1-1-100000000000000002-2-1-111-2211-1-1000000
χ442222-2-2-12-22-2-2-2-1-1-1-2-222-2-2-2222211-1-1-11111-111-1111-1-1-1-10000000000000000-2211-1-12-2-1-111000000
χ4522-2-22-222-2-20202-2-2000002i−2i002i−2i2-22002-200-200002i−2i002i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ4622-2-22-222-2-20202-2-2000002i−2i002i−2i2-22002-200-200002i−2i002i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000000
χ4722-2-22-222-2-20202-2-200000−2i2i00−2i2i2-22002-200-20000−2i2i00−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ4822-2-22-222-2-20202-2-200000−2i2i00−2i2i2-22002-200-20000−2i2i00−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000000000
χ4922-2-22-22-2220-202-2-22-2000002-2002-2-200-220022-200002-200−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ5022-2-22-22-2220-202-2-22-2000002-2002-2-200-220022-200002-200i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ5122-2-22-22-2220-202-2-2-2200000-22002-2-200-22002-220000-2200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ5222-2-22-22-2220-202-2-2-2200000-22002-2-200-22002-220000-2200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ5322-2-2-22222-20-202-2-2000002i−2i00−2i2i-22200-2200-200002i−2i00−2i2i−i2i2i2−i2−i2i2i2−i2−22−222−22−2000000000000000000
χ5422-2-2-22222-20-202-2-2000002i−2i00−2i2i-22200-2200-200002i−2i00−2i2ii2−i2−i2i2i2−i2−i2i22−22−2−22−22000000000000000000
χ5522-2-2-22222-20-202-2-200000−2i2i002i−2i-22200-2200-20000−2i2i002i−2i−i2i2i2−i2−i2i2i2−i22−22−2−22−22000000000000000000
χ5622-2-2-22222-20-202-2-200000−2i2i002i−2i-22200-2200-20000−2i2i002i−2ii2−i2−i2i2i2−i2−i2i2−22−222−22−2000000000000000000
χ5722-2-2-222-2-220202-2-22-200000-2200-22-2002-20022-20000-22002−22−2−22−222−2−22−222−2000000000000000000
χ5822-2-2-222-2-220202-2-22-200000-2200-22-2002-20022-20000-2200−22−222−22−2−222−22−2−22000000000000000000
χ5922-2-2-222-2-220202-2-2-22000002-200-22-2002-2002-2200002-2002−22−2−22−22−222−22−2−22000000000000000000
χ6022-2-2-222-2-220202-2-2-22000002-200-22-2002-2002-2200002-200−22−222−22−22−2−22−222−2000000000000000000
χ61444444-2-4-4-44-44-2-2-2004-4-4000000-2-222222-2-2200-220000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-200-444000000-2-22-2-222222002-20000000000000000000000000000000000000000
χ634444-4-4-2-44-4444-2-2-200-44-4000000222-2-2-2-2-2-2200220000000000000000000000000000000000000000
χ644444-4-4-2-44-4-44-4-2-2-2004-4400000022222-2-222200-2-20000000000000000000000000000000000000000
χ6544-4-44-4-24-4-4040-222000004i−4i004i−4i-22-200-220020000−2i2i00−2i2i0000000000000000000000000000000000
χ6644-4-44-4-24-4-4040-22200000−4i4i00−4i4i-22-200-2200200002i−2i002i−2i0000000000000000000000000000000000
χ6744-4-44-4-2-4440-40-2224-4000004-400-222002-200-2-220000-22000000000000000000000000000000000000
χ6844-4-44-4-2-4440-40-222-4400000-4400-222002-200-22-200002-2000000000000000000000000000000000000
χ6944-4-4-44-244-40-40-222000004i−4i00−4i4i2-2-2002-20020000−2i2i002i−2i0000000000000000000000000000000000
χ7044-4-4-44-244-40-40-22200000−4i4i004i−4i2-2-2002-200200002i−2i00−2i2i0000000000000000000000000000000000
χ7144-4-4-44-2-4-44040-2224-400000-44002-2200-2200-2-2200002-2000000000000000000000000000000000000
χ7244-4-4-44-2-4-44040-222-44000004-4002-2200-2200-22-20000-22000000000000000000000000000000000000
χ734-44-400400040-4-44-40000000000000000004-40000000000000000000000000000000000000002i−2i2i−2i00
χ744-44-400400040-4-44-40000000000000000004-4000000000000000000000000000000000000000−2i2i−2i2i00
χ754-44-4004000-404-44-4000000000000000000-440000000000000000000000000000000000000002-2-2200
χ764-44-4004000-404-44-4000000000000000000-44000000000000000000000000000000000000000-222-200
χ778-88-800-400080-84-44000000000000000000-44000000000000000000000000000000000000000000000
χ788-88-800-4000-8084-440000000000000000004-4000000000000000000000000000000000000000000000
χ798-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-400000044-400000000000000−4i34i30000000000000000000000000000000000000000000000000
χ818-8-8800-400000044-4000000000000004i3−4i30000000000000000000000000000000000000000000000000

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