Finite Group Databasebeta

← Group #10691576

Character table — Group #10691576

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order1222223444444666121212122244444661212121212122466668888121212121212242424242424242488888824242424888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111-1-111-1-1111111111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ611111111111111111111-1-111-1-1111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ911111111-1-1-11-1111-1-1-1-1111-1-1-1-11111-1-1-1-11-11111ii−i−i1-1-1-1-1-1iiii−i−i−i−iii−i−ii−iii−i−ii−i11-1-1ii−i−i1-1
χ1011111111-1-1-11-1111-1-1-1-1111-1-1-1-11111-1-1-1-11-11111ii−i−i1-1-1-1-1-1iiii−i−i−i−i−i−iiii−iii−i−i−ii-1-111−i−iii-11
χ1111111111-1-1-11-1111-1-1-1-1111-1-1-1-11111-1-1-1-11-11111−i−iii1-1-1-1-1-1−i−i−i−iiiiiii−i−i−ii−i−iiii−i-1-111ii−i−i-11
χ1211111111-1-1-11-1111-1-1-1-1111-1-1-1-11111-1-1-1-11-11111−i−iii1-1-1-1-1-1−i−i−i−iiiii−i−iii−ii−i−iii−ii11-1-1−i−iii1-1
χ1311111111-1-1-11-1111-1-1-1-1-1-11-111-11111-1-1-1-1-11-1-1-1-1ii−i−i1-11111iiii−i−i−i−iii−i−i−ii−i−iiii−i11-1-1−i−iii-11
χ1411111111-1-1-11-1111-1-1-1-1-1-11-111-11111-1-1-1-1-11-1-1-1-1ii−i−i1-11111iiii−i−i−i−i−i−iii−ii−i−iii−ii-1-111ii−i−i1-1
χ1511111111-1-1-11-1111-1-1-1-1-1-11-111-11111-1-1-1-1-11-1-1-1-1−i−iii1-11111−i−i−i−iiiiiii−i−ii−iii−i−ii−i-1-111−i−iii1-1
χ1611111111-1-1-11-1111-1-1-1-1-1-11-111-11111-1-1-1-1-11-1-1-1-1−i−iii1-11111−i−i−i−iiiii−i−iiii−iii−i−i−ii11-1-1ii−i−i-11
χ172222222-2222-22222222200-2-200-222-2-222-2-20000000000-2-20000000000002222000000-2-20000000000
χ182222222-2222-22222222200-2-200-222-2-222-2-20000000000-2-2000000000000-2-2-2-2000000220000000000
χ192222222-2-2-2-2-2-2222-2-2-2-200-2200222-2-2-2-2220000000000-220000000000002i2i−2i−2i000000−2i2i0000000000
χ202222222-2-2-2-2-2-2222-2-2-2-200-2200222-2-2-2-2220000000000-22000000000000−2i−2i2i2i0000002i−2i0000000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1-2-222-2-22-1-1-1-1-1-1-1-1-2-211112222-1-11111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1-2-222-2-22-1-1-1-1-1-1-1-1-2-21111-2-2-2-2-1-1111111111111000022-1-1-1-1000000000000
χ25222222-12-2-2-22-2-1-1-11111222-2-2-2-2-1-1-1-111112-2-1-1-1-12i2i−2i−2i-111111−i−i−i−iiiii00002i−2i−i−iii000000000000
χ26222222-12-2-2-22-2-1-1-11111222-2-2-2-2-1-1-1-111112-2-1-1-1-1−2i−2i2i2i-111111iiii−i−i−i−i0000−2i2iii−i−i000000000000
χ27222222-12-2-2-22-2-1-1-11111-2-22-222-2-1-1-1-11111-2211112i2i−2i−2i-11-1-1-1-1−i−i−i−iiiii0000−2i2iii−i−i000000000000
χ28222222-12-2-2-22-2-1-1-11111-2-22-222-2-1-1-1-11111-221111−2i−2i2i2i-11-1-1-1-1iiii−i−i−i−i00002i−2i−i−iii000000000000
χ292222-2-22222-22-2222222222-2-2-2-22-2-222-2-222-2222-2-20000-2-222-2-2000000000000000000000000000000
χ302222-2-22222-22-22222222-2-2-2-2222-2-222-2-2222-2-2-2220000-2-2-2-222000000000000000000000000000000
χ312222-2-222-2-2222222-2-2-2-222-2222-2-2-22222-2-2-2-222-2-20000-22-2-222000000000000000000000000000000
χ322222-2-222-2-2222222-2-2-2-2-2-2-22-2-2-2-2-22222-2-222-2-2220000-2222-2-2000000000000000000000000000000
χ332222-2-22-222-2-2-22222222002200-2-2-2-2-2-2-2-2-200000000002200000000000000000000000000002i−2i2i−2i00
χ342222-2-22-222-2-2-22222222002200-2-2-2-2-2-2-2-2-20000000000220000000000000000000000000000−2i2i−2i2i00
χ352222-2-22-2-2-22-22222-2-2-2-2002-2002-2-2-2-2222200000000002-200000000000000000000000000002-2-2200
χ362222-2-22-2-2-22-22222-2-2-2-2002-2002-2-2-2-2222200000000002-20000000000000000000000000000-222-200
χ372222-2-2-1222-22-2-1-1-1-1-1-1-122-2-2-2-2211-1-111-1-1-22-1-111000011-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ382222-2-2-1222-22-2-1-1-1-1-1-1-122-2-2-2-2211-1-111-1-1-22-1-111000011-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ392222-2-2-1222-22-2-1-1-1-1-1-1-1-2-2-2-222211-1-111-1-12-211-1-100001111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ402222-2-2-1222-22-2-1-1-1-1-1-1-1-2-2-2-222211-1-111-1-12-211-1-100001111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ412222-2-2-12-2-2222-1-1-1111122-2222-211-1-1-1-111-2-2-1-11100001-111-1-133−3−3−3−3330000003−3−33000000000000
χ422222-2-2-12-2-2222-1-1-1111122-2222-211-1-1-1-111-2-2-1-11100001-111-1-1−3−33333−3−3000000−333−3000000000000
χ432222-2-2-12-2-2222-1-1-11111-2-2-22-2-2-211-1-1-1-1112211-1-100001-1-1-11133−3−3−3−333000000−333−3000000000000
χ442222-2-2-12-2-2222-1-1-11111-2-2-22-2-2-211-1-1-1-1112211-1-100001-1-1-111−3−33333−3−30000003−3−33000000000000
χ452-2-222-2202-220-2-2-2222-2-200000002-2002-200000000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i000000002−22−2000000
χ462-2-222-2202-220-2-2-2222-2-200000002-2002-200000000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i00000000−22−22000000
χ472-2-222-2202-220-2-2-2222-2-200000002-2002-200000000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00000000−22−22000000
χ482-2-222-2202-220-2-2-2222-2-200000002-2002-200000000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i000000002−22−2000000
χ492-2-222-220-22-202-2-22-2-22200000002-200-22000000002−2−220000002−22−2−22−222-2-2200000000−222−2000000
χ502-2-222-220-22-202-2-22-2-22200000002-200-22000000002−2−220000002−22−2−22−22-222-2000000002−2−22000000
χ512-2-222-220-22-202-2-22-2-22200000002-200-2200000000−222−2000000−22−222−22−22-2-22000000002−2−22000000
χ522-2-222-220-22-202-2-22-2-22200000002-200-2200000000−222−2000000−22−222−22−2-222-200000000−222−2000000
χ53444444-2-4444-44-2-2-2-2-2-2-200-4-400-4-2-222-2-2220000000000220000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2222200-44004-2-22222-2-200000000002-20000000000000000000000000000000000
χ554444-4-4-2-444-4-4-4-2-2-2-2-2-2-2004400-4222222220000000000-2-20000000000000000000000000000000000
χ564444-4-4-2-4-4-44-44-2-2-22222004-40042222-2-2-2-20000000000-220000000000000000000000000000000000
χ5744-4-40044000-404-4-400004-400000004-40000004-4000000000000000000000000000000000000000000
χ5844-4-40044000-404-4-40000-4400000004-4000000-44000000000000000000000000000000000000000000
χ5944-4-4004-4000404-4-4000000004i−4i000-440000000000000000004i−4i000000000000000000000000000000
χ6044-4-4004-4000404-4-400000000−4i4i000-44000000000000000000−4i4i000000000000000000000000000000
χ6144-4-400-24000-40-22223−2323−234-40000000-220023−2300-220000000023−2300000000000000000000000000000000
χ6244-4-400-24000-40-22223−2323−23-440000000-220023−23002-200000000−232300000000000000000000000000000000
χ6344-4-400-24000-40-222−2323−23234-40000000-2200−232300-2200000000−232300000000000000000000000000000000
χ6444-4-400-24000-40-222−2323−2323-440000000-2200−2323002-20000000023−2300000000000000000000000000000000
χ6544-4-400-2-400040-22223−2323−2300004i−4i0002-200−23230000−2i32i300000000−2i2i000000000000000000000000000000
χ6644-4-400-2-400040-22223−2323−230000−4i4i0002-200−232300002i3−2i3000000002i−2i000000000000000000000000000000
χ6744-4-400-2-400040-222−2323−232300004i−4i0002-20023−2300002i3−2i300000000−2i2i000000000000000000000000000000
χ6844-4-400-2-400040-222−2323−23230000−4i4i0002-20023−230000−2i32i3000000002i−2i000000000000000000000000000000
χ694-4-444-4-204-440-422-2-2-2220000000-2200-2200000000−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i20000000000000000000000
χ704-4-444-4-204-440-422-2-2-2220000000-2200-22000000002i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i20000000000000000000000
χ714-4-444-4-20-44-40422-222-2-20000000-22002-20000000022−22−2222000000−22−222−22−20000000000000000000000
χ724-4-444-4-20-44-40422-222-2-20000000-22002-200000000−222222−220000002−22−2−22−220000000000000000000000
χ734-4-44-44404-4-404-4-4444-4-40000000-4400-44000000000000000000000000000000000000000000000000
χ744-4-44-4440-4440-4-4-44-4-4440000000-44004-4000000000000000000000000000000000000000000000000
χ754-4-44-44-204-4-40422-2-2-22200000002-2002-20000000000000000006−6−666−6−660000000000000000000000
χ764-4-44-44-204-4-40422-2-2-22200000002-2002-2000000000000000000−666−6−666−60000000000000000000000
χ774-4-44-44-20-4440-422-222-2-200000002-200-22000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ784-4-44-44-20-4440-422-222-2-200000002-200-22000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ798-88-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-88-800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000000000

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