Finite Group Databasebeta

← Group #10691583

Character table — Group #10691583

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222234444446661212121244444446612121212121244888812121212121212121212242424242424242488888824242424888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ911111111-1-1-11-1111-1-1-1-11-111-1-1-111-1-111-1-11-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−iii−i−ii−iii−i−i11-1-1i−iii−i−i1-1
χ1011111111-1-1-11-1111-1-1-1-11-111-1-1-111-1-111-1-11-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i−i−iiii−iii−i−i-1-111−ii−i−iii-11
χ1111111111-1-1-11-1111-1-1-1-11-111-1-1-111-1-111-1-11-1−i−iii1-11111-1-1-1-1−i−i−i−iiiiiii−i−i−ii−i−iii-1-111i−iii−i−i-11
χ1211111111-1-1-11-1111-1-1-1-11-111-1-1-111-1-111-1-11-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−i−iii−ii−i−iii11-1-1−ii−i−iii1-1
χ1311111111-1-1-11-1111-1-1-1-11-1-1-111-111-1-111-1-1-11ii−i−i1-1-1-1-1-11111iiii−i−i−i−iii−i−i−ii−i−iii11-1-1i−i−i−iii-11
χ1411111111-1-1-11-1111-1-1-1-11-1-1-111-111-1-111-1-1-11ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−i−iii−ii−i−iii-1-111−iiii−i−i1-1
χ1511111111-1-1-11-1111-1-1-1-11-1-1-111-111-1-111-1-1-11−i−iii1-1-1-1-1-11111−i−i−i−iiiiiii−i−ii−iii−i−i-1-111i−i−i−iii1-1
χ1611111111-1-1-11-1111-1-1-1-11-1-1-111-111-1-111-1-1-11−i−iii1-1-1-1-1-11111−i−i−i−iiiii−i−iiii−iii−i−i11-1-1−iiii−i−i-11
χ172222222-2222-222222222-2-20000-22222-2-2-2-2000000-2-2000000000000000022220000000000-2-2000000
χ182222222-2222-222222222-2-20000-22222-2-2-2-2000000-2-20000000000000000-2-2-2-2000000000022000000
χ192222222-2-2-2-2-2-2222-2-2-2-2-220000222-2-2-2-222000000-2200000000000000002i2i−2i−2i0000000000−2i2i000000
χ202222222-2-2-2-2-2-2222-2-2-2-2-220000222-2-2-2-222000000-220000000000000000−2i−2i2i2i00000000002i−2i000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ25222222-12-2-2-22-2-1-1-111112-222-2-2-2-1-111-1-1112-22i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii00002i−2i−i−iii000000000000
χ26222222-12-2-2-22-2-1-1-111112-222-2-2-2-1-111-1-1112-2−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i0000−2i2iii−i−i000000000000
χ27222222-12-2-2-22-2-1-1-111112-2-2-222-2-1-111-1-111-222i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii0000−2i2iii−i−i000000000000
χ28222222-12-2-2-22-2-1-1-111112-2-2-222-2-1-111-1-111-22−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i00002i−2i−i−iii000000000000
χ292222-2-22222-22-22222222-2-222-2-22-2-2-2-22222-220000-2-222-2-222-2-2000000000000000000000000000000
χ302222-2-22222-22-22222222-2-2-2-2222-2-2-2-222222-20000-2-2-2-222-2-222000000000000000000000000000000
χ312222-2-222-2-2222222-2-2-2-2-222222-2-2-22222-2-2-2-20000-2222-2-2-2-222000000000000000000000000000000
χ322222-2-222-2-2222222-2-2-2-2-22-2-2-2-2-2-2-22222-2-2220000-22-2-22222-2-2000000000000000000000000000000
χ332222-2-22-222-2-2-22222222220000-2-2-2-2-2-2-2-2-200000022000000000000000000000000000000002i−2i2i−2i00
χ342222-2-22-222-2-2-22222222220000-2-2-2-2-2-2-2-2-20000002200000000000000000000000000000000−2i2i−2i2i00
χ352222-2-22-2-2-22-22222-2-2-2-22-200002-2-222-2-2220000002-2000000000000000000000000000000002-2-2200
χ362222-2-22-2-2-22-22222-2-2-2-22-200002-2-222-2-2220000002-200000000000000000000000000000000-222-200
χ372222-2-2-1222-22-2-1-1-1-1-1-1-1-2-222-2-221111-1-1-1-1-22000011-1-111-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ382222-2-2-1222-22-2-1-1-1-1-1-1-1-2-222-2-221111-1-1-1-1-22000011-1-111-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ392222-2-2-1222-22-2-1-1-1-1-1-1-1-2-2-2-22221111-1-1-1-12-200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ402222-2-2-1222-22-2-1-1-1-1-1-1-1-2-2-2-22221111-1-1-1-12-200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ412222-2-2-12-2-2222-1-1-11111-222222-211-1-1-1-111-2-200001-1-1-11111-1-133−3−3−3−3330000003−3−33000000000000
χ422222-2-2-12-2-2222-1-1-11111-222222-211-1-1-1-111-2-200001-1-1-11111-1-1−3−33333−3−3000000−333−3000000000000
χ432222-2-2-12-2-2222-1-1-11111-22-2-2-2-2-211-1-1-1-1112200001-111-1-1-1-11133−3−3−3−333000000−333−3000000000000
χ442222-2-2-12-2-2222-1-1-11111-22-2-2-2-2-211-1-1-1-1112200001-111-1-1-1-111−3−33333−3−30000003−3−33000000000000
χ452-2-222-2202-2-2022-2-222-2-200000002-22-20000002−22−200000000002−22−22−22−22i−2i2i−2i000000−i2i2−i2i200000000
χ462-2-222-2202-2-2022-2-222-2-200000002-22-20000002−22−200000000002−22−22−22−2−2i2i−2i2i000000i2−i2i2−i200000000
χ472-2-222-2202-2-2022-2-222-2-200000002-22-2000000−22−220000000000−22−22−22−222i−2i2i−2i000000i2−i2i2−i200000000
χ482-2-222-2202-2-2022-2-222-2-200000002-22-2000000−22−220000000000−22−22−22−22−2i2i−2i2i000000−i2i2−i2i200000000
χ492-2-222-220-2220-22-2-2-2-22200000002-2-22000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i22-2-22000000−i2i2i2−i200000000
χ502-2-222-220-2220-22-2-2-2-22200000002-2-22000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2-222-2000000i2−i2−i2i200000000
χ512-2-222-220-2220-22-2-2-2-22200000002-2-22000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i22-2-22000000i2−i2−i2i200000000
χ522-2-222-220-2220-22-2-2-2-22200000002-2-22000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2-222-2000000−i2i2i2−i200000000
χ53444444-2-4444-44-2-2-2-2-2-2-2-4-40000-4-2-2-2-222220000002200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-22222-4400004-2-22222-2-20000002-200000000000000000000000000000000000000
χ554444-4-4-2-444-4-4-4-2-2-2-2-2-2-2440000-422222222000000-2-200000000000000000000000000000000000000
χ564444-4-4-2-4-4-44-44-2-2-222224-40000422-2-222-2-2000000-2200000000000000000000000000000000000000
χ5744-4-40044000-40-44-4000000004-4000004-400000000000000004-4000000000000000000000000000000
χ5844-4-40044000-40-44-400000000-44000004-40000000000000000-44000000000000000000000000000000
χ5944-4-4004-400040-44-40000004i−4i0000000-4400000000004i−4i000000000000000000000000000000000000
χ6044-4-4004-400040-44-4000000−4i4i0000000-440000000000−4i4i000000000000000000000000000000000000
χ6144-4-400-24000-402-2223−2323−2300004-400000-2223−23000000000023−2300-22000000000000000000000000000000
χ6244-4-400-24000-402-2223−2323−230000-4400000-2223−230000000000−2323002-2000000000000000000000000000000
χ6344-4-400-24000-402-22−2323−232300004-400000-22−23230000000000−232300-22000000000000000000000000000000
χ6444-4-400-24000-402-22−2323−23230000-4400000-22−2323000000000023−23002-2000000000000000000000000000000
χ6544-4-400-2-4000402-2223−2323−23004i−4i00000002-2−232300000000−2i2i00−2i32i300000000000000000000000000000000
χ6644-4-400-2-4000402-2223−2323−2300−4i4i00000002-2−2323000000002i−2i002i3−2i300000000000000000000000000000000
χ6744-4-400-2-4000402-22−2323−2323004i−4i00000002-223−2300000000−2i2i002i3−2i300000000000000000000000000000000
χ6844-4-400-2-4000402-22−2323−232300−4i4i00000002-223−23000000002i−2i00−2i32i300000000000000000000000000000000
χ694-4-444-4-204-4-404-222-2-2220000000-22-2200000022−2222−220000000000−22−22−22−220000000000000000000000
χ704-4-444-4-204-4-404-222-2-2220000000-22-22000000−2222−222200000000002−22−22−22−20000000000000000000000
χ714-4-444-4-20-4440-4-22222-2-20000000-222-2000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000
χ724-4-444-4-20-4440-4-22222-2-20000000-222-20000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000
χ734-4-44-44404-440-44-4-444-4-40000000-44-4400000000000000000000000000000000000000000000000000
χ744-4-44-4440-44-4044-4-4-4-4440000000-444-400000000000000000000000000000000000000000000000000
χ754-4-44-44-204-440-4-222-2-22200000002-22-200000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ764-4-44-44-204-440-4-222-2-22200000002-22-200000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ774-4-44-44-20-44-404-22222-2-200000002-2-22000000000000000000006−6−66−666−60000000000000000000000
χ784-4-44-44-20-44-404-22222-2-200000002-2-2200000000000000000000−666−66−6−660000000000000000000000
χ798-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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