Finite Group Databasebeta

← Group #10689409

Character table — Group #10689409

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121244888812121212121212121212242424242424242444448888888844121212124444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1
χ911-1-1-111-111-1-111-11-1-1111-1-1-1ii−i−i-11111-1-1-1-11i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-111-1-11111-1-1-1-1i−iii−i−i1-1ii−i−iii−i−i
χ1011-1-1-111-111-1-111-11-1-1111-1-1-1ii−i−i-11111-1-1-1-11i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1-1-111-1-1-1-11111i−iii−i−i-11−i−iii−i−iii
χ1111-1-1-111-111-1-111-11-1-1111-1-1-1ii−i−i-11111-1-1-1-11i−i-1-1111-1iiii−i−i−i−i-1-1-1-1111111-1-1-1-1-1-11111−ii−i−iii1-1ii−i−i−i−iii
χ1211-1-1-111-111-1-111-11-1-1111-1-1-1ii−i−i-11111-1-1-1-11i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111-1-1111111-1-1-1-1−ii−i−iii-11−i−iiiii−i−i
χ1311-1-1-111-111-1-111-11-1-1111-1-1-1−i−iii-11111-1-1-1-11−ii11-1-11-1−i−i−i−iiiii1111-1-1-1-111-1-11111-1-1-1-1−ii−i−iii1-1−i−iii−i−iii
χ1411-1-1-111-111-1-111-11-1-1111-1-1-1−i−iii-11111-1-1-1-11−ii11-1-11-1−i−i−i−iiiii1111-1-1-1-1-1-111-1-1-1-11111−ii−i−iii-11ii−i−iii−i−i
χ1511-1-1-111-111-1-111-11-1-1111-1-1-1−i−iii-11111-1-1-1-11−ii-1-1111-1−i−i−i−iiiii-1-1-1-1111111-1-1-1-1-1-11111i−iii−i−i1-1−i−iiiii−i−i
χ1611-1-1-111-111-1-111-11-1-1111-1-1-1−i−iii-11111-1-1-1-11−ii-1-1111-1−i−i−i−iiiii-1-1-1-11111-1-1111111-1-1-1-1i−iii−i−i-11ii−i−i−i−iii
χ17222222222222-2-2-22-222222222222-2-22-2-222-2-22-2-20000-2-222-2-222-2-2000000000000000000000000000000000000
χ18222222222222-2-2-22-22222222-2-2-2-2-2-22-2-222-2-22220000-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222-2-2-2222-2222222220000-2-2-222-2-222-2000000-2-20000000000000000222200000000000000-2-200000000
χ20222222222-2-2-2222-2222222220000-2-2-222-2-222-2000000-2-20000000000000000-2-2-2-2000000000000002200000000
χ21222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-2000000220000000000000000000000000000000000002-22-20000
χ22222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-200000022000000000000000000000000000000000000-22-220000
χ2322222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111100000000000022-1-1-1-10000000000
χ2722222222-1222-2-2-22-2-1-1-1-1-1-1-12222-2-2-111-1-111-1-2-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ2822222222-1222-2-2-22-2-1-1-1-1-1-1-12222-2-2-111-1-111-1-2-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ2922222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-2-2-2-2-111-1-111-12200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3022222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-2-2-2-2-111-1-111-12200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ31222-22-2-2-22-22-200020-22-2-22-222-22-200-2002-2002000000002-2002-200000000000000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2
χ32222-22-2-2-22-22-200020-22-2-22-222-22-200-2002-2002000000002-2002-200000000000000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2
χ33222-22-2-2-22-22-200020-22-2-22-22-22-2200-2002-200200000000-2200-2200000000000000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2
χ34222-22-2-2-22-22-200020-22-2-22-22-22-2200-2002-200200000000-2200-2200000000000000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2
χ3522-22-2-2-222-2-220002022-2-2-22-22i−2i−2i2i00-200-22002000000002i−2i00−2i2i00000000000000−i2−i2i2i2i2i2−i2−i20000000000002−2−22
χ3622-22-2-2-222-2-220002022-2-2-22-22i−2i−2i2i00-200-22002000000002i−2i00−2i2i00000000000000i2i2−i2−i2−i2−i2i2i2000000000000−222−2
χ3722-22-2-2-222-2-220002022-2-2-22-2−2i2i2i−2i00-200-2200200000000−2i2i002i−2i00000000000000−i2−i2i2i2i2i2−i2−i2000000000000−222−2
χ3822-22-2-2-222-2-220002022-2-2-22-2−2i2i2i−2i00-200-2200200000000−2i2i002i−2i00000000000000i2i2−i2−i2−i2−i2i2i20000000000002−2−22
χ3922-2-2-222-222-2-2-2-2222-2222-2-2-22i2i−2i−2i2-22-2-2-2-2222−2i2i0000-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ4022-2-2-222-222-2-2-2-2222-2222-2-2-2−2i−2i2i2i2-22-2-2-2-22222i−2i0000-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4122-2-2-222-22-22222-2-2-2-2222-2-2-200002-2-22222-2-2-2000000-22000000000000000022-2-200000000000000-2200000000
χ4222-2-2-222-22-22222-2-2-2-2222-2-2-200002-2-22222-2-2-2000000-220000000000000000-2-222000000000000002-200000000
χ4322-2-2-222-22-222-2-22-22-2222-2-2-20000-22-2-2-22222-20000002-20000000000000000000000000000000000002i−2i−2i2i0000
χ4422-2-2-222-22-222-2-22-22-2222-2-2-20000-22-2-2-22222-20000002-2000000000000000000000000000000000000−2i2i2i−2i0000
χ4522-2-2-222-2-12-2-222-22-21-1-1-11112i2i−2i−2i-22-1-1-11111-12i−2i22-2-2-11−i−i−i−iiiii-1-1-1-111110000000000002i−2i−i−iii0000000000
χ4622-2-2-222-2-12-2-222-22-21-1-1-11112i2i−2i−2i-22-1-1-11111-12i−2i-2-222-11−i−i−i−iiiii1111-1-1-1-1000000000000−2i2iii−i−i0000000000
χ4722-2-2-222-2-12-2-222-22-21-1-1-1111−2i−2i2i2i-22-1-1-11111-1−2i2i22-2-2-11iiii−i−i−i−i-1-1-1-11111000000000000−2i2iii−i−i0000000000
χ4822-2-2-222-2-12-2-222-22-21-1-1-1111−2i−2i2i2i-22-1-1-11111-1−2i2i-2-222-11iiii−i−i−i−i1111-1-1-1-10000000000002i−2i−i−iii0000000000
χ4922-2-2-222-2-12-2-2-2-22221-1-1-11112i2i−2i−2i2-2-11111-1-1-1−2i2i00001-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000000000003−3−330000000000
χ5022-2-2-222-2-12-2-2-2-22221-1-1-11112i2i−2i−2i2-2-11111-1-1-1−2i2i00001-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000000000−333−30000000000
χ5122-2-2-222-2-12-2-2-2-22221-1-1-1111−2i−2i2i2i2-2-11111-1-1-12i−2i00001-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000000000−333−30000000000
χ5222-2-2-222-2-12-2-2-2-22221-1-1-1111−2i−2i2i2i2-2-11111-1-1-12i−2i00001-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000000000003−3−330000000000
χ532-222-22-2-220002-2-202-2-22-222-200000002-2002-2000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i2−22−22−22−20000000000000000
χ542-222-22-2-220002-2-202-2-22-222-200000002-2002-2000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i−22−22−22−220000000000000000
χ552-222-22-2-220002-2-202-2-22-222-200000002-2002-2000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i−22−22−22−220000000000000000
χ562-222-22-2-220002-2-202-2-22-222-200000002-2002-2000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i2−22−22−22−20000000000000000
χ572-2-2-222-2220002-220-22-22-2-2-2200000002-200-22000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i22i−2i−2i2i2−22−2−22−220000000000000000
χ582-2-2-222-2220002-220-22-22-2-2-2200000002-200-22000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i−22−222−22−20000000000000000
χ592-2-2-222-2220002-220-22-22-2-2-2200000002-200-22000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i22i−2i−2i2i−22−222−22−20000000000000000
χ602-2-2-222-2220002-220-22-22-2-2-2200000002-200-22000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i2−22−2−22−220000000000000000
χ6144444444-2-4-4-4444-44-2-2-2-2-2-2-20000-4-42-2-222-2-220000002200000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-200004422222222000000-2-200000000000000000000000000000000000000000000
χ63444-44-4-4-444-44000-40-44-4-44-44000000400-4400-40000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-24-44000-402-222-22-2000000-2002-2002000000000023−230023−23000000000000000000000000000000000000
χ65444-44-4-4-4-24-44000-402-222-22-2000000-2002-20020000000000−232300−2323000000000000000000000000000000000000
χ66444-44-4-4-4-2-44-4000402-222-22-24-44-400200-2200-200000000-2200-2200000000000000000000000000000000000000
χ67444-44-4-4-4-2-44-4000402-222-22-2-44-4400200-2200-2000000002-2002-200000000000000000000000000000000000000
χ6844-44-4-4-44444-4000-4044-4-4-44-40000004004-400-40000000000000000000000000000000000000000000000000000
χ6944-44-4-4-44-244-4000-40-2-2222-22000000-200-220020000000000−2i32i3002i3−2i3000000000000000000000000000000000000
χ7044-44-4-4-44-244-4000-40-2-2222-22000000-200-2200200000000002i3−2i300−2i32i3000000000000000000000000000000000000
χ7144-44-4-4-44-2-4-4400040-2-2222-224i−4i−4i4i002002-200-200000000−2i2i002i−2i00000000000000000000000000000000000000
χ7244-44-4-4-44-2-4-4400040-2-2222-22−4i4i4i−4i002002-200-2000000002i−2i00−2i2i00000000000000000000000000000000000000
χ7344-4-4-444-4-2-44444-4-4-42-2-2-222200004-42-2-2-2-22220000002-200000000000000000000000000000000000000000000
χ7444-4-4-444-4-2-444-4-44-442-2-2-22220000-44222-2-2-2-22000000-2200000000000000000000000000000000000000000000
χ754-444-44-4-44000-4440-4-4-44-444-40000000-4400-4400000000000000000000000000000000000000000000000000000
χ764-444-44-4-4-20004-4-40422-22-2-220000000-2200-22000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ774-444-44-4-4-20004-4-40422-22-2-220000000-2200-220002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ784-444-44-4-4-2000-4440-422-22-2-2200000002-2002-2000000000000000006−6−666−6−660000000000000000000000000000
χ794-444-44-4-4-2000-4440-422-22-2-2200000002-2002-200000000000000000−666−6−666−60000000000000000000000000000
χ804-44-4-4-4444000000004-4-444-4-40000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ814-44-4-4-4444000000004-4-444-4-4000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ824-4-444-44-4400000000-4-4-44-4440000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ834-4-444-44-4400000000-4-4-44-444000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ844-4-4-444-444000-44-4044-44-4-4-440000000-44004-400000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-20004-440-4-22-2222-20000000-22002-2000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ864-4-4-444-44-20004-440-4-22-2222-20000000-22002-20002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ874-4-4-444-44-2000-44-404-22-2222-200000002-200-22000000000000000006−6−66−666−60000000000000000000000000000
χ884-4-4-444-44-2000-44-404-22-2222-200000002-200-2200000000000000000−666−66−6−660000000000000000000000000000
χ898-88-8-8-888-400000000-444-4-444000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-88-8-400000000444-44-4-4000000000000000000000000000000000000000000000000000000000000000000

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