Finite Group Databasebeta

← Group #10690021

Character table — Group #10690021

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
χ91-1-11-111-1111-11-1-1-11-1-111-1-11ii−i−i1-111-111-1-1-1i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-111-1-11-1ii−i−i11-1-1
χ101-1-11-111-1111-11-1-1-11-1-111-1-11ii−i−i1-111-111-1-1-1i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii1-111-1-1-11−i−iii-1-111
χ111-1-11-111-1111-11-1-1-11-1-111-1-11ii−i−i1-111-111-1-1-1i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−i−i−iiiii-11-1-1111-1ii−i−i-1-111
χ121-1-11-111-1111-11-1-1-11-1-111-1-11ii−i−i1-111-111-1-1-1i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii-1-111iiii−i−i−i−i-11-1-111-11−i−iii11-1-1
χ131-1-11-111-1111-11-1-1-11-1-111-1-11−i−iii1-111-111-1-1-1−iiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1iiii−i−i−i−i-11-1-1111-1−i−iii-1-111
χ141-1-11-111-1111-11-1-1-11-1-111-1-11−i−iii1-111-111-1-1-1−iiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−i−i−iiiii-11-1-111-11ii−i−i11-1-1
χ151-1-11-111-1111-11-1-1-11-1-111-1-11−i−iii1-111-111-1-1-1−ii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-111-1-11-1−i−iii11-1-1
χ161-1-11-111-1111-11-1-1-11-1-111-1-11−i−iii1-111-111-1-1-1−ii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i1-111-1-1-11ii−i−i-1-111
χ17222222222222-2-2-22-222222222222-2-2222-2-2-2-22-2-20000-2-222-2-222-2-2000000000000000000000000000000000000
χ18222222222222-2-2-22-22222222-2-2-2-2-2-2222-2-2-2-22220000-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222-2-2-2222-2222222220000-2-2-2-2-22222-2000000-2-20000000000000000222200000000000000-2-200000000
χ20222222222-2-2-2222-2222222220000-2-2-2-2-22222-2000000-2-20000000000000000-2-2-2-2000000000000002200000000
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
χ2722222222-1222-2-2-22-2-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ2822222222-1222-2-2-22-2-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ2922222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-12200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3022222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-12200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ31222-2-2-22-22000-22-20222-2-2-2-220000000002-22-2000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i22-22-2−i2−i2i2i2−i2−i2i2i20000000000000000
χ32222-2-2-22-22000-22-20222-2-2-2-220000000002-22-2000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2-22-22i2i2−i2−i2i2i2−i2−i20000000000000000
χ33222-2-2-22-22000-22-20222-2-2-2-220000000002-22-2000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i22-22-2i2i2−i2−i2i2i2−i2−i20000000000000000
χ34222-2-2-22-22000-22-20222-2-2-2-220000000002-22-2000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2-22-22−i2−i2i2i2−i2−i2i2i20000000000000000
χ3522-222-2-2-222-22000-202-22-22-2-22-22-2002-220000-2000000002-2002-2000000000000002−22−22−22−20000000000002−22−2
χ3622-222-2-2-222-22000-202-22-22-2-22-22-2002-220000-2000000002-2002-200000000000000−22−22−22−22000000000000−22−22
χ3722-222-2-2-222-22000-202-22-22-2-2-22-22002-220000-200000000-2200-22000000000000002−22−22−22−2000000000000−22−22
χ3822-222-2-2-222-22000-202-22-22-2-2-22-22002-220000-200000000-2200-2200000000000000−22−22−22−220000000000002−22−2
χ392-222-2-2-2222-2-200020-222-2-22-22i−2i−2i2i002-2-200002000000002i−2i00−2i2i00000000000000−i2i2−i2i2i2−i2i2−i2000000000000−222−2
χ402-222-2-2-2222-2-200020-222-2-22-22i−2i−2i2i002-2-200002000000002i−2i00−2i2i00000000000000i2−i2i2−i2−i2i2−i2i20000000000002−2−22
χ412-222-2-2-2222-2-200020-222-2-22-2−2i2i2i−2i002-2-20000200000000−2i2i002i−2i00000000000000−i2i2−i2i2i2−i2i2−i20000000000002−2−22
χ422-222-2-2-2222-2-200020-222-2-22-2−2i2i2i−2i002-2-20000200000000−2i2i002i−2i00000000000000i2−i2i2−i2−i2i2−i2i2000000000000−222−2
χ432-2-22-222-2222-2-222-2-2-2-222-2-222i2i−2i−2i-2222-2-2-222-2−2i2i0000-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ442-2-22-222-2222-2-222-2-2-2-222-2-22−2i−2i2i2i-2222-2-2-222-22i−2i0000-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ452-2-22-222-22-2-222-2-222-2-222-2-220000-22-2-2222-2-22000000-22000000000000000022-2-200000000000000-2200000000
χ462-2-22-222-22-2-222-2-222-2-222-2-220000-22-2-2222-2-22000000-220000000000000000-2-222000000000000002-200000000
χ472-2-22-222-22-2-22-2222-2-2-222-2-2200002-2-2-22-2-22220000002-20000000000000000000000000000000000002i−2i−2i2i0000
χ482-2-22-222-22-2-22-2222-2-2-222-2-2200002-2-2-22-2-22220000002-2000000000000000000000000000000000000−2i2i2i−2i0000
χ492-2-22-222-2-122-22-2-2-2211-1-111-12i2i−2i−2i2-2-1-11-1-11112i−2i2i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-1110000000000
χ502-2-22-222-2-122-22-2-2-2211-1-111-12i2i−2i−2i2-2-1-11-1-11112i−2i−2i−2i2i2i-11−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-10000000000
χ512-2-22-222-2-122-22-2-2-2211-1-111-1−2i−2i2i2i2-2-1-11-1-1111−2i2i2i2i−2i−2i-11iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-10000000000
χ522-2-22-222-2-122-22-2-2-2211-1-111-1−2i−2i2i2i2-2-1-11-1-1111−2i2i−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-1110000000000
χ532-2-22-222-2-122-2-222-2-211-1-111-12i2i−2i−2i-22-1-1111-1-11−2i2i00001-1−i−iiiii−i−i33−3−3−3−33300000000000000−i3i3i3−i30000000000
χ542-2-22-222-2-122-2-222-2-211-1-111-12i2i−2i−2i-22-1-1111-1-11−2i2i00001-1−i−iiiii−i−i−3−33333−3−300000000000000i3−i3−i3i30000000000
χ552-2-22-222-2-122-2-222-2-211-1-111-1−2i−2i2i2i-22-1-1111-1-112i−2i00001-1ii−i−i−i−iii33−3−3−3−33300000000000000i3−i3−i3i30000000000
χ562-2-22-222-2-122-2-222-2-211-1-111-1−2i−2i2i2i-22-1-1111-1-112i−2i00001-1ii−i−i−i−iii−3−33333−3−300000000000000−i3i3i3−i30000000000
χ572-2-2-22-2222000-2-2202-2-2-2-22220000000002-2-220002−2−2200000000002−22−2−22−222-2-2222−2−2−2−2220000000000000000
χ582-2-2-22-2222000-2-2202-2-2-2-22220000000002-2-220002−2−2200000000002−22−2−22−22-222-2−2−22222−2−20000000000000000
χ592-2-2-22-2222000-2-2202-2-2-2-22220000000002-2-22000−222−20000000000−22−222−22−22-2-22−2−22222−2−20000000000000000
χ602-2-2-22-2222000-2-2202-2-2-2-22220000000002-2-22000−222−20000000000−22−222−22−2-222-222−2−2−2−2220000000000000000
χ6144444444-2-4-4-4444-44-2-2-2-2-2-2-20000-4-4222-2-2-2-220000002200000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-200004422222222000000-2-200000000000000000000000000000000000000000000
χ63444-4-4-44-440004-440-444-4-4-4-44000000000-44-4400000000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-20004-440-4-2-22222-20000000002-22-2000000000000000006−6−666−6−660000000000000000000000000000
χ65444-4-4-44-4-20004-440-4-2-22222-20000000002-22-200000000000000000−666−6−666−60000000000000000000000000000
χ66444-4-4-44-4-2000-44-404-2-22222-2000000000-22-22000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ67444-4-4-44-4-2000-44-404-2-22222-2000000000-22-220002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ6844-444-4-4-44-44-4000404-44-44-4-4000000-44-4000040000000000000000000000000000000000000000000000000000
χ6944-444-4-4-4-24-44000-40-22-22-2224-44-400-22-20000200000000-2200-2200000000000000000000000000000000000000
χ7044-444-4-4-4-24-44000-40-22-22-222-44-4400-22-200002000000002-2002-200000000000000000000000000000000000000
χ7144-444-4-4-4-2-44-400040-22-22-2220000002-220000-2000000000023−230023−23000000000000000000000000000000000000
χ7244-444-4-4-4-2-44-400040-22-22-2220000002-220000-20000000000−232300−2323000000000000000000000000000000000000
χ7344-4-4-44-444000000004-4-44-44-40000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ7444-4-4-44-444000000004-4-44-44-4000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ754-444-4-4-444-444000-40-444-4-44-4000000-4440000-40000000000000000000000000000000000000000000000000000
χ764-444-4-4-44-24-4-4000402-2-222-224i−4i−4i4i00-2220000-200000000−2i2i002i−2i00000000000000000000000000000000000000
χ774-444-4-4-44-24-4-4000402-2-222-22−4i4i4i−4i00-2220000-2000000002i−2i00−2i2i00000000000000000000000000000000000000
χ784-444-4-4-44-2-444000-402-2-222-220000002-2-2000020000000000−2i32i3002i3−2i3000000000000000000000000000000000000
χ794-444-4-4-44-2-444000-402-2-222-220000002-2-20000200000000002i3−2i300−2i32i3000000000000000000000000000000000000
χ804-44-444-4-4400000000-44-444-4-40000000000000000000000000000000000000000002-2-22-222-20000000000000000
χ814-44-444-4-4400000000-44-444-4-4000000000000000000000000000000000000000000-222-22-2-220000000000000000
χ824-4-44-444-4-2-4-444-4-44422-2-222-20000-4422-2-2-222-20000002-200000000000000000000000000000000000000000000
χ834-4-44-444-4-2-4-44-4444-422-2-222-200004-422-222-2-2-2000000-2200000000000000000000000000000000000000000000
χ844-4-4-44-444400044-40-4-4-4-4-4444000000000-444-400000000000000000000000000000000000000000000000000000
χ854-4-4-44-444-200044-40-42222-2-2-20000000002-2-2200000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ864-4-4-44-444-200044-40-42222-2-2-20000000002-2-2200000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ874-4-4-44-444-2000-4-44042222-2-2-2000000000-222-200022−22−22220000000000−22−222−22−20000000000000000000000000000
χ884-4-4-44-444-2000-4-44042222-2-2-2000000000-222-2000−222222−2200000000002−22−2−22−220000000000000000000000000000
χ8988-8-8-88-88-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000
χ908-88-888-8-8-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000

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