Finite Group Databasebeta

← Group #10845425

Character table — Group #10845425

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444412121212121212122244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11111
χ9111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-11-11111-1-11-1-1-111-1-1
χ10111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-11-1-1-1-111-1111-1-111
χ11111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111-1-1-1-1-1111-11111-1-1
χ12111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-111111-1-1-11-1-1-1-111
χ13111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-11-111-1-1-1-11-111-1-111
χ14111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1-11-1-11111-11-1-111-1-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-111-1-1-1-1111-1-1-111111-1-1-1-1-111
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-111-1-1-1-111-1111-1-1-1-1-111111-1-1
χ172222222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-22222-2-2000000000000000000000000000022000000-2-2000000
χ182222222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-22222-2-20000000000000000000000000000-2-200000022000000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-22222-2-2-2-2-2-200000000000000000000000000002-2000000-22000000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-22222-2-2-2-2-2-20000000000000000000000000000-220000002-2000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-21111-1-1-1-10000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-222-1-1-1-111110000000000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-1110000000000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-10000000000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-12-2-2211-1-1-1-1110000000000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-222-2-1-11111-1-10000000000000000
χ2922-2-22-2-22200002-2-2222-22-2-2-200000022-2-22-2000000002-2000000002222-2-2-2-200000000000000002i−2i2i−2i00000000
χ3022-2-22-2-22200002-2-2222-22-2-2-200000022-2-22-2000000002-2000000002222-2-2-2-20000000000000000−2i2i−2i2i00000000
χ3122-2-22-2-22200002-2-2222-22-2-2-2000000-2-2222-2000000002-200000000-2-2-2-2222200000000000000002i−2i−2i2i00000000
χ3222-2-22-2-22200002-2-2222-22-2-2-2000000-2-2222-2000000002-200000000-2-2-2-222220000000000000000−2i2i2i−2i00000000
χ332-22-2-2-222200002-22-2-2-222-22-20000002i−2i2i−2i2-200000000-22000000002i2i−2i−2i2i2i−2i−2i000000000000002i−2i0000002-20000
χ342-22-2-2-222200002-22-2-2-222-22-20000002i−2i2i−2i2-200000000-22000000002i2i−2i−2i2i2i−2i−2i00000000000000−2i2i000000-220000
χ352-22-2-2-222200002-22-2-2-222-22-2000000−2i2i−2i2i2-200000000-2200000000−2i−2i2i2i−2i−2i2i2i000000000000002i−2i000000-220000
χ362-22-2-2-222200002-22-2-2-222-22-2000000−2i2i−2i2i2-200000000-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000−2i2i0000002-20000
χ372-2-22-22-22222-2-222-2-2-2-2-222-222-22i2i−2i−2i2i−2i−2i2i2222-2-222-2-2-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ382-2-22-22-22222-2-222-2-2-2-2-222-222-2−2i−2i2i2i−2i2i2i−2i2222-2-222-2-2-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ392-2-22-22-22222-2-2-2-222-2-2-222-22-2200000000-2-2-2-22222-2-22200000000000000000000000000000000000000002-22-2
χ402-2-22-22-22222-2-2-2-222-2-2-222-22-2200000000-2-2-2-22222-2-2220000000000000000000000000000000000000000-22-22
χ412-2-22-22-222-2-22222-2-2-2-2-222-22-222i2i−2i−2i−2i2i2i−2i22-2-222-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ422-2-22-22-222-2-22222-2-2-2-2-222-22-22−2i−2i2i2i2i−2i−2i2i22-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ432-2-22-22-222-2-222-2-222-2-2-222-222-200000000-2-222-2-2-2-2222200000000000000000000000000000000000000002-2-22
χ442-2-22-22-222-2-222-2-222-2-2-222-222-200000000-2-222-2-2-2-222220000000000000000000000000000000000000000-222-2
χ452-2-22-22-22-122-2-222-2-2111-1-11-12-22i2i−2i−2i2i−2i−2i2i-1-1-1-111-1-11111−i−i−i−iiiii−i−iiiii−i−i00003−33−3−i3i3−i3i30000000000000000
χ462-2-22-22-22-122-2-222-2-2111-1-11-12-22i2i−2i−2i2i−2i−2i2i-1-1-1-111-1-11111−i−i−i−iiiii−i−iiiii−i−i0000−33−33i3−i3i3−i30000000000000000
χ472-2-22-22-22-122-2-222-2-2111-1-11-12-2−2i−2i2i2i−2i2i2i−2i-1-1-1-111-1-11111iiii−i−i−i−iii−i−i−i−iii00003−33−3i3−i3i3−i30000000000000000
χ482-2-22-22-22-122-2-222-2-2111-1-11-12-2−2i−2i2i2i−2i2i2i−2i-1-1-1-111-1-11111iiii−i−i−i−iii−i−i−i−iii0000−33−33−i3i3−i3i30000000000000000
χ492-2-22-22-22-1-2-22222-2-2111-1-11-1-222i2i−2i−2i−2i2i2i−2i-1-111-1-111-1-111−i−i−i−iiiiiii−i−i−i−iii00003−3−33−i3i3i3−i30000000000000000
χ502-2-22-22-22-1-2-22222-2-2111-1-11-1-222i2i−2i−2i−2i2i2i−2i-1-111-1-111-1-111−i−i−i−iiiiiii−i−i−i−iii0000−333−3i3−i3−i3i30000000000000000
χ512-2-22-22-22-1-2-22222-2-2111-1-11-1-22−2i−2i2i2i2i−2i−2i2i-1-111-1-111-1-111iiii−i−i−i−i−i−iiiii−i−i00003−3−33i3−i3−i3i30000000000000000
χ522-2-22-22-22-1-2-22222-2-2111-1-11-1-22−2i−2i2i2i2i−2i−2i2i-1-111-1-111-1-111iiii−i−i−i−i−i−iiiii−i−i0000−333−3−i3i3i3−i30000000000000000
χ5344444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-400000000222222-2-2-2-22200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-222222200000000000000000000000000000000000000000000
χ554444-4-4-4-444-44-400004-44-4-4-4400000000000000004-44-40000000000000000000000000000000000000000000000
χ564444-4-4-4-44-44-4400004-44-4-4-440000000000000000-44-440000000000000000000000000000000000000000000000
χ574444-4-4-4-4-24-44-40000-22-2222-20000000000000000-22-220066−6−666−6−66−66−66−66−60000000000000000000000000000
χ584444-4-4-4-4-24-44-40000-22-2222-20000000000000000-22-2200−6−666−6−666−66−66−66−660000000000000000000000000000
χ594444-4-4-4-4-2-44-440000-22-2222-200000000000000002-22-20066−6−666−6−6−66−66−66−660000000000000000000000000000
χ604444-4-4-4-4-2-44-440000-22-2222-200000000000000002-22-200−6−666−6−6666−66−66−66−60000000000000000000000000000
χ6144-4-44-4-4440000-444-444-44-4-4-40000000000-4400000000-4400000000000000000000000000000000000000000000
χ6244-4-44-4-44-200004-4-44-2-22-222200000044-4-4-2200000000-2200000000-2-2-2-222220000000000000000000000000000
χ6344-4-44-4-44-200004-4-44-2-22-2222000000-4-444-2200000000-22000000002222-2-2-2-20000000000000000000000000000
χ6444-4-44-4-44-20000-444-4-2-22-222200000000002-2000000002-2−2i32i3−2i32i3−2i32i3−2i32i3000000000000000000000000000000000000
χ6544-4-44-4-44-20000-444-4-2-22-222200000000002-2000000002-22i3−2i32i3−2i32i3−2i32i3−2i3000000000000000000000000000000000000
χ6644-4-4-444-44000000004-4-4-444-400−2i22i2−2i22i20000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ6744-4-4-444-44000000004-4-4-444-4002i2−2i22i2−2i200000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ6844-4-4-444-4-200000000-2222-2-2200−2i22i2−2i22i2000000−2i32i3−2i32i3000000i2−i2−i2i2i2−i2−i2i26−66−6−66−660000000000000000000000000000
χ6944-4-4-444-4-200000000-2222-2-2200−2i22i2−2i22i20000002i3−2i32i3−2i3000000i2−i2−i2i2i2−i2−i2i2−66−666−66−60000000000000000000000000000
χ7044-4-4-444-4-200000000-2222-2-22002i2−2i22i2−2i2000000−2i32i3−2i32i3000000−i2i2i2−i2−i2i2i2−i2−66−666−66−60000000000000000000000000000
χ7144-4-4-444-4-200000000-2222-2-22002i2−2i22i2−2i20000002i3−2i32i3−2i3000000−i2i2i2−i2−i2i2i2−i26−66−6−66−660000000000000000000000000000
χ724-44-444-4-4400000000-444-44-4-40022−22−2222000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ734-44-444-4-4400000000-444-44-4-400−222222−220000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ744-44-444-4-4-2000000002-2-22-2220022−22−2222000000−2i32i32i3−2i3000000−222−22−2−22i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ754-44-444-4-4-2000000002-2-22-2220022−22−22220000002i3−2i3−2i32i3000000−222−22−2−22−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ764-44-444-4-4-2000000002-2-22-22200−222222−22000000−2i32i32i3−2i30000002−2−22−222−2−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ774-44-444-4-4-2000000002-2-22-22200−222222−220000002i3−2i3−2i32i30000002−2−22−222−2i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ784-44-4-4-44440000-44-44-4-444-44-40000000000-44000000004-400000000000000000000000000000000000000000000
χ794-44-4-4-444-200004-44-422-2-22-220000004i−4i4i−4i-22000000002-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ804-44-4-4-444-200004-44-422-2-22-22000000−4i4i−4i4i-22000000002-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ814-44-4-4-444-20000-44-4422-2-22-2200000000002-200000000-2223−2323−23−2323−2323000000000000000000000000000000000000
χ824-44-4-4-444-20000-44-4422-2-22-2200000000002-200000000-22−2323−232323−2323−23000000000000000000000000000000000000
χ834-4-444-44-444-4-440000-44-4-4-44400000000000000004-4-440000000000000000000000000000000000000000000000
χ844-4-444-44-44-444-40000-44-4-4-4440000000000000000-444-40000000000000000000000000000000000000000000000
χ854-4-444-44-4-24-4-4400002-2222-2-20000000000000000-222-200i6i6−i6−i6−i6−i6i6i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ864-4-444-44-4-24-4-4400002-2222-2-20000000000000000-222-200−i6−i6i6i6i6i6−i6−i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ874-4-444-44-4-2-444-400002-2222-2-200000000000000002-2-2200i6i6−i6−i6−i6−i6i6i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ884-4-444-44-4-2-444-400002-2222-2-200000000000000002-2-2200−i6−i6i6i6i6i6−i6−i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ894-4-44-44-44-244-4-4-4-444222-2-22-2-44000000002222-2-2-2-222-2-200000000000000000000000000000000000000000000
χ904-4-44-44-44-2-4-444-4-444222-2-22-24-40000000022-2-22222-2-2-2-200000000000000000000000000000000000000000000

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