Finite Group Databasebeta

← Group #10844815

Character table — Group #10844815

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444412121212121212124444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111
χ9111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11-111-1-11-111-1-1
χ10111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-111-11-1-111-11-1-111
χ11111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1-1111-1-1-11-1-111
χ12111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1111-1-1-1111-111-1-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-11111-1-1-11-1-111-1111-1-1
χ14111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111-1-1111-111-1-11-1-1-111
χ15111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-111-1-11-1-1-1111-1-1-111
χ16111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1-1-111-1111-1-1-1111-1-1
χ172222222222222-2-2-2-22222222-2-2000000002222-2-2-2-2-2-2-2-200000000000000000000000000000000220000-2-20000
χ182222222222222-2-2-2-22222222-2-2000000002222-2-2-2-2-2-2-2-200000000000000000000000000000000-2-20000220000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-22222-2-2-2-2000000000000000000000000000000002-20000-220000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-22222-2-2-2-200000000000000000000000000000000-2200002-20000
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
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-1110000000000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-10000000000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-12-2-22-1-11111-1-10000000000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-1-222-211-1-1-1-1110000000000000000
χ2922-22-2-22-2200002-2-2222-2-2-2-22002i2i−2i−2i0000000000002-22-22i2i2i2i−2i−2i−2i−2i000000000000000000002i−2i00002-200000000
χ3022-22-2-22-2200002-2-2222-2-2-2-22002i2i−2i−2i0000000000002-22-22i2i2i2i−2i−2i−2i−2i00000000000000000000−2i2i0000-2200000000
χ3122-22-2-22-2200002-2-2222-2-2-2-2200−2i−2i2i2i0000000000002-22-2−2i−2i−2i−2i2i2i2i2i000000000000000000002i−2i0000-2200000000
χ3222-22-2-22-2200002-2-2222-2-2-2-2200−2i−2i2i2i0000000000002-22-2−2i−2i−2i−2i2i2i2i2i00000000000000000000−2i2i00002-200000000
χ332-22-22-22-2200002-22-2-2-22-2-222002-22-20000000000002-2-2222-2-222-2-200000000000000000000002i−2i00002i−2i000000
χ342-22-22-22-2200002-22-2-2-22-2-222002-22-20000000000002-2-2222-2-222-2-20000000000000000000000−2i2i0000−2i2i000000
χ352-22-22-22-2200002-22-2-2-22-2-22200-22-220000000000002-2-22-2-222-2-22200000000000000000000002i−2i0000−2i2i000000
χ362-22-22-22-2200002-22-2-2-22-2-22200-22-220000000000002-2-22-2-222-2-2220000000000000000000000−2i2i00002i−2i000000
χ372-2-2-2-2222222-2-222-2-2-2-2-222-222-22i−2i−2i2i2i2i−2i−2i22-2-222-2-222-2-22i2i−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ382-2-2-2-2222222-2-222-2-2-2-2-222-222-2−2i2i2i−2i−2i−2i2i2i22-2-222-2-222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ392-2-2-2-2222222-2-2-2-222-2-2-222-22-220000000022-2-2-2-222-2-22200000000000000000000000000000000000000002-22-2
χ402-2-2-2-2222222-2-2-2-222-2-2-222-22-220000000022-2-2-2-222-2-2220000000000000000000000000000000000000000-22-22
χ412-2-2-2-22222-2-22222-2-2-2-2-222-22-222i−2i−2i2i−2i−2i2i2i-2-222-2-22222-2-22i2i−2i−2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ422-2-2-2-22222-2-22222-2-2-2-2-222-22-22−2i2i2i−2i2i2i−2i−2i-2-222-2-22222-2-2−2i−2i2i2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ432-2-2-2-22222-2-222-2-222-2-2-222-222-200000000-2-22222-2-2-2-22200000000000000000000000000000000000000002-2-22
χ442-2-2-2-22222-2-222-2-222-2-2-222-222-200000000-2-22222-2-2-2-2220000000000000000000000000000000000000000-222-2
χ452-2-2-2-2222-122-2-222-2-2111-1-11-12-22i−2i−2i2i2i2i−2i−2i-1-111-1-111-1-111−i−iiiii−i−i−i−i−i−iiiii00003−33−3−i3i3−i3i30000000000000000
χ462-2-2-2-2222-122-2-222-2-2111-1-11-12-22i−2i−2i2i2i2i−2i−2i-1-111-1-111-1-111−i−iiiii−i−i−i−i−i−iiiii0000−33−33i3−i3i3−i30000000000000000
χ472-2-2-2-2222-122-2-222-2-2111-1-11-12-2−2i2i2i−2i−2i−2i2i2i-1-111-1-111-1-111ii−i−i−i−iiiiiii−i−i−i−i00003−33−3i3−i3i3−i30000000000000000
χ482-2-2-2-2222-122-2-222-2-2111-1-11-12-2−2i2i2i−2i−2i−2i2i2i-1-111-1-111-1-111ii−i−i−i−iiiiiii−i−i−i−i0000−33−33−i3i3−i3i30000000000000000
χ492-2-2-2-2222-1-2-22222-2-2111-1-11-1-222i−2i−2i2i−2i−2i2i2i11-1-111-1-1-1-111−i−iiiii−i−iiiii−i−i−i−i00003−3−33−i3i3i3−i30000000000000000
χ502-2-2-2-2222-1-2-22222-2-2111-1-11-1-222i−2i−2i2i−2i−2i2i2i11-1-111-1-1-1-111−i−iiiii−i−iiiii−i−i−i−i0000−333−3i3−i3−i3i30000000000000000
χ512-2-2-2-2222-1-2-22222-2-2111-1-11-1-22−2i2i2i−2i2i2i−2i−2i11-1-111-1-1-1-111ii−i−i−i−iii−i−i−i−iiiii00003−3−33i3−i3−i3i30000000000000000
χ522-2-2-2-2222-1-2-22222-2-2111-1-11-1-22−2i2i2i−2i2i2i−2i−2i11-1-111-1-1-1-111ii−i−i−i−iii−i−i−i−iiiii0000−333−3−i3i3i3−i30000000000000000
χ5344444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222222200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244000000002222-2-2-2-2222200000000000000000000000000000000000000000000
χ55444-4-44-4-444-44-400004-4-44-44-400000000004-44-40000000000000000000000000000000000000000000000000000
χ56444-4-44-4-44-44-4400004-4-44-44-40000000000-44-440000000000000000000000000000000000000000000000000000
χ57444-4-44-4-4-24-44-40000-222-22-220000000000-22-22000000006−66−66−66−666−6−666−6−60000000000000000000000000000
χ58444-4-44-4-4-24-44-40000-222-22-220000000000-22-2200000000−66−66−66−66−6−666−6−6660000000000000000000000000000
χ59444-4-44-4-4-2-44-440000-222-22-2200000000002-22-2000000006−66−66−66−6−6−666−6−6660000000000000000000000000000
χ60444-4-44-4-4-2-44-440000-222-22-2200000000002-22-200000000−66−66−66−6666−6−666−6−60000000000000000000000000000
χ6144-44-4-44-440000-444-444-4-4-4-44000000000000000000-44-4400000000000000000000000000000000000000000000
χ6244-44-4-44-4-200004-4-44-2-22222-2004i4i−4i−4i000000000000-22-22−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ6344-44-4-44-4-200004-4-44-2-22222-200−4i−4i4i4i000000000000-22-222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ6444-44-4-44-4-20000-444-4-2-22222-20000000000000000002-22-20000000023−2323−2323−2323−230000000000000000000000000000
χ6544-44-4-44-4-20000-444-4-2-22222-20000000000000000002-22-200000000−2323−2323−2323−23230000000000000000000000000000
χ6644-4-44-4-444000000004-44-44-4-400000022−2222−220000000000000000000022−22−222222−22−22220000000000000000000000000000
χ6744-4-44-4-444000000004-44-44-4-4000000−2222−222200000000000000000000−222222−22−222222−220000000000000000000000000000
χ6844-4-44-4-44-200000000-22-22-22200000022−2222−220000−2i32i3−2i32i30000i6−i6i6−i6−i6i6−i6i6−222−2−222−20000000000000000000000000000
χ6944-4-44-4-44-200000000-22-22-22200000022−2222−2200002i3−2i32i3−2i30000−i6i6−i6i6i6−i6i6−i6−222−2−222−20000000000000000000000000000
χ7044-4-44-4-44-200000000-22-22-222000000−2222−22220000−2i32i3−2i32i30000−i6i6−i6i6i6−i6i6−i62−2−222−2−220000000000000000000000000000
χ7144-4-44-4-44-200000000-22-22-222000000−2222−222200002i3−2i32i3−2i30000i6−i6i6−i6−i6i6−i6i62−2−222−2−220000000000000000000000000000
χ724-444-4-4-44400000000-44-4-444-4000000−2i22i22i2−2i200000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ734-444-4-4-44400000000-44-4-444-40000002i2−2i2−2i22i2000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ744-444-4-4-44-2000000002-222-2-22000000−2i22i22i2−2i20000−2i32i32i3−2i300006−6−666−6−66i2−i2−i2i2−i2i2i2−i20000000000000000000000000000
χ754-444-4-4-44-2000000002-222-2-22000000−2i22i22i2−2i200002i3−2i3−2i32i30000−666−6−666−6i2−i2−i2i2−i2i2i2−i20000000000000000000000000000
χ764-444-4-4-44-2000000002-222-2-220000002i2−2i2−2i22i20000−2i32i32i3−2i30000−666−6−666−6−i2i2i2−i2i2−i2−i2i20000000000000000000000000000
χ774-444-4-4-44-2000000002-222-2-220000002i2−2i2−2i22i200002i3−2i3−2i32i300006−6−666−6−66−i2i2i2−i2i2−i2−i2i20000000000000000000000000000
χ784-44-44-44-440000-44-44-4-44-4-444000000000000000000-444-400000000000000000000000000000000000000000000
χ794-44-44-44-4-200004-44-422-222-2-2004-44-4000000000000-222-2-2-222-2-222000000000000000000000000000000000000
χ804-44-44-44-4-200004-44-422-222-2-200-44-44000000000000-222-222-2-222-2-2000000000000000000000000000000000000
χ814-44-44-44-4-20000-44-4422-222-2-20000000000000000002-2-2200000000−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000
χ824-44-44-44-4-20000-44-4422-222-2-20000000000000000002-2-22000000002i3−2i32i3−2i3−2i32i3−2i32i30000000000000000000000000000
χ834-4-4444-4-444-4-440000-4444-4-4-400000000004-4-440000000000000000000000000000000000000000000000000000
χ844-4-4444-4-44-444-40000-4444-4-4-40000000000-444-40000000000000000000000000000000000000000000000000000
χ854-4-4444-4-4-24-4-4400002-2-2-22220000000000-222-200000000i6−i6−i6i6−i6i6i6−i6i6i6−i6−i6−i6−i6i6i60000000000000000000000000000
χ864-4-4444-4-4-24-4-4400002-2-2-22220000000000-222-200000000−i6i6i6−i6i6−i6−i6i6−i6−i6i6i6i6i6−i6−i60000000000000000000000000000
χ874-4-4444-4-4-2-444-400002-2-2-222200000000002-2-2200000000i6−i6−i6i6−i6i6i6−i6−i6−i6i6i6i6i6−i6−i60000000000000000000000000000
χ884-4-4444-4-4-2-444-400002-2-2-222200000000002-2-2200000000−i6i6i6−i6i6−i6−i6i6i6i6−i6−i6−i6−i6i6i60000000000000000000000000000
χ894-4-4-4-4444-244-4-4-4-444222-2-22-2-4400000000-2-22222-2-222-2-200000000000000000000000000000000000000000000
χ904-4-4-4-4444-2-4-444-4-444222-2-22-24-40000000022-2-2-2-22222-2-200000000000000000000000000000000000000000000

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