Finite Group Databasebeta

← Group #10844793

Character table — Group #10844793

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order12222222344444444666666644888888881212121212121212121212122424242424242424242424242424242422446666121212122244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111
χ911111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-11-1-1-11-111-1-1
χ1011111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-111-1111-11-1-111
χ1111111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-11-1-1-11-1-111
χ1211111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-1111-1111-111-1-1
χ1311111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-11111-1-111-11-1-1-1111-1-1
χ1411111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111-1-111-1-11-1111-1-1-111
χ1511111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-111-1-1111-1-1-11-1-1-111
χ1611111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1-1-111-1-1-1111-1111-1-1
χ17222222222-2-22222-2-22222222-2-200000000-2-22222-2-2-2-2-2-200000000000000000000000000000000002200-2-20000
χ18222222222-2-22222-2-22222222-2-200000000-2-22222-2-2-2-2-2-20000000000000000000000000000000000-2-200220000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-200000000000000000000000000000000002-200-220000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-20000000000000000000000000000000000-22002-20000
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
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-1110000000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-10000000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-12-2-22-1-11111-1-10000000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-222-211-1-1-1-1110000000000000000
χ29222-22-2-2-222-20000-2222-22-2-2-2002i2i−2i−2i00002-2000000002-22i2i2i2i−2i−2i−2i−2i000000000000000000002-22i−2i000000000000
χ30222-22-2-2-222-20000-2222-22-2-2-2002i2i−2i−2i00002-2000000002-22i2i2i2i−2i−2i−2i−2i00000000000000000000-22−2i2i000000000000
χ31222-22-2-2-222-20000-2222-22-2-2-200−2i−2i2i2i00002-2000000002-2−2i−2i−2i−2i2i2i2i2i000000000000000000002-2−2i2i000000000000
χ32222-22-2-2-222-20000-2222-22-2-2-200−2i−2i2i2i00002-2000000002-2−2i−2i−2i−2i2i2i2i2i00000000000000000000-222i−2i000000000000
χ332-222-22-2-222-200002-2-2-222-2-22002-22-200002-200000000-2222-2-222-2-20000000000000000000000002i−2i002i−2i000000
χ342-222-22-2-222-200002-2-2-222-2-22002-22-200002-200000000-2222-2-222-2-2000000000000000000000000−2i2i00−2i2i000000
χ352-222-22-2-222-200002-2-2-222-2-2200-22-2200002-200000000-22-2-222-2-2220000000000000000000000002i−2i00−2i2i000000
χ362-222-22-2-222-200002-2-2-222-2-2200-22-2200002-200000000-22-2-222-2-222000000000000000000000000−2i2i002i−2i000000
χ372-22-2-2-22222222-2-2-2-2-2-2-2222-22-22i−2i−2i2i2i2i−2i−2i2222-2-222-2-2-2-22i2i−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ382-22-2-2-22222222-2-2-2-2-2-2-2222-22-2−2i2i2i−2i−2i−2i2i2i2222-2-222-2-2-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ392-22-2-2-222222-2-222-2-2-2-2-2222-2-222i−2i−2i2i−2i−2i2i2i22-2-222-2-222-2-22i2i−2i−2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ402-22-2-2-222222-2-222-2-2-2-2-2222-2-22−2i2i2i−2i2i2i−2i−2i22-2-222-2-222-2-2−2i−2i2i2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ412-22-2-2-2222-2-222-2-222-2-2-2222-2-2200000000-2-222-2-2-2-2222200000000000000000000000000000000000000002-22-2
χ422-22-2-2-2222-2-222-2-222-2-2-2222-2-2200000000-2-222-2-2-2-222220000000000000000000000000000000000000000-22-22
χ432-22-2-2-2222-2-2-2-22222-2-2-2222-22-200000000-2-2-2-22222-2-22200000000000000000000000000000000000000002-2-22
χ442-22-2-2-2222-2-2-2-22222-2-2-2222-22-200000000-2-2-2-22222-2-2220000000000000000000000000000000000000000-222-2
χ452-22-2-2-222-12222-2-2-2-2111-1-1-112-22i−2i−2i2i2i2i−2i−2i-1-1-1-111-1-11111−i−iiiii−i−i−i−i−i−iiiii0000−i3i3−i3i33−33−30000000000000000
χ462-22-2-2-222-12222-2-2-2-2111-1-1-112-22i−2i−2i2i2i2i−2i−2i-1-1-1-111-1-11111−i−iiiii−i−i−i−i−i−iiiii0000i3−i3i3−i3−33−330000000000000000
χ472-22-2-2-222-12222-2-2-2-2111-1-1-112-2−2i2i2i−2i−2i−2i2i2i-1-1-1-111-1-11111ii−i−i−i−iiiiiii−i−i−i−i0000−i3i3−i3i3−33−330000000000000000
χ482-22-2-2-222-12222-2-2-2-2111-1-1-112-2−2i2i2i−2i−2i−2i2i2i-1-1-1-111-1-11111ii−i−i−i−iiiiiii−i−i−i−i0000i3−i3i3−i33−33−30000000000000000
χ492-22-2-2-222-122-2-222-2-2111-1-1-11-222i−2i−2i2i−2i−2i2i2i-1-111-1-111-1-111−i−iiiii−i−iiiii−i−i−i−i0000−i3i3i3−i33−3−330000000000000000
χ502-22-2-2-222-122-2-222-2-2111-1-1-11-222i−2i−2i2i−2i−2i2i2i-1-111-1-111-1-111−i−iiiii−i−iiiii−i−i−i−i0000i3−i3−i3i3−333−30000000000000000
χ512-22-2-2-222-122-2-222-2-2111-1-1-11-22−2i2i2i−2i2i2i−2i−2i-1-111-1-111-1-111ii−i−i−i−iii−i−i−i−iiiii0000−i3i3i3−i3−333−30000000000000000
χ522-22-2-2-222-122-2-222-2-2111-1-1-11-22−2i2i2i−2i2i2i−2i−2i-1-111-1-111-1-111ii−i−i−i−iii−i−i−i−iiiii0000i3−i3−i3i33−3−330000000000000000
χ5344444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-40000000022-2-2-2-222222200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24400000000222222-2-2-2-22200000000000000000000000000000000000000000000
χ55444-44-4-4-44-4400004-444-44-4-4-40000000000-4400000000-4400000000000000000000000000000000000000000000
χ56444-44-4-4-4-24-40000-44-2-22-2222004i4i−4i−4i0000-2200000000-22−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ57444-44-4-4-4-24-40000-44-2-22-222200−4i−4i4i4i0000-2200000000-222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ58444-44-4-4-4-2-4400004-4-2-22-222200000000002-2000000002-2000000002323−23−232323−23−230000000000000000000000000000
χ59444-44-4-4-4-2-4400004-4-2-22-222200000000002-2000000002-200000000−23−232323−23−2323230000000000000000000000000000
χ6044-44-4-4-444004-44-4004-4-4-44-440000000000004-44-400000000000000000000000000000000000000000000000000
χ6144-44-4-4-44400-44-44004-4-4-44-44000000000000-44-4400000000000000000000000000000000000000000000000000
χ6244-44-4-4-44-2004-44-400-2222-22-2000000000000-22-22000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i60000000000000000000000000000
χ6344-44-4-4-44-2004-44-400-2222-22-2000000000000-22-22000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i60000000000000000000000000000
χ6444-44-4-4-44-200-44-4400-2222-22-20000000000002-22-2000000i6−i6i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6−i6i60000000000000000000000000000
χ6544-44-4-4-44-200-44-4400-2222-22-20000000000002-22-2000000−i6i6−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6i6−i60000000000000000000000000000
χ6644-4-4-444-44000000004-44-4-44-4000000−2i22i2−2i22i200000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ6744-4-4-444-44000000004-44-4-44-40000002i2−2i22i2−2i2000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ6844-4-4-444-4-200000000-22-222-22000000−2i22i2−2i22i2000000−2i32i3−2i32i3006−66−6−66−66i2−i2−i2i2i2−i2−i2i20000000000000000000000000000
χ6944-4-4-444-4-200000000-22-222-22000000−2i22i2−2i22i20000002i3−2i32i3−2i300−66−666−66−6i2−i2−i2i2i2−i2−i2i20000000000000000000000000000
χ7044-4-4-444-4-200000000-22-222-220000002i2−2i22i2−2i2000000−2i32i3−2i32i300−66−666−66−6−i2i2i2−i2−i2i2i2−i20000000000000000000000000000
χ7144-4-4-444-4-200000000-22-222-220000002i2−2i22i2−2i20000002i3−2i32i3−2i3006−66−6−66−66−i2i2i2−i2−i2i2i2−i20000000000000000000000000000
χ724-444-44-4-44-440000-44-4-444-4-440000000000-44000000004-400000000000000000000000000000000000000000000
χ734-444-44-4-4-24-400004-422-2-222-2004-44-40000-22000000002-2-2-222-2-222000000000000000000000000000000000000
χ744-444-44-4-4-24-400004-422-2-222-200-44-440000-22000000002-222-2-222-2-2000000000000000000000000000000000000
χ754-444-44-4-4-2-440000-4422-2-222-200000000002-200000000-2200000000−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000
χ764-444-44-4-4-2-440000-4422-2-222-200000000002-200000000-22000000002i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000
χ774-44-4-4-444-2-4-444-4-444222-2-2-22-440000000022-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ784-44-4-4-444-2-4-4-4-44444222-2-2-224-4000000002222-2-2-2-222-2-200000000000000000000000000000000000000000000
χ794-4-444-44-4400000000-44-4-4-44400000022−22−22220000000000000000000022−22−2222−222222−220000000000000000000000000000
χ804-4-444-44-4400000000-44-4-4-444000000−222222−2200000000000000000000−222222−2222−22−22220000000000000000000000000000
χ814-4-444-44-4-2000000002-2222-2-200000022−22−2222000000−2i32i32i3−2i300i6−i6−i6i6i6−i6−i6i6−222−22−2−220000000000000000000000000000
χ824-4-444-44-4-2000000002-2222-2-200000022−22−22220000002i3−2i3−2i32i300−i6i6i6−i6−i6i6i6−i6−222−22−2−220000000000000000000000000000
χ834-4-444-44-4-2000000002-2222-2-2000000−222222−22000000−2i32i32i3−2i300−i6i6i6−i6−i6i6i6−i62−2−22−222−20000000000000000000000000000
χ844-4-444-44-4-2000000002-2222-2-2000000−222222−220000002i3−2i3−2i32i300i6−i6−i6i6i6−i6−i6i62−2−22−222−20000000000000000000000000000
χ854-4-4-444-444004-4-4400-444-44-4-40000000000004-4-4400000000000000000000000000000000000000000000000000
χ864-4-4-444-44400-444-400-444-44-4-4000000000000-444-400000000000000000000000000000000000000000000000000
χ874-4-4-444-44-2004-4-44002-2-22-222000000000000-222-20000006−6−66−666−66−66−6−66−660000000000000000000000000000
χ884-4-4-444-44-2004-4-44002-2-22-222000000000000-222-2000000−666−66−6−66−66−666−66−60000000000000000000000000000
χ894-4-4-444-44-200-444-4002-2-22-2220000000000002-2-220000006−6−66−666−6−66−666−66−60000000000000000000000000000
χ904-4-4-444-44-200-444-4002-2-22-2220000000000002-2-22000000−666−66−6−666−66−6−66−660000000000000000000000000000

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