Finite Group Databasebeta

← Group #10690968

Character table — Group #10690968

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222222222344446666666444444444466661212121212121212121212121212121212121212121212122444661212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-11-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-111−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ21222222222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111112-2-22-1-11111-1-10000000000000000
χ22222222222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-222-211-1-1-1-1110000000000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ2722222222-2-2-2-2222222222222-2-222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2822222222-2-2-2-2222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-2-2-22222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-2-2-22222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-12222-2-222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-1111122-2-2-1-1-1-111110000000000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-12222-2-222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-11111-2-2221111-1-1-1-10000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-12-22-2-1-111-1-1110000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-1-22-2211-1-111-1-10000000000000000
χ372-2-222-2-2222-2-220000-2-222-2-220000002-22-222-2-2000000000000000022-2-222-2-200000000000000000000−i2i2−i2i2−i2i2−i2i2
χ382-2-222-2-2222-2-220000-2-222-2-220000002-22-222-2-2000000000000000022-2-222-2-200000000000000000000i2−i2i2−i2i2−i2i2−i2
χ392-2-222-2-2222-2-220000-2-222-2-22000000-22-2222-2-20000000000000000-2-222-2-22200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ402-2-222-2-2222-2-220000-2-222-2-22000000-22-2222-2-20000000000000000-2-222-2-22200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ412-2-222-2-22-2-22220000-2-222-2-220000002-2-22-2-222000000000000000022-2-2-2-222000000000000000000002−2−222−2−22
χ422-2-222-2-22-2-22220000-2-222-2-220000002-2-22-2-222000000000000000022-2-2-2-22200000000000000000000−222−2−222−2
χ432-2-222-2-22-2-22220000-2-222-2-22000000-222-2-2-2220000000000000000-2-22222-2-2000000000000000000002−2−22−222−2
χ442-2-222-2-22-2-22220000-2-222-2-22000000-222-2-2-2220000000000000000-2-22222-2-200000000000000000000−222−22−2−22
χ452-2-2-2-22222-22-2222-2-2-2-2-2-22222-2000000002-22-222-2-222-2-2000000000000000000000000000000002i−2i2i−2i00000000
χ462-2-2-2-22222-22-2222-2-2-2-2-2-22222-2000000002-22-222-2-222-2-200000000000000000000000000000000−2i2i−2i2i00000000
χ472-2-2-2-22222-22-22-2-222-2-2-2-2222-22000000002-22-2-2-222-2-22200000000000000000000000000002i−2i2i−2i000000000000
χ482-2-2-2-22222-22-22-2-222-2-2-2-2222-22000000002-22-2-2-222-2-2220000000000000000000000000000−2i2i−2i2i000000000000
χ492-2-2-2-2222-22-22222-2-2-2-2-2-2222-2200000000-22-22-2-22222-2-200000000000000000000000000002-2-22000000000000
χ502-2-2-2-2222-22-22222-2-2-2-2-2-2222-2200000000-22-22-2-22222-2-20000000000000000000000000000-222-2000000000000
χ512-2-2-2-2222-22-222-2-222-2-2-2-22222-200000000-22-2222-2-2-2-222000000000000000000000000000000002-2-2200000000
χ522-2-2-2-2222-22-222-2-222-2-2-2-22222-200000000-22-2222-2-2-2-22200000000000000000000000000000000-222-200000000
χ53444-4-4-4-444-4-444000044-4-4-4-4400000000004-4-440000000000000000000000000000000000000000000000000000
χ54444-4-4-4-444-4-44-20000-2-22222-20000000000-222-2000000002323−23−232323−23−23000000000000000000000000000000000000
χ55444-4-4-4-444-4-44-20000-2-22222-20000000000-222-200000000−23−232323−23−232323000000000000000000000000000000000000
χ56444-4-4-4-44-444-44000044-4-4-4-440000000000-444-40000000000000000000000000000000000000000000000000000
χ57444-4-4-4-44-444-4-20000-2-22222-200000000002-2-22000000002323−23−23−23−232323000000000000000000000000000000000000
χ58444-4-4-4-44-444-4-20000-2-22222-200000000002-2-2200000000−23−2323232323−23−23000000000000000000000000000000000000
χ5944-44-44-4-40000400004-44-44-4-400004i−4i000000000000000000004i−4i4i−4i000000000000000000000000000000000000
χ6044-44-44-4-40000400004-44-44-4-40000−4i4i00000000000000000000−4i4i−4i4i000000000000000000000000000000000000
χ6144-44-44-4-40000-20000-22-22-22200004i−4i00000000−2i32i3−2i32i300000000−2i2i−2i2i000023−2323−230000000000000000000000000000
χ6244-44-44-4-40000-20000-22-22-22200004i−4i000000002i3−2i32i3−2i300000000−2i2i−2i2i0000−2323−23230000000000000000000000000000
χ6344-44-44-4-40000-20000-22-22-2220000−4i4i00000000−2i32i3−2i32i3000000002i−2i2i−2i0000−2323−23230000000000000000000000000000
χ6444-44-44-4-40000-20000-22-22-2220000−4i4i000000002i3−2i32i3−2i3000000002i−2i2i−2i000023−2323−230000000000000000000000000000
χ6544-4-44-44-4000044i−4i4i−4i4-4-44-44-40000000000000000004i−4i4i−4i00000000000000000000000000000000000000000000
χ6644-4-44-44-400004−4i4i−4i4i4-4-44-44-4000000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000
χ6744-4-44-44-40000-24i−4i4i−4i-222-22-22000000000000000000−2i2i−2i2i0000−2i32i32i3−2i323−2323−2300000000000000000000000000000000
χ6844-4-44-44-40000-24i−4i4i−4i-222-22-22000000000000000000−2i2i−2i2i00002i3−2i3−2i32i3−2323−232300000000000000000000000000000000
χ6944-4-44-44-40000-2−4i4i−4i4i-222-22-220000000000000000002i−2i2i−2i0000−2i32i32i3−2i3−2323−232300000000000000000000000000000000
χ7044-4-44-44-40000-2−4i4i−4i4i-222-22-220000000000000000002i−2i2i−2i00002i3−2i3−2i32i323−2323−2300000000000000000000000000000000
χ714-444-4-44-4000044i−4i−4i4i-444-4-44-40000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ724-444-4-44-400004−4i4i4i−4i-444-4-44-4000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ734-444-4-44-40000-24i−4i−4i4i2-2-222-22000000000000000000−2i2i2i−2i−2i32i3−2i32i30000000023−23−23230000000000000000000000000000
χ744-444-4-44-40000-24i−4i−4i4i2-2-222-22000000000000000000−2i2i2i−2i2i3−2i32i3−2i300000000−232323−230000000000000000000000000000
χ754-444-4-44-40000-2−4i4i4i−4i2-2-222-220000000000000000002i−2i−2i2i−2i32i3−2i32i300000000−232323−230000000000000000000000000000
χ764-444-4-44-40000-2−4i4i4i−4i2-2-222-220000000000000000002i−2i−2i2i2i3−2i32i3−2i30000000023−23−23230000000000000000000000000000
χ774-44-444-4-4000040000-44-444-4-4004i−4i0000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ784-44-444-4-4000040000-44-444-4-400−4i4i000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ794-44-444-4-40000-200002-22-2-222004i−4i0000000000−2i32i32i3−2i30000−2i2i2i−2i000023−23−232300000000000000000000000000000000
χ804-44-444-4-40000-200002-22-2-222004i−4i00000000002i3−2i3−2i32i30000−2i2i2i−2i0000−232323−2300000000000000000000000000000000
χ814-44-444-4-40000-200002-22-2-22200−4i4i0000000000−2i32i32i3−2i300002i−2i−2i2i0000−232323−2300000000000000000000000000000000
χ824-44-444-4-40000-200002-22-2-22200−4i4i00000000002i3−2i3−2i32i300002i−2i−2i2i000023−23−232300000000000000000000000000000000
χ834-4-444-4-4444-4-4-2000022-2-222-20000004-44-4-2-2220000000000000000-2-222-2-2220000000000000000000000000000
χ844-4-444-4-4444-4-4-2000022-2-222-2000000-44-44-2-222000000000000000022-2-222-2-20000000000000000000000000000
χ854-4-444-4-44-4-444-2000022-2-222-20000004-4-4422-2-20000000000000000-2-22222-2-20000000000000000000000000000
χ864-4-444-4-44-4-444-2000022-2-222-2000000-444-422-2-2000000000000000022-2-2-2-2220000000000000000000000000000
χ874-4-4-4-44444-44-4-244-4-42222-2-2-24-400000000-22-22-2-222-2-22200000000000000000000000000000000000000000000
χ884-4-4-4-44444-44-4-2-4-4442222-2-2-2-4400000000-22-2222-2-222-2-200000000000000000000000000000000000000000000
χ894-4-4-4-4444-44-44-244-4-42222-2-2-2-44000000002-22-222-2-2-2-22200000000000000000000000000000000000000000000
χ904-4-4-4-4444-44-44-2-4-4442222-2-2-24-4000000002-22-2-2-22222-2-200000000000000000000000000000000000000000000

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