Finite Group Databasebeta

← Group #10858377

Character table — Group #10858377

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212121212121616161624242424242424244848
order122222223444466666664444121212121212121244444444888812121212121212121212242424242424242422224444121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111
χ511111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-1-111-1-1-11
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-1111-1
χ1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-1-111-1-11-1
χ1211111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1111-1-111-11
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-11-1-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11-11111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1111-1-1-1-1-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-111111-1-11-1
χ17222222222-2-2-2-2222222222-2-22222-2-2-2-20000000000000000-2-2000000000000000022-2-200002-200000000
χ18222222222-2-2-2-2222222222-2-22222-2-2-2-20000000000000000-2-20000000000000000-2-2220000-2200000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000000022000000000000000022220000-2-200000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-20000000000000000220000000000000000-2-2-2-200002200000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000011110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-21111-1-111111111111100000000-1-1-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-10000000011110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-12222-2-2-2-2-2-222-1-1-1-1111111-1-1-1-1111100000000-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-2-2-22222-2-2-1-1-1-11111111111-1-1-1-10000000011-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-22222-2-222-2-2111111-1-1-1-11111-1-1-1-100000000-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-2-2-22222-2-222111111-1-1-1-1-1-1-1-111110000000011-1-10000000000
χ292222-2-2-2-222-22-222-2-2-22-20000000022-2-22-2000000000022-2-20000000000000022-2-20000000000002-20000
χ302222-2-2-2-222-22-222-2-2-22-20000000022-2-22-2000000000022-2-200000000000000-2-222000000000000-220000
χ312222-2-2-2-222-22-222-2-2-22-20000000022-2-2-220000000000-2-2220000000000000022-2-2000000000000-220000
χ322222-2-2-2-222-22-222-2-2-22-20000000022-2-2-220000000000-2-22200000000000000-2-2220000000000002-20000
χ332-2-222-2-222-2-222-2-2-22-222000000002-22-200002-200000000000022-2-2000000002-22-2000000000000002-200
χ342-2-222-2-222-2-222-2-2-22-222000000002-22-200002-200000000000022-2-200000000-22-2200000000000000-2200
χ352-2-222-2-222-2-222-2-2-22-222000000002-22-20000-22000000000000-2-222000000002-22-200000000000000-2200
χ362-2-222-2-222-2-222-2-2-22-222000000002-22-20000-22000000000000-2-22200000000-22-22000000000000002-200
χ372-2-22-222-222-2-22-2-22-222-22i−2i2i−2i2i2i−2i−2i-222-2002-2002i−2i000000002i−2i000000000000000000002-22i−2i0000000000
χ382-2-22-222-222-2-22-2-22-222-22i−2i2i−2i2i2i−2i−2i-222-200-2200−2i2i000000002i−2i00000000000000000000-22−2i2i0000000000
χ392-2-22-222-222-2-22-2-22-222-2−2i2i−2i2i−2i−2i2i2i-222-2002-200−2i2i00000000−2i2i000000000000000000002-2−2i2i0000000000
χ402-2-22-222-222-2-22-2-22-222-2−2i2i−2i2i−2i−2i2i2i-222-200-22002i−2i00000000−2i2i00000000000000000000-222i−2i0000000000
χ412-2-22-222-22-222-2-2-22-222-22i−2i−2i2i2i2i−2i−2i2-2-220000000000000000−2i2i0000000000002-2-2200000000002i−2i000000
χ422-2-22-222-22-222-2-2-22-222-22i−2i−2i2i2i2i−2i−2i2-2-220000000000000000−2i2i000000000000-222-20000000000−2i2i000000
χ432-2-22-222-22-222-2-2-22-222-2−2i2i2i−2i−2i−2i2i2i2-2-2200000000000000002i−2i0000000000002-2-220000000000−2i2i000000
χ442-2-22-222-22-222-2-2-22-222-2−2i2i2i−2i−2i−2i2i2i2-2-2200000000000000002i−2i000000000000-222-200000000002i−2i000000
χ452-2-22-222-2-12-2-2211-11-1-112i−2i2i−2i−i−iii1-1-11002-2002i−2i0000−i3i3−i3i3−ii3−33−3−i3−i3i3i333−3−300000000-11−ii0000000000
χ462-2-22-222-2-12-2-2211-11-1-112i−2i2i−2i−i−iii1-1-11002-2002i−2i0000i3−i3i3−i3−ii−33−33i3i3−i3−i3−3−33300000000-11−ii0000000000
χ472-2-22-222-2-12-2-2211-11-1-112i−2i2i−2i−i−iii1-1-1100-2200−2i2i0000−i3i3−i3i3−ii3−33−3i3i3−i3−i3−3−333000000001-1i−i0000000000
χ482-2-22-222-2-12-2-2211-11-1-112i−2i2i−2i−i−iii1-1-1100-2200−2i2i0000i3−i3i3−i3−ii−33−33−i3−i3i3i333−3−3000000001-1i−i0000000000
χ492-2-22-222-2-12-2-2211-11-1-11−2i2i−2i2iii−i−i1-1-11002-200−2i2i0000−i3i3−i3i3i−i−33−33−i3−i3i3i3−3−33300000000-11i−i0000000000
χ502-2-22-222-2-12-2-2211-11-1-11−2i2i−2i2iii−i−i1-1-11002-200−2i2i0000i3−i3i3−i3i−i3−33−3i3i3−i3−i333−3−300000000-11i−i0000000000
χ512-2-22-222-2-12-2-2211-11-1-11−2i2i−2i2iii−i−i1-1-1100-22002i−2i0000−i3i3−i3i3i−i−33−33i3i3−i3−i333−3−3000000001-1−ii0000000000
χ522-2-22-222-2-12-2-2211-11-1-11−2i2i−2i2iii−i−i1-1-1100-22002i−2i0000i3−i3i3−i3i−i3−33−3−i3−i3i3i3−3−333000000001-1−ii0000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-222220000000000000000220000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222222220000000000000000-2-20000000000000000000000000000000000
χ554444-4-4-4-44-44-4444-4-4-44-400000000-4-4440000000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-24-44-4-2-2222-2200000000-2-2224-40000000000-2-222000000000000000000000000000000000000
χ574444-4-4-4-4-24-44-4-2-2222-2200000000-2-222-44000000000022-2-2000000000000000000000000000000000000
χ584444-4-4-4-4-2-44-44-2-2222-220000000022-2-200000000000000000023−23−2323000000000000000000000000000000
χ594444-4-4-4-4-2-44-44-2-2222-220000000022-2-2000000000000000000−232323−23000000000000000000000000000000
χ6044-4-444-4-4400004-4-444-4-400000000000000000000000000000000000000000000004-40000000000000000
χ6144-4-444-4-4400004-4-444-4-40000000000000000000000000000000000000000000000-440000000000000000
χ6244-4-4-4-444400004-44-4-4-44000000000000000000000022−22000000000022−2222−2200000000000000000000000000
χ6344-4-4-4-444400004-44-4-4-440000000000000000000000−22220000000000−2222−222200000000000000000000000000
χ6444-4-4-4-444-20000-22-2222-2000023−2323−230000000000000022−220000000000−22−226−66−60000000000000000000000
χ6544-4-4-4-444-20000-22-2222-2000023−2323−2300000000000000−222200000000002−22−2−66−660000000000000000000000
χ6644-4-4-4-444-20000-22-2222-20000−2323−23230000000000000022−220000000000−22−22−66−660000000000000000000000
χ6744-4-4-4-444-20000-22-2222-20000−2323−232300000000000000−222200000000002−22−26−66−60000000000000000000000
χ684-44-44-44-440000-4444-4-4-40000000000000000000022−22000000000000000022−22−22220000000000000000000000
χ694-44-44-44-440000-4444-4-4-400000000000000000000−22220000000000000000−222222−220000000000000000000000
χ704-44-44-44-4-200002-2-2-22220000−2i32i32i3−2i300000000000022−22000000000000−i6i6i6−i6−222−20000000000000000000000
χ714-44-44-44-4-200002-2-2-22220000−2i32i32i3−2i3000000000000−2222000000000000i6−i6−i6i62−2−220000000000000000000000
χ724-44-44-44-4-200002-2-2-222200002i3−2i3−2i32i300000000000022−22000000000000i6−i6−i6i6−222−20000000000000000000000
χ734-44-44-44-4-200002-2-2-222200002i3−2i3−2i32i3000000000000−2222000000000000−i6i6i6−i62−2−220000000000000000000000
χ744-44-4-44-4440000-44-4-44-440000000000000000000000000000000000000000000000004-400000000000000
χ754-44-4-44-4440000-44-4-44-44000000000000000000000000000000000000000000000000-4400000000000000
χ764-4-444-4-44444-4-4-4-4-44-44400000000-44-440000000000000000000000000000000000000000000000000000
χ774-4-444-4-44-244-4-4222-22-2-2000000002-22-2000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ784-4-444-4-44-244-4-4222-22-2-2000000002-22-20000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ794-4-444-4-44-2-4-444222-22-2-200000000-22-2200004-4000000000000-2-222000000000000000000000000000000
χ804-4-444-4-44-2-4-444222-22-2-200000000-22-220000-4400000000000022-2-2000000000000000000000000000000
χ814-4-44-444-4-2-444-422-22-2-224i−4i−4i4i−2i−2i2i2i-222-200000000000000002i−2i0000000000000000000000000000000000
χ824-4-44-444-4-2-444-422-22-2-22−4i4i4i−4i2i2i−2i−2i-222-20000000000000000−2i2i0000000000000000000000000000000000
χ8388-8-888-8-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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