Finite Group Databasebeta

← Group #10829068

Character table — Group #10829068

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222224444444444888888888888888888888888121212121616161616161616242424242424242424244848
order12222222223666444466666624444444661212121212121212121212121212444444121212121212244444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-111111111-1-111-1-1-1-1-11-1-11-11111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11-111-11-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-11111-11-1-11-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111111-111-111111-1-1
χ911111111111111-1-1-1-11111111-11-111-1-11111-1-1-1-1-1-1-1-1111111111-1-1-111-1-1-1-11-1-1111-1-11-1
χ1011111111111111-1-1-1-11111111-11-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-111-1-111-111-1-1-111-11
χ1111111111111111-1-1-1-11111111-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-11-1-11-1-111-11
χ1211111111111111-1-1-1-11111111-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-111-111-1-11-1
χ1311111111111111-1-1-1-1111111-11-1111-1-1-1-1-1-1-1-111-1-11111111111-11-1-1-1-1111-1-11-1-111-1-1-11
χ1411111111111111-1-1-1-1111111-11-1111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-11-1-1-1-111-111-111-1-1111-1
χ1511111111111111-1-1-1-1111111-11-11-1-111-1-1-1-1-1-111-1-111-1-1-1-111111-11111-1-11-1-11-1-1-1-1111-1
χ1611111111111111-1-1-1-1111111-11-11-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11-11111-1-1-111-11111-1-1-11
χ172222222222-1-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1000000000000
χ182222222222-1-1-1-12222-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000-2-2111111000000000000
χ192222222222-1-1-1-12222-1-1-1-1-1-1-2-2-2-222221111-1-111-1-111-1-1-1-10000-2-2-1-11111000000000000
χ202222222222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-111-1-111111100002211-1-1-1-1000000000000
χ212222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-12-22-222-2-2-1-1-1-111111111-1-1-1-100002-211-1-111000000000000
χ222222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-12-22-2-2-222-1-1-1-11111111111110000-22-1-111-1-1000000000000
χ232222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-22-2222-2-2111111-1-111-1-1-1-1-1-10000-221111-1-1000000000000
χ242222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-22-22-2-222111111-1-111-1-1111100002-2-1-1-1-111000000000000
χ2522222-2-2-2-22222222-2-22-2-22-2-20000000000002200-2-200000022-2-2000000000200-20000000
χ2622222-2-2-2-22222222-2-22-2-22-2-20000000000002200-2-2000000-2-222000000000-20020000000
χ2722222-2-2-2-222222-2-2222-2-22-2-2000000000000-2-2002200000022-2-2000000000-20020000000
χ2822222-2-2-2-222222-2-2222-2-22-2-2000000000000-2-20022000000-2-222000000000200-20000000
χ292222-22-22-2-222220000-22-2-22-2020-200000000002200-2-200002-22-200000000200-200000000
χ302222-22-22-2-222220000-22-2-22-2020-200000000002200-2-20000-22-2200000000-200200000000
χ312222-22-22-2-222220000-22-2-22-20-2020000000000-2-2002200002-22-200000000-200200000000
χ322222-22-22-2-222220000-22-2-22-20-2020000000000-2-200220000-22-2200000000200-200000000
χ332222-2-22-22-222220000-2-22-2-2220-20000022-2-20000000000002-2-220000000000-2002000000
χ342222-2-22-22-222220000-2-22-2-2220-20000022-2-2000000000000-222-20000000000200-2000000
χ352222-2-22-22-222220000-2-22-2-22-20200000-2-2220000000000002-2-220000000000200-2000000
χ362222-2-22-22-222220000-2-22-2-22-20200000-2-222000000000000-222-20000000000-2002000000
χ372-22-2-22-2-22222-2-22i−2i2i−2i-2-2222-200002i−2i2-200002i−2i002i−2i002i2i−2i−2i0000002-20000000000000000
χ382-22-2-22-2-22222-2-22i−2i2i−2i-2-2222-20000−2i2i-2200002i−2i002i−2i00−2i−2i2i2i000000-220000000000000000
χ392-22-2-22-2-22222-2-2−2i2i−2i2i-2-2222-200002i−2i-220000−2i2i00−2i2i002i2i−2i−2i000000-220000000000000000
χ402-22-2-22-2-22222-2-2−2i2i−2i2i-2-2222-20000−2i2i2-20000−2i2i00−2i2i00−2i−2i2i2i0000002-20000000000000000
χ412-22-2-22-2-222-1-1112i−2i2i−2i11-1-1-1100002i−2i2-2−i3i3−i3i3−ii3−3−ii3−3−i−iii000000-113−3−i3i3000000000000
χ422-22-2-22-2-222-1-1112i−2i2i−2i11-1-1-1100002i−2i2-2i3−i3i3−i3−ii−33−ii−33−i−iii000000-11−33i3−i3000000000000
χ432-22-2-22-2-222-1-1112i−2i2i−2i11-1-1-110000−2i2i-22−i3i3−i3i3−ii3−3−ii3−3ii−i−i0000001-1−33i3−i3000000000000
χ442-22-2-22-2-222-1-1112i−2i2i−2i11-1-1-110000−2i2i-22i3−i3i3−i3−ii−33−ii−33ii−i−i0000001-13−3−i3i3000000000000
χ452-22-2-22-2-222-1-111−2i2i−2i2i11-1-1-1100002i−2i-22−i3i3−i3i3i−i−33i−i−33−i−iii0000001-13−3i3−i3000000000000
χ462-22-2-22-2-222-1-111−2i2i−2i2i11-1-1-1100002i−2i-22i3−i3i3−i3i−i3−3i−i3−3−i−iii0000001-1−33−i3i3000000000000
χ472-22-2-22-2-222-1-111−2i2i−2i2i11-1-1-110000−2i2i2-2−i3i3−i3i3i−i−33i−i−33ii−i−i000000-11−33−i3i3000000000000
χ482-22-2-22-2-222-1-111−2i2i−2i2i11-1-1-110000−2i2i2-2i3−i3i3−i3i−i3−3i−i3−3ii−i−i000000-113−3i3−i3000000000000
χ492-22-2-2-222-2222-2-22i−2i−2i2i-22-22-220000000000002i−2i00−2i2i0000000000000000000000002i−2i2-200
χ502-22-2-2-222-2222-2-22i−2i−2i2i-22-22-220000000000002i−2i00−2i2i000000000000000000000000−2i2i-2200
χ512-22-2-2-222-2222-2-2−2i2i2i−2i-22-22-22000000000000−2i2i002i−2i0000000000000000000000002i−2i-2200
χ522-22-2-2-222-2222-2-2−2i2i2i−2i-22-22-22000000000000−2i2i002i−2i000000000000000000000000−2i2i2-200
χ5344444-4-4-4-44-2-2-2-244-4-4-222-222000000000000-2-20022000000000000000000000000000000
χ5444444-4-4-4-44-2-2-2-2-4-444-222-2220000000000002200-2-2000000000000000000000000000000
χ554444-44-44-4-4-2-2-2-200002-222-22040-40000000000-2-200220000000000000000000000000000
χ564444-44-44-4-4-2-2-2-200002-222-220-40400000000002200-2-20000000000000000000000000000
χ574444-4-44-44-4-2-2-2-2000022-222-240-400000-2-222000000000000000000000000000000000000
χ584444-4-44-44-4-2-2-2-2000022-222-2-4040000022-2-2000000000000000000000000000000000000
χ594-44-4444-4-4-444-4-400004-4-4-444000000000000000000000000000000000000000000000000
χ604-44-4444-4-4-4-2-2220000-2222-2-20000000000000023−2300−23230000000000000000000000000000
χ614-44-4444-4-4-4-2-2220000-2222-2-200000000000000−23230023−230000000000000000000000000000
χ624-44-44-4-444-444-4-40000444-4-4-4000000000000000000000000000000000000000000000000
χ634-44-44-4-444-4-2-2220000-2-2-222200000000−2i32i32i3−2i3000000000000000000000000000000000000
χ644-44-44-4-444-4-2-2220000-2-2-2222000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ654-44-4-4-444-44-2-2224i−4i−4i4i2-22-22-2000000000000−2i2i002i−2i000000000000000000000000000000
χ664-44-4-4-444-44-2-222−4i4i4i−4i2-22-22-20000000000002i−2i00−2i2i000000000000000000000000000000
χ6788-8-80000008-88-80000000000000000000000000000000000000000000000000000000000
χ6888-8-8000000-44-4400000000000000000000000000000023−2323−23000000000000000000000000
χ6988-8-8000000-44-44000000000000000000000000000000−2323−2323000000000000000000000000
χ708-8-880000008-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-88000000-444-4000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ728-8-88000000-444-40000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000

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