Finite Group Databasebeta

← Group #13150708

Character table — Group #13150708

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1222344666121212122466121233666666366666666666121212121212121212121212121212122244222444444466661212121266121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-11111-111-1-1-1-1-11111-1-111-1-111-1-1-1-111
χ611111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1-11111-1-1-111-1-111-1-1-1-11111-1-1
χ711111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-111-1-1
χ811111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1111-1-111-1-111-1-111-1-111
χ911111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11-111-111-1-1-1-1111-11-11-11-1
χ1011111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-111-1111-1-1-1-111-11-11-11-11
χ1111111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11-1-11-1-11111-1-11-11-1-11-11
χ1211111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-111-1-11-1-1-11111-1-1-11-111-11-1
χ1311111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-111-1-11-11-11-11111-1-1-1-11-1-11-111-1
χ1411111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-11-111-11-1-1-111111-1-1-1-1-111-11-1-11
χ1511111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-111-11-1-111-11-11-1-1-1-111111-1-111-1-11
χ1611111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-111-1-111-1-1111-1-1-1-1-11111-111-1-111-1
χ17222222222222222222222-12-1-12-12-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000022220000000000000-1-1-1-10000
χ18222222222222222222222-12-1-12-12-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000-2-2-2-2000000000000011110000
χ1922222222222222222222-12-122-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000022022000000000000-1-1-1-1
χ2022222222222222222222-12-122-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000-2-20-2-20000000000001111
χ2122222222222222-2-2-2-2-2-22-12-1-12-12-1-2-211-1-11111-1-1-11122-2-2-1-1-1-111110000022-2-20000000000000-1-1110000
χ2222222222222222-2-2-2-2-2-22-12-1-12-12-1-2-211-1-11111-1-1-11122-2-2-1-1-1-1111100000-2-222000000000000011-1-10000
χ2322222222222222-2-2-2-2-2-2-12-122-12-1-111-2-2-1-11111-122-2-2-1-111-1-1-1-11111000000000220-2-2000000000000-1-111
χ2422222222222222-2-2-2-2-2-2-12-122-12-1-111-2-2-1-11111-122-2-2-1-111-1-1-1-11111000000000-2-202200000000000011-1-1
χ2522222-2-2222-2-2-2-22-222-2-22-12-1-12-12-122-1-1-1-1-1-1-1-1-11111-2-2-2-211111111000002-22-20000000000000-11-110000
χ2622222-2-2222-2-2-2-22-222-2-22-12-1-12-12-122-1-1-1-1-1-1-1-1-11111-2-2-2-21111111100000-22-2200000000000001-11-10000
χ2722222-2-2222-2-2-2-22-222-2-2-12-122-12-1-1-1-122-1-1-1-1-1-1-1-2-2-2-21111111111110000000002-202-2000000000000-11-11
χ2822222-2-2222-2-2-2-22-222-2-2-12-122-12-1-1-1-122-1-1-1-1-1-1-1-2-2-2-2111111111111000000000-220-220000000000001-11-1
χ2922222-2-2222-2-2-2-2-22-2-2222-12-1-12-12-1-2-211-1-11111-111-1-1-2-2221111-1-1-1-1000002-2-220000000000000-111-10000
χ3022222-2-2222-2-2-2-2-22-2-2222-12-1-12-12-1-2-211-1-11111-111-1-1-2-2221111-1-1-1-100000-222-200000000000001-1-110000
χ3122222-2-2222-2-2-2-2-22-2-222-12-122-12-1-111-2-2-1-11111-1-2-22211-1-11111-1-1-1-10000000002-20-22000000000000-111-1
χ3222222-2-2222-2-2-2-2-22-2-222-12-122-12-1-111-2-2-1-11111-1-2-22211-1-11111-1-1-1-1000000000-2202-20000000000001-1-11
χ332-2-2222-2-2-2222-2-200000022-2-22-2-2220000-2-2000022-2002-20022-2-200002-22-200000000002-2002-20000000000
χ342-2-2222-2-2-2222-2-200000022-2-22-2-2220000-2-2000022-2002-20022-2-20000-22-220000000000-2200-220000000000
χ352-2-222-22-2-22-2-22200000022-2-22-2-2220000-2-200002-2200-2200-2-22200002-2-2200000000002-200-220000000000
χ362-2-222-22-2-22-2-22200000022-2-22-2-2220000-2-200002-2200-2200-2-2220000-222-20000000000-22002-20000000000
χ3744444444444444444444-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000
χ3844444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-21222211-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000
χ3944444-4-4444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-21-2-2-2-2111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4044444-4-4444-4-4-4-4-44-4-444-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4144-4-44004-4-400000000004444-4-4-4-4400004-40000-40000000000000000000000000000000000000000000000
χ4244-4-44004-4-400000000004-24-22-42-4-20000-22000020023−23000000002323−23−23000000000000000000000000000000
χ4344-4-44004-4-400000000004-24-22-42-4-20000-220000200−232300000000−23−232323000000000000000000000000000000
χ4444-4-44004-4-40000000000-24-24-42-42-2−2i32i300-22−2i3−2i32i32i320000000000000000000000000000000000000000000000
χ4544-4-44004-4-40000000000-24-24-42-42-22i3−2i300-222i32i3−2i3−2i320000000000000000000000000000000000000000000000
χ4644-4-44004-4-40000000000-2-2-2-222221−2i32i3001-1i3i3−i3−i3-10023−2300003i−3i3i−3i−3−333000000000000000000000000000000
χ4744-4-44004-4-40000000000-2-2-2-222221−2i32i3001-1i3i3−i3−i3-100−23230000−3i3i−3i3i33−3−3000000000000000000000000000000
χ4844-4-44004-4-40000000000-2-2-2-2222212i3−2i3001-1−i3−i3i3i3-10023−230000−3i3i−3i3i−3−333000000000000000000000000000000
χ4944-4-44004-4-40000000000-2-2-2-2222212i3−2i3001-1−i3−i3i3i3-100−232300003i−3i3i−3i33−3−3000000000000000000000000000000
χ504-44-4400-44-4000000000044-4-4-444-440000-440000-40000000000000000000000000000000000000000000000
χ514-44-4400-44-400000000004-2-4224-2-4-200−2i32i32-2−2i32i3−2i32i320000000000000000000000000000000000000000000000
χ524-44-4400-44-400000000004-2-4224-2-4-2002i3−2i32-22i3−2i32i3−2i320000000000000000000000000000000000000000000000
χ534-44-4400-44-40000000000-242-4-4-242-200002-20000200000023−23000023−2323−23000000000000000000000000000000
χ544-44-4400-44-40000000000-242-4-4-242-200002-200002000000−23230000−2323−2323000000000000000000000000000000
χ554-44-4400-44-40000000000-2-2222-2-22100−2i32i3-11i3−i3i3−i3-100000023−233i−3i−3i3i−33−33000000000000000000000000000000
χ564-44-4400-44-40000000000-2-2222-2-22100−2i32i3-11i3−i3i3−i3-1000000−2323−3i3i3i−3i3−33−3000000000000000000000000000000
χ574-44-4400-44-40000000000-2-2222-2-221002i3−2i3-11−i3i3−i3i3-100000023−23−3i3i3i−3i−33−33000000000000000000000000000000
χ584-44-4400-44-40000000000-2-2222-2-221002i3−2i3-11−i3i3−i3i3-1000000−23233i−3i−3i3i3−33−3000000000000000000000000000000
χ594-4-4444-4-4-4444-4-40000004-2-42-2-424-20000220000-2-22004-400-2-2220000000000000000000000000000000000
χ604-4-4444-4-4-4444-4-4000000-242-442-4-2-20000220000-24-400-2200-2-2220000000000000000000000000000000000
χ614-4-4444-4-4-4444-4-4000000-2-222-222-210000-1-13-3-331-2200-220011-1-13-3-33000000000000000000000000000000
χ624-4-4444-4-4-4444-4-4000000-2-222-222-210000-1-1-333-31-2200-220011-1-1-333-3000000000000000000000000000000
χ634-4-444-44-4-44-4-4440000004-2-42-2-424-20000220000-22-200-440022-2-20000000000000000000000000000000000
χ644-4-444-44-4-44-4-444000000-242-442-4-2-20000220000-2-44002-20022-2-20000000000000000000000000000000000
χ654-4-444-44-4-44-4-444000000-2-222-222-210000-1-13-3-3312-2002-200-1-111-333-3000000000000000000000000000000
χ664-4-444-44-4-44-4-444000000-2-222-222-210000-1-1-333-312-2002-200-1-1113-3-33000000000000000000000000000000
χ676666-366-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000022222000000200-1-1-1-1-1-1-1-100000000
χ686666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-2-2-2-2000000-2001111111100000000
χ696666-366-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000002222-2000000-200-1-111-1-11100000000
χ706666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-2-2-2200000020011-1-111-1-100000000
χ716666-3-6-6-3-3-333336-6-3-33300000000000000000000000000000000000022-2-2-2000000200-1-11111-1-100000000
χ726666-3-6-6-3-3-333336-6-3-333000000000000000000000000000000000000-2-2222000000-20011-1-1-1-11100000000
χ736666-3-6-6-3-3-33333-6633-3-300000000000000000000000000000000000022-2-22000000-200-1-1-1-1111100000000
χ746666-3-6-6-3-3-33333-6633-3-3000000000000000000000000000000000000-2-222-20000002001111-1-1-1-100000000
χ756-6-66-36-633-3-3-33300−3i33i3−3i33i30000000000000000000000000000000000002-22-20000000000-11−i3i3-11−i3i300000000
χ766-6-66-36-633-3-3-33300−3i33i3−3i33i3000000000000000000000000000000000000-22-2200000000001-1i3−i31-1i3−i300000000
χ776-6-66-36-633-3-3-333003i3−3i33i3−3i30000000000000000000000000000000000002-22-20000000000-11i3−i3-11i3−i300000000
χ786-6-66-36-633-3-3-333003i3−3i33i3−3i3000000000000000000000000000000000000-22-2200000000001-1−i3i31-1−i3i300000000
χ796-6-66-3-6633-333-3-300−3i33i33i3−3i30000000000000000000000000000000000002-2-220000000000-11i3−i31-1−i3i300000000
χ806-6-66-3-6633-333-3-300−3i33i33i3−3i3000000000000000000000000000000000000-222-200000000001-1−i3i3-11i3−i300000000
χ816-6-66-3-6633-333-3-3003i3−3i3−3i33i30000000000000000000000000000000000002-2-220000000000-11−i3i31-1i3−i300000000
χ826-6-66-3-6633-333-3-3003i3−3i3−3i33i3000000000000000000000000000000000000-222-200000000001-1i3−i3-11−i3i300000000
χ831212-12-12-600-66663−6363−63000000000000000000000000000000000000000000000000000000000000000000000000
χ841212-12-12-600-666−6363−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-1212-12-6006-6663−63−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-12-6006-66−636363−63000000000000000000000000000000000000000000000000000000000000000000000000

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