Finite Group Databasebeta

← Group #13150856

Character table — Group #13150856

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1222344666121212122466121233666666366666666666121212121212121212121212121212122244244444444466121212121212612121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-11-11-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111111-11-1-11-1-11-111-1-1-1-11111-1-11-11-1
χ611111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1111-1-1-1-111-1-111-11-11
χ711111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11-1-11-1-11111-1-111-1-1-11-11
χ811111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1111-111-1-1-11111-1-1-1-1111-11-1
χ911111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11-11-11-111111-1-1-1-11-1-111-1-11
χ1011111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-11-11-11111-1-1-1-1-111-1-111-1
χ1111111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-111111-1-11-111-1
χ1211111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-11-1-1-1-11111-111-11-1-11
χ1311111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-111-1-1111-1-1-111-1-111-1-11-11-111-1-1
χ1411111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-111-1-1-1-111111-1-111-1-1-11-11-1-111
χ1511111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1111-1-111-1-1-111-1-111-1-1111-11-1-1-111
χ1611111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-111-1-111-1111-1-1-1-111-1-111-11-1111-1-1
χ17222222222222222222222-12-1-1-122-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000202020020000000000-1-1-1-10000
χ18222222222222222222222-12-1-1-122-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-20-20-200-2000000000011110000
χ1922222222222222222222-12-1222-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000022022000000000000-1-1-1-1
χ2022222222222222222222-12-1222-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000-2-20-2-20000000000001111
χ2122222222222222-2-2-2-2-2-22-12-1-1-122-1-2-211-1-11111-1-1-11122-2-2-1-1-1-1111100002020-200-20000000000-1-1110000
χ2222222222222222-2-2-2-2-2-22-12-1-1-122-1-2-211-1-11111-1-1-11122-2-2-1-1-1-111110000-20-202002000000000011-1-10000
χ2322222222222222-2-2-2-2-2-2-12-1222-1-1-111-2-2-1-11111-122-2-2-1-111-1-1-1-111110000000002-202-2000000000000-11-11
χ2422222222222222-2-2-2-2-2-2-12-1222-1-1-111-2-2-1-11111-122-2-2-1-111-1-1-1-11111000000000-220-220000000000001-11-1
χ2522222-2-2222-2-2-2-22-222-2-22-12-1-1-122-122-1-1-1-1-1-1-1-1-11111-2-2-2-211111111000020-20-20020000000000-111-10000
χ2622222-2-2222-2-2-2-22-222-2-22-12-1-1-122-122-1-1-1-1-1-1-1-1-11111-2-2-2-2111111110000-2020200-200000000001-1-110000
χ2722222-2-2222-2-2-2-22-222-2-2-12-1222-1-1-1-1-122-1-1-1-1-1-1-1-2-2-2-21111111111110000000002-20-22000000000000-111-1
χ2822222-2-2222-2-2-2-22-222-2-2-12-1222-1-1-1-1-122-1-1-1-1-1-1-1-2-2-2-2111111111111000000000-2202-20000000000001-1-11
χ2922222-2-2222-2-2-2-2-22-2-2222-12-1-1-122-1-2-211-1-11111-111-1-1-2-2221111-1-1-1-1000020-20200-20000000000-11-110000
χ3022222-2-2222-2-2-2-2-22-2-2222-12-1-1-122-1-2-211-1-11111-111-1-1-2-2221111-1-1-1-10000-2020-200200000000001-11-10000
χ3122222-2-2222-2-2-2-2-22-2-222-12-1222-1-1-111-2-2-1-11111-1-2-22211-1-11111-1-1-1-1000000000220-2-2000000000000-1-111
χ3222222-2-2222-2-2-2-2-22-2-222-12-1222-1-1-111-2-2-1-11111-1-2-22211-1-11111-1-1-1-1000000000-2-202200000000000011-1-1
χ332-22-222i−2i2-2-22i2i−2i−2i00000022-22-2-22-2200002-20000-22i−2i002i−2i002i2i−2i−2i00002-22i−2i00000000002-200002i−2i00000000
χ342-22-222i−2i2-2-22i2i−2i−2i00000022-22-2-22-2200002-20000-22i−2i002i−2i002i2i−2i−2i0000-22−2i2i0000000000-220000−2i2i00000000
χ352-22-22−2i2i2-2-2−2i−2i2i2i00000022-22-2-22-2200002-20000-2−2i2i00−2i2i00−2i−2i2i2i00002-2−2i2i00000000002-20000−2i2i00000000
χ362-22-22−2i2i2-2-2−2i−2i2i2i00000022-22-2-22-2200002-20000-2−2i2i00−2i2i00−2i−2i2i2i0000-222i−2i0000000000-2200002i−2i00000000
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
χ4144-4-4400-44-40000000000444-44-4-4-440000-440000-40000000000000000000000000000000000000000000000
χ4244-4-4400-44-400000000004-242-22-4-4-200002-2000020023−23000000002323−23−23000000000000000000000000000000
χ4344-4-4400-44-400000000004-242-22-4-4-200002-20000200−232300000000−23−232323000000000000000000000000000000
χ4444-4-4400-44-40000000000-24-2-44-422-2−2i32i3002-2−2i3−2i32i32i320000000000000000000000000000000000000000000000
χ4544-4-4400-44-40000000000-24-2-44-422-22i3−2i3002-22i32i3−2i3−2i320000000000000000000000000000000000000000000000
χ4644-4-4400-44-40000000000-2-2-22-22221−2i32i300-11i3i3−i3−i3-10023−2300003i−3i3i−3i−3−333000000000000000000000000000000
χ4744-4-4400-44-40000000000-2-2-22-22221−2i32i300-11i3i3−i3−i3-100−23230000−3i3i−3i3i33−3−3000000000000000000000000000000
χ4844-4-4400-44-40000000000-2-2-22-222212i3−2i300-11−i3−i3i3i3-10023−230000−3i3i−3i3i−3−333000000000000000000000000000000
χ4944-4-4400-44-40000000000-2-2-22-222212i3−2i300-11−i3−i3i3i3-100−232300003i−3i3i−3i33−3−3000000000000000000000000000000
χ504-44-444i−4i4-4-44i4i−4i−4i0000004-2-4-2224-4-20000-2200002−2i2i004i−4i00−2i−2i2i2i0000000000000000000000000000000000
χ514-44-444i−4i4-4-44i4i−4i−4i000000-2424-4-4-22-20000-22000024i−4i00−2i2i00−2i−2i2i2i0000000000000000000000000000000000
χ524-44-444i−4i4-4-44i4i−4i−4i000000-2-22-222-22100001-13-33-3-1−2i2i00−2i2i00ii−i−i3i−3i3i−3i000000000000000000000000000000
χ534-44-444i−4i4-4-44i4i−4i−4i000000-2-22-222-22100001-1-33-33-1−2i2i00−2i2i00ii−i−i−3i3i−3i3i000000000000000000000000000000
χ544-44-44−4i4i4-4-4−4i−4i4i4i0000004-2-4-2224-4-20000-22000022i−2i00−4i4i002i2i−2i−2i0000000000000000000000000000000000
χ554-44-44−4i4i4-4-4−4i−4i4i4i000000-2424-4-4-22-20000-2200002−4i4i002i−2i002i2i−2i−2i0000000000000000000000000000000000
χ564-44-44−4i4i4-4-4−4i−4i4i4i000000-2-22-222-22100001-13-33-3-12i−2i002i−2i00−i−iii−3i3i−3i3i000000000000000000000000000000
χ574-44-44−4i4i4-4-4−4i−4i4i4i000000-2-22-222-22100001-1-33-33-12i−2i002i−2i00−i−iii3i−3i3i−3i000000000000000000000000000000
χ584-4-44400-4-44000000000044-4-4-44-4440000-4-4000040000000000000000000000000000000000000000000000
χ594-4-44400-4-4400000000004-2-422-2-44-200−2i32i322−2i32i32i3−2i3-20000000000000000000000000000000000000000000000
χ604-4-44400-4-4400000000004-2-422-2-44-2002i3−2i3222i3−2i3−2i32i3-20000000000000000000000000000000000000000000000
χ614-4-44400-4-440000000000-242-4-442-2-20000220000-2000000−2i32i30000−2i32i32i3−2i3000000000000000000000000000000
χ624-4-44400-4-440000000000-242-4-442-2-20000220000-20000002i3−2i300002i3−2i3−2i32i3000000000000000000000000000000
χ634-4-44400-4-440000000000-2-2222-22-2100−2i32i3-1-1i3−i3−i3i31000000−2i32i33-3-33i3−i3−i3i3000000000000000000000000000000
χ644-4-44400-4-440000000000-2-2222-22-2100−2i32i3-1-1i3−i3−i3i310000002i3−2i3-333-3−i3i3i3−i3000000000000000000000000000000
χ654-4-44400-4-440000000000-2-2222-22-21002i3−2i3-1-1−i3i3i3−i31000000−2i32i3-333-3i3−i3−i3i3000000000000000000000000000000
χ664-4-44400-4-440000000000-2-2222-22-21002i3−2i3-1-1−i3i3i3−i310000002i3−2i33-3-33−i3i3i3−i3000000000000000000000000000000
χ676666-366-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000022220202000000-1-1-1-1-1-1-1-100000000
χ686666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-2-2-20-20-20000001111111100000000
χ696666-366-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000022220-20-2000000-1-11111-1-100000000
χ706666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-2-2-2020200000011-1-1-1-11100000000
χ716666-3-6-6-3-3-333336-6-3-33300000000000000000000000000000000000022-2-20-202000000-1-1-1-1111100000000
χ726666-3-6-6-3-3-333336-6-3-333000000000000000000000000000000000000-2-222020-20000001111-1-1-1-100000000
χ736666-3-6-6-3-3-33333-6633-3-300000000000000000000000000000000000022-2-2020-2000000-1-111-1-11100000000
χ746666-3-6-6-3-3-33333-6633-3-3000000000000000000000000000000000000-2-2220-20200000011-1-111-1-100000000
χ756-66-6-36i−6i-333−3i−3i3i3i00−3i33i333−330000000000000000000000000000000000002-22i−2i0000000000-11−i3i33−3−ii00000000
χ766-66-6-36i−6i-333−3i−3i3i3i00−3i33i333−33000000000000000000000000000000000000-22−2i2i00000000001-1i3−i3−33i−i00000000
χ776-66-6-36i−6i-333−3i−3i3i3i003i3−3i3−33330000000000000000000000000000000000002-22i−2i0000000000-11i3−i3−33−ii00000000
χ786-66-6-36i−6i-333−3i−3i3i3i003i3−3i3−3333000000000000000000000000000000000000-22−2i2i00000000001-1−i3i33−3i−i00000000
χ796-66-6-3−6i6i-3333i3i−3i−3i00−3i33i3−33330000000000000000000000000000000000002-2−2i2i0000000000-11−i3i3−33i−i00000000
χ806-66-6-3−6i6i-3333i3i−3i−3i00−3i33i3−3333000000000000000000000000000000000000-222i−2i00000000001-1i3−i33−3−ii00000000
χ816-66-6-3−6i6i-3333i3i−3i−3i003i3−3i333−330000000000000000000000000000000000002-2−2i2i0000000000-11i3−i33−3i−i00000000
χ826-66-6-3−6i6i-3333i3i−3i−3i003i3−3i333−33000000000000000000000000000000000000-222i−2i00000000001-1−i3i3−33−ii00000000
χ831212-12-12-6006-6663−6363−63000000000000000000000000000000000000000000000000000000000000000000000000
χ841212-12-12-6006-66−6363−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-60066-6−6i36i36i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-60066-66i3−6i3−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000

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