Finite Group Databasebeta

← Group #13166355

Character table — Group #13166355

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222444444444444444444888888888888888812121212121212121212121212121212121218181818181818183636363636363636363636363636108108108108108108
order12442346121233666666612121212121212121233666666121212121212121224666666661212121212121212224466121244446121212121212121212244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-1-1ii−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-1−i−iii
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii11ii−i−i
χ911-1-111-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-11-111-1-111-1-1-111-11-1
χ1011-1-111-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-111-1-111-1-1-11-111-1-1-111-1-111-11-11-11
χ1111-1-111-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-111-1-111i−i−ii-11ii−i−i−i−iii1-1i−i−ii
χ1211-1-111-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-111-1-111−iii−i-11−i−iiiii−i−i1-1−iii−i
χ1311-1-111-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-11-11-11-111-1-111-1-11-1-11-11
χ1411-1-111-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-111-1-1-111-1-1111-11-11-1
χ1511-1-111-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111i−i−ii-11ii−i−i−i−iii-11−iii−i
χ1611-1-111-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111−iii−i-11−i−iiiii−i−i-11i−i−ii
χ1722222-12-1-1-122-1222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000
χ1822222-12-1-1-122-1222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-2-2-2-2-1-111111111000000
χ1922222-12-1-1-122-1222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-211112i2i−2i−2i11−i−i−i−iiiii000000
χ2022222-12-1-1-122-1222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-21111−2i−2i2i2i11iiii−i−i−i−i000000
χ212222-22-222222-2-2-2-2-222-22222-2-2-2-222-2-2-2-2222222-2-2-2-20000000000000000002-22-222220000-2-200000000000000
χ222222-22-222222-2-2-2-2-222-22222-2-2-2-222-2-2-2-2222222-2-2-2-2000000000000000000-22-22-2-2-2-200002200000000000000
χ232222-2-1-2-1-1-1221-2-2-2-22212222-2-2-2-2-1-11111-1-1-1-1-1-111110000000000000000002-22-2-1-1-1-1000011−i3i3−i3i3−i3i3−i3i3000000
χ242222-2-1-2-1-1-1221-2-2-2-22212222-2-2-2-2-1-11111-1-1-1-1-1-111110000000000000000002-22-2-1-1-1-1000011i3−i3i3−i3i3−i3i3−i3000000
χ252222-2-1-2-1-1-1221-2-2-2-22212222-2-2-2-2-1-11111-1-1-1-1-1-11111000000000000000000-22-2211110000-1-13−33−3−33−33000000
χ262222-2-1-2-1-1-1221-2-2-2-22212222-2-2-2-2-1-11111-1-1-1-1-1-11111000000000000000000-22-2211110000-1-1−33−333−33−3000000
χ2722-2-22-1-2-11122-12222221-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000022-2-2-1-1112-22-2-11-1-111-1-111000000
χ2822-2-22-1-2-11122-12222221-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000022-2-2-1-111-22-22-1111-1-111-1-1000000
χ2922-2-22-1-2-11122-12222221-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000-2-22211-1-12i−2i−2i2i1-1−i−iiiii−i−i000000
χ3022-2-22-1-2-11122-12222221-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000-2-22211-1-1−2i2i2i−2i1-1ii−i−i−i−iii000000
χ3122-2-2-2222-2-222-2-2-2-2-2222-2-2-2-2222222-2-2-2-222-2-2-2-222220000000000000000002-2-2222-2-20000-2200000000000000
χ3222-2-2-2222-2-222-2-2-2-2-2222-2-2-2-2222222-2-2-2-222-2-2-2-22222000000000000000000-222-2-2-22200002-200000000000000
χ3322-2-2-2-12-111221-2-2-2-222-1-2-2-2-22222-1-11111-1-11111-1-1-1-10000000000000000002-2-22-1-11100001-1−i3i3i3−i3−i3i3i3−i3000000
χ3422-2-2-2-12-111221-2-2-2-222-1-2-2-2-22222-1-11111-1-11111-1-1-1-10000000000000000002-2-22-1-11100001-1i3−i3−i3i3i3−i3−i3i3000000
χ3522-2-2-2-12-111221-2-2-2-222-1-2-2-2-22222-1-11111-1-11111-1-1-1-1000000000000000000-222-211-1-10000-113−3−33−333−3000000
χ3622-2-2-2-12-111221-2-2-2-222-1-2-2-2-22222-1-11111-1-11111-1-1-1-1000000000000000000-222-211-1-10000-11−333−33−3−33000000
χ3744444444441-2411-2-21-2411-2-211-2-21-211-2-21-211-2-211-2-2441111-2-2-2-21111-2-2-2-20000000000000000000000000000
χ3844444444441-2411-2-21-2411-2-211-2-21-211-2-21-211-2-211-2-2-4-4-1-1-1-12222-1-1-1-122220000000000000000000000000000
χ394444444444-214-2-211-214-2-211-2-211-21-2-211-21-2-211-2-21144-2-2-2-21111-2-2-2-211110000000000000000000000000000
χ404444444444-214-2-211-214-2-211-2-211-21-2-211-21-2-211-2-211-4-42222-1-1-1-12222-1-1-1-10000000000000000000000000000
χ414444-44-44441-2-4-1-1221-2-411-2-2-1-1221-2-1-1221-211-2-2-1-1220033-3-3000033-3-300000000000000000000000000000000
χ424444-44-44441-2-4-1-1221-2-411-2-2-1-1221-2-1-1221-211-2-2-1-12200-3-3330000-3-33300000000000000000000000000000000
χ434444-44-4444-21-422-1-1-21-4-2-21122-1-1-2122-1-1-21-2-21122-1-100000033-3-3000033-3-30000000000000000000000000000
χ444444-44-4444-21-422-1-1-21-4-2-21122-1-1-2122-1-1-21-2-21122-1-1000000-3-3330000-3-3330000000000000000000000000000
χ4544-4-444-44-4-41-2411-2-21-2-4-1-122-1-1221-211-2-21-2-1-122-1-1224-41111-2-2-2-2-1-1-1-122220000000000000000000000000000
χ4644-4-444-44-4-41-2411-2-21-2-4-1-122-1-1221-211-2-21-2-1-122-1-122-44-1-1-1-122221111-2-2-2-20000000000000000000000000000
χ4744-4-444-44-4-4-214-2-211-21-422-1-122-1-1-21-2-211-2122-1-122-1-14-4-2-2-2-211112222-1-1-1-10000000000000000000000000000
χ4844-4-444-44-4-4-214-2-211-21-422-1-122-1-1-21-2-211-2122-1-122-1-1-442222-1-1-1-1-2-2-2-211110000000000000000000000000000
χ4944-4-4-4444-4-41-2-4-1-1221-24-1-12211-2-21-2-1-1221-2-1-12211-2-20033-3-30000-3-33300000000000000000000000000000000
χ5044-4-4-4444-4-41-2-4-1-1221-24-1-12211-2-21-2-1-1221-2-1-12211-2-200-3-333000033-3-300000000000000000000000000000000
χ5144-4-4-4444-4-4-21-422-1-1-21422-1-1-2-211-2122-1-1-2122-1-1-2-21100000033-3-30000-3-3330000000000000000000000000000
χ5244-4-4-4444-4-4-21-422-1-1-21422-1-1-2-211-2122-1-1-2122-1-1-2-211000000-3-333000033-3-30000000000000000000000000000
χ534-44i−4i040-44i−4i1-203-300-120i−i2i−2i3i−3i001-23-300-12i−i2i−2i3i−3i0000−i3i3−i3i300−2i32i33−33−30023−230000000000000000000000000000
χ544-44i−4i040-44i−4i1-203-300-120i−i2i−2i3i−3i001-23-300-12i−i2i−2i3i−3i0000i3−i3i3−i3002i3−2i3−33−3300−23230000000000000000000000000000
χ554-44i−4i040-44i−4i1-20-3300-120i−i2i−2i−3i3i001-2-3300-12i−i2i−2i−3i3i0000−i3i3i3−i3−2i32i3003−3−3323−23000000000000000000000000000000
χ564-44i−4i040-44i−4i1-20-3300-120i−i2i−2i−3i3i001-2-3300-12i−i2i−2i−3i3i0000i3−i3−i3i32i3−2i300−333−3−2323000000000000000000000000000000
χ574-44i−4i040-44i−4i4400000-4-404i−4i−4i4i0000440000-4-44i−4i−4i4i00000000000000000000000000000000000000000000000000
χ584-44i−4i040-44i−4i-210003-32-10−2i2i−ii003i−3i-21003-32-1−2i2i−ii003i−3i0000−2i32i3−i3i3i3−i30023−233−3−330000000000000000000000000000
χ594-44i−4i040-44i−4i-210003-32-10−2i2i−ii003i−3i-21003-32-1−2i2i−ii003i−3i00002i3−2i3i3−i3−i3i300−2323−333−30000000000000000000000000000
χ604-44i−4i040-44i−4i-21000-332-10−2i2i−ii00−3i3i-2100-332-1−2i2i−ii00−3i3i00−2i32i300i3−i3i3−i323−2300−33−330000000000000000000000000000
χ614-44i−4i040-44i−4i-21000-332-10−2i2i−ii00−3i3i-2100-332-1−2i2i−ii00−3i3i002i3−2i300−i3i3−i3i3−2323003−33−30000000000000000000000000000
χ624-44i−4i0-202−2i2i4400000-4-404i−4i−4i4i0000-2-2000022−2i2i2i−2i00000000000000000000000000−2i32i323−2300000000000000000000
χ634-44i−4i0-202−2i2i4400000-4-404i−4i−4i4i0000-2-2000022−2i2i2i−2i000000000000000000000000002i3−2i3−232300000000000000000000
χ644-4−4i4i040-4−4i4i1-203-300-120−ii−2i2i−3i3i001-23-300-12−ii−2i2i−3i3i0000−i3i3−i3i300−2i32i3−33−3300−23230000000000000000000000000000
χ654-4−4i4i040-4−4i4i1-203-300-120−ii−2i2i−3i3i001-23-300-12−ii−2i2i−3i3i0000i3−i3i3−i3002i3−2i33−33−30023−230000000000000000000000000000
χ664-4−4i4i040-4−4i4i1-20-3300-120−ii−2i2i3i−3i001-2-3300-12−ii−2i2i3i−3i0000−i3i3i3−i3−2i32i300−333−3−2323000000000000000000000000000000
χ674-4−4i4i040-4−4i4i1-20-3300-120−ii−2i2i3i−3i001-2-3300-12−ii−2i2i3i−3i0000i3−i3−i3i32i3−2i3003−3−3323−23000000000000000000000000000000
χ684-4−4i4i040-4−4i4i4400000-4-40−4i4i4i−4i0000440000-4-4−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4−4i4i040-4−4i4i-210003-32-102i−2ii−i00−3i3i-21003-32-12i−2ii−i00−3i3i0000−2i32i3−i3i3i3−i300−2323−333−30000000000000000000000000000
χ704-4−4i4i040-4−4i4i-210003-32-102i−2ii−i00−3i3i-21003-32-12i−2ii−i00−3i3i00002i3−2i3i3−i3−i3i30023−233−3−330000000000000000000000000000
χ714-4−4i4i040-4−4i4i-21000-332-102i−2ii−i003i−3i-2100-332-12i−2ii−i003i−3i00−2i32i300i3−i3i3−i3−2323003−33−30000000000000000000000000000
χ724-4−4i4i040-4−4i4i-21000-332-102i−2ii−i003i−3i-2100-332-12i−2ii−i003i−3i002i3−2i300−i3i3−i3i323−2300−33−330000000000000000000000000000
χ734-4−4i4i0-2022i−2i4400000-4-40−4i4i4i−4i0000-2-20000222i−2i−2i2i00000000000000000000000000−2i32i3−232300000000000000000000
χ744-4−4i4i0-2022i−2i4400000-4-40−4i4i4i−4i0000-2-20000222i−2i−2i2i000000000000000000000000002i3−2i323−2300000000000000000000
χ7588888-48-4-4-42-4-422-4-42-4-422-4-422-4-4-12-1-122-12-1-122-1-1220000000000000000000000000000000000000000000000
χ7688888-48-4-4-4-42-4-4-422-42-4-4-422-4-4222-122-1-12-122-1-122-1-10000000000000000000000000000000000000000000000
χ778888-8-4-8-4-4-42-44-2-2442-4422-4-4-2-244-1211-2-2-12-1-12211-2-20000000000000000000000000000000000000000000000
χ788888-8-4-8-4-4-4-42444-2-2-424-4-42244-2-22-1-2-2112-122-1-1-2-2110000000000000000000000000000000000000000000000
χ7988-8-88-4-8-4442-4-422-4-42-44-2-244-2-244-12-1-122-1211-2-211-2-20000000000000000000000000000000000000000000000
χ8088-8-88-4-8-444-42-4-4-422-42444-2-244-2-22-122-1-12-1-2-211-2-2110000000000000000000000000000000000000000000000
χ8188-8-8-8-48-4442-44-2-2442-4-4-2-24422-4-4-1211-2-2-1211-2-2-1-1220000000000000000000000000000000000000000000000
χ8288-8-8-8-48-444-42444-2-2-42-444-2-2-4-4222-1-2-2112-1-2-21122-1-10000000000000000000000000000000000000000000000
χ838-88i−8i0-404−4i4i2-406-600-2402i−2i4i−4i6i−6i00-12-33001-2−ii−2i2i−3i3i000000000000000000000000000000000000000000000000
χ848-88i−8i0-404−4i4i2-40-6600-2402i−2i4i−4i−6i6i00-123-3001-2−ii−2i2i3i−3i000000000000000000000000000000000000000000000000
χ858-88i−8i0-404−4i4i-420006-64-20−4i4i−2i2i006i−6i2-100-33-212i−2ii−i00−3i3i0000000000000000000000000000000000000000000000
χ868-88i−8i0-404−4i4i-42000-664-20−4i4i−2i2i00−6i6i2-1003-3-212i−2ii−i003i−3i0000000000000000000000000000000000000000000000
χ878-8−8i8i0-4044i−4i2-406-600-240−2i2i−4i4i−6i6i00-12-33001-2i−i2i−2i3i−3i000000000000000000000000000000000000000000000000
χ888-8−8i8i0-4044i−4i2-40-6600-240−2i2i−4i4i6i−6i00-123-3001-2i−i2i−2i−3i3i000000000000000000000000000000000000000000000000
χ898-8−8i8i0-4044i−4i-420006-64-204i−4i2i−2i00−6i6i2-100-33-21−2i2i−ii003i−3i0000000000000000000000000000000000000000000000
χ908-8−8i8i0-4044i−4i-42000-664-204i−4i2i−2i006i−6i2-1003-3-21−2i2i−ii00−3i3i0000000000000000000000000000000000000000000000

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