Finite Group Databasebeta

← Group #13167434

Character table — Group #13167434

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222244444444444444888888888888888888181818181818181836363636363636363636363636363636363636363636363636363636363672727272
order1244234612123366666121212121212123366666661212121212121212122244661212224444446666688881212121212121212121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-11-111111-1-1-111-111-1-11111-1-1-1-1-111-11111-1-1-1-1-111-111111-11-111-1-1-111-1-111-1-1-111-1-11111-1-1-1-111-1-1
χ61111-11-111111-1-1-111-111-1-11111-1-1-1-1-111-11111-1-1-1-1-111-111111-11-1-1-111-111-1-1-1-111-111-1-1-1-1-1-11111-1-111
χ71111-11-111111-1-1-111-111-1-11111-1-1-1-1-111-11111-1-1-1-1-111-11111-11-1111-1-1-1-1-111-1-111-1-1-1111111-1-1-1-1-1-111
χ81111-11-111111-1-1-111-111-1-11111-1-1-1-1-111-11111-1-1-1-1-111-11111-11-11-1-111-1-1-11111-1-1-1-1-111-1-1-1-1111111-1-1
χ911-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1i−ii−i-11111i−ii−i1-1-1-1-1ii−i−iii−i−ii−ii−i
χ1011-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−ii−ii-11111−ii−ii1-1-1-1-1−i−iii−i−iii−ii−ii
χ1111-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111i−ii−i-1-1-1-1-1−ii−ii11111ii−i−iii−i−i−ii−ii
χ1211-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111−ii−ii-1-1-1-1-1i−ii−i11111−i−iii−i−iiii−ii−i
χ1311-1-1-1111-1-111-1-1-1111-1-111-1-111-1-1-1-1-1111-1-1-1-111111-11-1-1-1111-1-11i−i−ii111-1-1i−i−ii-1-1-111ii−i−i−i−iiii−i−ii
χ1411-1-1-1111-1-111-1-1-1111-1-111-1-111-1-1-1-1-1111-1-1-1-111111-11-1-1-1111-1-11−iii−i111-1-1−iii−i-1-1-111−i−iiiii−i−i−iii−i
χ1511-1-1-1111-1-111-1-1-1111-1-111-1-111-1-1-1-1-1111-1-1-1-111111-11-1-1-111-111-1i−i−ii1-1-111−iii−i-111-1-1ii−i−i−i−iii−iii−i
χ1611-1-1-1111-1-111-1-1-1111-1-111-1-111-1-1-1-1-1111-1-1-1-111111-11-1-1-111-111-1−iii−i1-1-111i−i−ii-111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222222222222222222222222222222222-2-2-2-2-2-2-2-200000000-200000000-20000000000000000
χ1822222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-100002222-100000000-10000-1-1-1-1-1-1-1-10000
χ1922222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-2-100000000-10000111111110000
χ2022222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1-2-2-2-2111100000000100000000100003−33−33−33−30000
χ2122222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1-2-2-2-211110000000010000000010000−33−33−33−330000
χ222222-22-222222-2-2-222-222-2-22222-2-2-2-2-222-22222-2-2-2-22-2-22-2-2-2-20000000020000000020000000000000000
χ232222-2-1-2-1-1-1221-2-222122-2-222-1-1-21111-1-1-2-1-1-1-111112-2-22111100000000-100000000-100003−33−3−33−330000
χ242222-2-1-2-1-1-1221-2-222122-2-222-1-1-21111-1-1-2-1-1-1-111112-2-22111100000000-100000000-10000−33−333−33−30000
χ252222-2-1-2-1-1-1221-2-222122-2-222-1-1-21111-1-1-2-1-1-1-11111-222-2-1-1-1-1000022-2-210000000010000-1-1-1-111110000
χ262222-2-1-2-1-1-1221-2-222122-2-222-1-1-21111-1-1-2-1-1-1-11111-222-2-1-1-1-10000-2-222100000000100001111-1-1-1-10000
χ2722-2-222-22-2-22222222-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-222-2-222-2-200000000200000000-20000000000000000
χ2822-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-21111111122-2-2-1-11100000000-10000000010000−i3i3i3−i3−i3i3i3−i30000
χ2922-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-21111111122-2-2-1-11100000000-10000000010000i3−i3−i3i3i3−i3−i3i30000
χ3022-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-211111111-2-22211-1-100002i−2i2i−2i100000000-10000−i−iii−i−iii0000
χ3122-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-211111111-2-22211-1-10000−2i2i−2i2i100000000-10000ii−i−iii−i−i0000
χ3222-2-2-2222-2-222-2-2-2222-2-222-2-222-2-2-2-2-2222-2-2-2-22222-22-2222-2-200000000-20000000020000000000000000
χ3322-2-2-2-12-111221-2-222-1-2-222-2-2-1-1-21111-1-121111-1-1-1-12-22-211-1-100002i−2i−2i2i-10000000010000−i−iiiii−i−i0000
χ3422-2-2-2-12-111221-2-222-1-2-222-2-2-1-1-21111-1-121111-1-1-1-12-22-211-1-10000−2i2i2i−2i-10000000010000ii−i−i−i−iii0000
χ3522-2-2-2-12-111221-2-222-1-2-222-2-2-1-1-21111-1-121111-1-1-1-1-22-22-1-11100000000100000000-10000−i3i3i3−i3i3−i3−i3i30000
χ3622-2-2-2-12-111221-2-222-1-2-222-2-2-1-1-21111-1-121111-1-1-1-1-22-22-1-11100000000100000000-10000i3−i3−i3i3−i3i3i3−i30000
χ3744444444441-24-2-21-24-2-2-2-2111-2111-2-21-2111-2-211-2-200000000000000000000022220000000000000-1-1-1-1
χ3844444444441-24-2-21-24-2-2-2-2111-2111-2-21-2111-2-211-2-2000000000000000000000-2-2-2-200000000000001111
χ394444444444-21411-2141111-2-2-21-2-2-211-21-2-2-211-2-21100000000222200000-1-1-1-100000-1-1-1-1000000000000
χ404444444444-21411-2141111-2-2-21-2-2-211-21-2-2-211-2-21100000000-2-2-2-2000001111000001111000000000000
χ414444-44-44441-2-4221-2-4-2-222111-2-1-1-1221-2-111-2-2-1-12200000000000000000000022-2-20000000000000-1-111
χ424444-44-44441-2-4221-2-4-2-222111-2-1-1-1221-2-111-2-2-1-122000000000000000000000-2-222000000000000011-1-1
χ434444-44-4444-21-4-1-1-21-411-1-1-2-2-21222-1-1-212-2-21122-1-1000000002-22-200000-1-11100000-1-111000000000000
χ444444-44-4444-21-4-1-1-21-411-1-1-2-2-21222-1-1-212-2-21122-1-100000000-22-220000011-1-10000011-1-1000000000000
χ4544-4-444-44-4-41-24-2-21-2-42222-1-11-2111-2-21-2-1-1-122-1-1220000000000000000000002i−2i2i−2i0000000000000−ii−ii
χ4644-4-444-44-4-41-24-2-21-2-42222-1-11-2111-2-21-2-1-1-122-1-122000000000000000000000−2i2i−2i2i0000000000000i−ii−i
χ4744-4-444-44-4-4-21411-21-4-1-1-1-122-21-2-2-211-21222-1-122-1-10000000022-2-200000-1-1-1-1000001111000000000000
χ4844-4-444-44-4-4-21411-21-4-1-1-1-122-21-2-2-211-21222-1-122-1-100000000-2-22200000111100000-1-1-1-1000000000000
χ4944-4-4-4444-4-41-2-4221-2422-2-2-1-11-2-1-1-1221-21-1-12211-2-20000000000000000000002i−2i−2i2i0000000000000−iii−i
χ5044-4-4-4444-4-41-2-4221-2422-2-2-1-11-2-1-1-1221-21-1-12211-2-2000000000000000000000−2i2i2i−2i0000000000000i−i−ii
χ5144-4-4-4444-4-4-21-4-1-1-214-1-11122-21222-1-1-21-222-1-1-2-211000000002-2-2200000-1-1110000011-1-1000000000000
χ5244-4-4-4444-4-4-21-4-1-1-214-1-11122-21222-1-1-21-222-1-1-2-21100000000-222-20000011-1-100000-1-111000000000000
χ534-44i−4i040-44i−4i44000-4-404i−4i004i−4i4400000-4-404i−4i4i−4i0000000000000000000000000000000000000000000000
χ544-44i−4i040-44i−4i-2103-32-10i−i3i−3i−2i2i-210003-32-10−2i2ii−i003i−3i00000000000000000−i3i3−i3i3000003−33−3000000000000
χ554-44i−4i040-44i−4i-2103-32-10i−i3i−3i−2i2i-210003-32-10−2i2ii−i003i−3i00000000000000000i3−i3i3−i300000−33−33000000000000
χ564-44i−4i040-44i−4i-210-332-10i−i−3i3i−2i2i-21000-332-10−2i2ii−i00−3i3i00000000000000000−i3i3i3−i3000003−3−33000000000000
χ574-44i−4i040-44i−4i-210-332-10i−i−3i3i−2i2i-21000-332-10−2i2ii−i00−3i3i00000000000000000i3−i3−i3i300000−333−3000000000000
χ584-44i−4i0-202−2i2i44000-4-404i−4i004i−4i-2-200000220−2i2i−2i2i00000000−2i32i323−230000000000000000000000000000000000
χ594-44i−4i0-202−2i2i44000-4-404i−4i004i−4i-2-200000220−2i2i−2i2i000000002i3−2i3−23230000000000000000000000000000000000
χ604-4−4i4i040-4−4i4i44000-4-40−4i4i00−4i4i4400000-4-40−4i4i−4i4i0000000000000000000000000000000000000000000000
χ614-4−4i4i040-4−4i4i-2103-32-10−ii−3i3i2i−2i-210003-32-102i−2i−ii00−3i3i00000000000000000−i3i3−i3i300000−33−33000000000000
χ624-4−4i4i040-4−4i4i-2103-32-10−ii−3i3i2i−2i-210003-32-102i−2i−ii00−3i3i00000000000000000i3−i3i3−i3000003−33−3000000000000
χ634-4−4i4i040-4−4i4i-210-332-10−ii3i−3i2i−2i-21000-332-102i−2i−ii003i−3i00000000000000000−i3i3i3−i300000−333−3000000000000
χ644-4−4i4i040-4−4i4i-210-332-10−ii3i−3i2i−2i-21000-332-102i−2i−ii003i−3i00000000000000000i3−i3−i3i3000003−3−33000000000000
χ654-4−4i4i0-2022i−2i44000-4-40−4i4i00−4i4i-2-2000002202i−2i2i−2i00000000−2i32i3−23230000000000000000000000000000000000
χ664-4−4i4i0-2022i−2i44000-4-40−4i4i00−4i4i-2-2000002202i−2i2i−2i000000002i3−2i323−230000000000000000000000000000000000
χ6788888-48-4-4-42-4-4-4-42-4-4-4-4-4-422-122-1-122-122-1-122-1-122000000000000000000000000000000000000000000
χ6888888-48-4-4-4-42-422-42-42222-4-42-1-422-1-12-1-422-1-122-1-1000000000000000000000000000000000000000000
χ698888-8-4-8-4-4-42-44442-44-4-44422-12-211-2-2-12-2-1-12211-2-2000000000000000000000000000000000000000000
χ708888-8-4-8-4-4-4-424-2-2-42422-2-2-4-42-14-2-2112-1422-1-1-2-211000000000000000000000000000000000000000000
χ7188-8-88-4-8-4442-4-4-4-42-444444-2-2-122-1-122-12-211-2-211-2-2000000000000000000000000000000000000000000
χ7288-8-88-4-8-444-42-422-424-2-2-2-2442-1-422-1-12-14-2-211-2-211000000000000000000000000000000000000000000
χ7388-8-8-8-48-4442-44442-4-444-4-4-2-2-12-211-2-2-12211-2-2-1-122000000000000000000000000000000000000000000
χ7488-8-8-8-48-444-424-2-2-42-4-2-222442-14-2-2112-1-4-2-21122-1-1000000000000000000000000000000000000000000
χ758-88i−8i080-88i−8i2-4000-240−4i4i002i−2i2-400000-2402i−2i−4i4i0000000000000000000000000000000000000000000000
χ768-88i−8i0-404−4i4i2-4000-240−4i4i002i−2i-120−3i33i3001-20−ii2i−2i33−3300000000000000000000000000000000000000000000
χ778-88i−8i0-404−4i4i2-4000-240−4i4i002i−2i-1203i3−3i3001-20−ii2i−2i−333300000000000000000000000000000000000000000000
χ788-88i−8i0-404−4i4i-4206-64-202i−2i6i−6i−4i4i2-1000-33-2102i−2i−ii00−3i3i000000000000000000000000000000000000000000
χ798-88i−8i0-404−4i4i-420-664-202i−2i−6i6i−4i4i2-10003-3-2102i−2i−ii003i−3i000000000000000000000000000000000000000000
χ808-8−8i8i080-8−8i8i2-4000-2404i−4i00−2i2i2-400000-240−2i2i4i−4i0000000000000000000000000000000000000000000000
χ818-8−8i8i0-4044i−4i2-4000-2404i−4i00−2i2i-120−3i33i3001-20i−i−2i2i−333300000000000000000000000000000000000000000000
χ828-8−8i8i0-4044i−4i2-4000-2404i−4i00−2i2i-1203i3−3i3001-20i−i−2i2i33−3300000000000000000000000000000000000000000000
χ838-8−8i8i0-4044i−4i-4206-64-20−2i2i−6i6i4i−4i2-1000-33-210−2i2ii−i003i−3i000000000000000000000000000000000000000000
χ848-8−8i8i0-4044i−4i-420-664-20−2i2i6i−6i4i−4i2-10003-3-210−2i2ii−i00−3i3i000000000000000000000000000000000000000000

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