Finite Group Databasebeta

← Group #11772564

Character table — Group #11772564

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111224444444444444444448888888812121212242424242424242424242424242424242424242424243636363672727272
order1222222233666666666666666666666644444444441212121212121212121212121212121222448888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111-1-11111111111-1-111-1-111-1-1-1-1-1-11111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ6111111-1-11111111111-1-111-1-111-1-1-1-1-1-11111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ7111111-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ8111111-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ91-1-111-11-1111111-1-1-1-111-1-1-1-11-1111-1-1-1ii−i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i1-1-111-11-1
χ101-1-111-11-1111111-1-1-1-111-1-1-1-11-1111-1-1-1ii−i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii1-1-11-11-11
χ111-1-111-11-1111111-1-1-1-111-1-1-1-11-1111-1-1-1−i−iii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i1-1-11-11-11
χ121-1-111-11-1111111-1-1-1-111-1-1-1-11-1111-1-1-1−i−iii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii1-1-111-11-1
χ131-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-1-1-1111ii−i−i−ii1-1-11ii−i−i−i−iii11-1-1-1-1111-11-1−iii−i
χ141-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-1-1-1111ii−i−i−ii-111-1ii−i−i−i−iii-1-11111-1-11-11-1i−i−ii
χ151-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-1-1-1111−i−iiii−i1-1-11−i−iiiii−i−i11-1-1-1-1111-11-1i−i−ii
χ161-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-1-1-1111−i−iiii−i-111-1−i−iiiii−i−i-1-11111-1-11-11-1−iii−i
χ172222222222222222222222222222222200000000000000000000000000-2-2-2-20000
χ18222222-2-22222222222-2-222-2-222-2-2-2-2-2-200000000000000000000000000-2-2220000
χ192-2-222-22-2222222-2-2-2-222-2-2-2-22-2222-2-2-200000000000000000000000000-222-20000
χ202-2-222-2-22222222-2-2-2-2-2-2-2-2222-2-2-2-222200000000000000000000000000-22-220000
χ21444444441-2111-211-2-2-2-211-2-2-2-211-211-22222220000-1-1-1-1-1-1-1-10000000000000000
χ22444444441-2111-211-2-2-2-211-2-2-2-211-211-2-2-2-2-2-2-20000111111110000000000000000
χ2344444444-21-2-2-21-2-21111-2-21111-2-21-2-21000000222200000000-1-1-1-1-1-1-1-100000000
χ2444444444-21-2-2-21-2-21111-2-21111-2-21-2-21000000-2-2-2-2000000001111111100000000
χ25444444-4-41-2111-211-2-2221122-2-2-1-12-1-122222-2-20000-1-1-1-111110000000000000000
χ26444444-4-41-2111-211-2-2221122-2-2-1-12-1-12-2-2-2-22200001111-1-1-1-10000000000000000
χ27444444-4-4-21-2-2-21-2-211-1-1-2-2-1-11122-122-10000002i2i−2i−2i00000000−i−i−i−iiiii00000000
χ28444444-4-4-21-2-2-21-2-211-1-1-2-2-1-11122-122-1000000−2i−2i2i2i00000000iiii−i−i−i−i00000000
χ294444-4-400444-4-444-444004-400-4-40000000000000000000000000000000000000000
χ304444-4-400-21-2221-221133-2233-1-100-300-30000000000000000003−33−33−33−300000000
χ314444-4-400-21-2221-221133-2233-1-100-300-3000000000000000000−33−33−33−3300000000
χ324444-4-400-21-2221-2211-3-3-22-3-3-1-1003003000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ334444-4-400-21-2221-2211-3-3-22-3-3-1-1003003000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ3444-4-400001-2-13-321-32-2−2i32i3-13−2i32i300−i3i30−i3i302i−2i2i−2i000000i−ii−i3−33−30000000000000000
χ3544-4-400001-2-13-321-32-2−2i32i3-13−2i32i300−i3i30−i3i30−2i2i−2i2i000000−ii−ii−33−330000000000000000
χ3644-4-400001-2-13-321-32-22i3−2i3-132i3−2i300i3−i30i3−i302i−2i2i−2i000000i−ii−i−33−330000000000000000
χ3744-4-400001-2-13-321-32-22i3−2i3-132i3−2i300i3−i30i3−i30−2i2i−2i2i000000−ii−ii3−33−30000000000000000
χ3844-4-4000044-400-440-4400-4000000000002i−2i2i−2i000000−2i2i−2i2i00000000000000000000
χ3944-4-4000044-400-440-4400-400000000000−2i2i−2i2i0000002i−2i2i−2i00000000000000000000
χ404-44-400001-2-13-32-13-22−2i32i31-32i3−2i300−i3i30i3−i302-2-220000001-1-11−i3i3i3−i30000000000000000
χ414-44-400001-2-13-32-13-22−2i32i31-32i3−2i300−i3i30i3−i30-222-2000000-111-1i3−i3−i3i30000000000000000
χ424-44-400001-2-13-32-13-222i3−2i31-3−2i32i300i3−i30−i3i302-2-220000001-1-11i3−i3−i3i30000000000000000
χ434-44-400001-2-13-32-13-222i3−2i31-3−2i32i300i3−i30−i3i30-222-2000000-111-1−i3i3i3−i30000000000000000
χ444-44-4000044-400-4-404-4004000000000002-2-22000000-222-200000000000000000000
χ454-44-4000044-400-4-404-400400000000000-222-20000002-2-2200000000000000000000
χ464-4-444-44-41-2111-2-1-122-2-2-1-122-2211-2-1-122i2i−2i−2i2i−2i0000−i−iii−i−iii0000000000000000
χ474-4-444-44-41-2111-2-1-122-2-2-1-122-2211-2-1-12−2i−2i2i2i−2i2i0000ii−i−iii−i−i0000000000000000
χ484-4-444-44-4-21-2-2-2122-1-11122-1-11-1-2-2122-10000002i−2i2i−2i00000000−i−iii−i−iii00000000
χ494-4-444-44-4-21-2-2-2122-1-11122-1-11-1-2-2122-1000000−2i2i−2i2i00000000ii−i−iii−i−i00000000
χ504-4-444-4-441-2111-2-1-12222-1-1-2-2-22-1-1211-22i2i−2i−2i−2i2i0000−i−iiiii−i−i0000000000000000
χ514-4-444-4-441-2111-2-1-12222-1-1-2-2-22-1-1211-2−2i−2i2i2i2i−2i0000ii−i−i−i−iii0000000000000000
χ524-4-444-4-44-21-2-2-2122-1-1-1-122111-122-1-2-210000002-2-2200000000-1-11111-1-100000000
χ534-4-444-4-44-21-2-2-2122-1-1-1-122111-122-1-2-21000000-222-20000000011-1-1-1-11100000000
χ544-4-44-4400444-4-44-44-4-400-4400-440000000000000000000000000000000000000000
χ554-4-44-4400-21-22212-2-1-1332-2-3-3-1100-3003000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ564-4-44-4400-21-22212-2-1-1332-2-3-3-1100-3003000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ574-4-44-4400-21-22212-2-1-1-3-32-233-1100300-30000000000000000003−3−33−333−300000000
χ584-4-44-4400-21-22212-2-1-1-3-32-233-1100300-3000000000000000000−333−33−3−3300000000
χ598888-8-8002-42-2-2-42-2-4-4002-200440000000000000000000000000000000000000000
χ6088-8-800002-4-2-664264-400-2-600000000000000000000000000000000000000000000
χ6188-8-80000-42400-2-40-22−2i32i340−2i32i3002i3−2i302i3−2i300000000000000000000000000000000000
χ6288-8-80000-42400-2-40-222i3−2i3402i3−2i300−2i32i30−2i32i300000000000000000000000000000000000
χ638-88-800002-4-2-664-2-6-44002600000000000000000000000000000000000000000000
χ648-88-80000-42400-2402-2−2i32i3-402i3−2i3002i3−2i30−2i32i300000000000000000000000000000000000
χ658-88-80000-42400-2402-22i3−2i3-40−2i32i300−2i32i302i3−2i300000000000000000000000000000000000
χ668-8-88-88002-42-2-2-4-224400-22004-40000000000000000000000000000000000000000

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