Finite Group Databasebeta

← Group #13154852

Character table — Group #13154852

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222224444444444888888888888888888889912121818181818181824242424242424243636363636363636363636363636108108108108108108
order1222236663366666666336666666666666666664444444121212121212121212121212888812122424242424242424448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-111111111ii−i−i-1-1iiii−i−i−i−i-1-1ii−i−i
χ6111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-111111111−i−iii-1-1−i−i−i−iiiii-1-1−i−iii
χ7111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i11−i−iii
χ8111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii11ii−i−i
χ9111-1-11-1-11111-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111i−i1-1-111-1-1iiii−i−i−i−ii−ii−i1-1ii−i−iii−i−ii−i1-11-1
χ10111-1-11-1-11111-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111i−i1-1-111-1-1iiii−i−i−i−i−ii−ii1-1−i−iii−i−iiii−i-11-11
χ11111-1-11-1-11111-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111−ii1-1-111-1-1−i−i−i−iiiiii−ii−i1-1ii−i−iii−i−i−ii-11-11
χ12111-1-11-1-11111-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111−ii1-1-111-1-1−i−i−i−iiiii−ii−ii1-1−i−iii−i−iii−ii1-11-1
χ13111-1-11-1-11111-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1i−i-111-1-111iiii−i−i−i−i1-1-11-1111-1-1-1-111−ii−iii−i
χ14111-1-11-1-11111-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1i−i-111-1-111iiii−i−i−i−i-111-1-11-1-11111-1-1−iii−i−ii
χ15111-1-11-1-11111-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1−ii-111-1-111−i−i−i−iiiii1-1-11-1111-1-1-1-111i−ii−i−ii
χ16111-1-11-1-11111-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1−ii-111-1-111−i−i−i−iiiii-111-1-11-1-11111-1-1i−i−iii−i
χ1722222-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12200222-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1000000
χ1822222-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12200222-1-1-1-100000000-2-2-2-2-1-111111111000000
χ1922222-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2-21111000000002i2i−2i−2i11−i−i−i−iiiii000000
χ2022222-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2111100000000−2i−2i2i2i11iiii−i−i−i−i000000
χ21222-2-2-111-122-1122-2-2-2-2-1-122-2-2-1-1-1-1-1-11111111122002-2-2-1-111000000002i−2i2i−2i-11−i−iii−i−iii000000
χ22222-2-2-111-122-1122-2-2-2-2-1-122-2-2-1-1-1-1-1-11111111122002-2-2-1-11100000000−2i2i−2i2i-11ii−i−iii−i−i000000
χ23222-2-2-111-122-1122-2-2-2-2-1-122-2-2-1-1-1-1-1-111111111-2-200-22211-1-1000000002-2-221-1-1-11111-1-1000000
χ24222-2-2-111-122-1122-2-2-2-2-1-122-2-2-1-1-1-1-1-111111111-2-200-22211-1-100000000-222-21-111-1-1-1-111000000
χ2522-22-2222222-2-222-2-2-2-222-2-22222-2-2-2-22222-2-2-2-22200-2-222222000000000000-2-200000000000000
χ2622-22-2222222-2-222-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2-2-20022-2-2-2-2-20000000000002200000000000000
χ2722-22-2-1-1-1-1221122-2-2-2-2-1-1-2-222-1-11111-1-1-1-111112200-2-22-1-1-1-100000000000011−i3i3−i3i3−i3i3−i3i3000000
χ2822-22-2-1-1-1-1221122-2-2-2-2-1-1-2-222-1-11111-1-1-1-111112200-2-22-1-1-1-100000000000011i3−i3i3−i3i3−i3i3−i3000000
χ2922-22-2-1-1-1-1221122-2-2-2-2-1-1-2-222-1-11111-1-1-1-11111-2-20022-21111000000000000-1-13−33−3−33−33000000
χ3022-22-2-1-1-1-1221122-2-2-2-2-1-1-2-222-1-11111-1-1-1-11111-2-20022-21111000000000000-1-1−33−333−33−3000000
χ3122-2-222-2-2222-2222222222-2-2-2-222-2-2-2-2-2-2-2-222222200-22-222-2-2000000000000-2200000000000000
χ3222-2-222-2-2222-2222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2002-22-2-2220000000000002-200000000000000
χ3322-2-22-111-1221-1222222-1-1-2-2-2-2-1-111111111-1-1-1-12200-22-2-1-1110000000000001-13−3−333−3−33000000
χ3422-2-22-111-1221-1222222-1-1-2-2-2-2-1-111111111-1-1-1-12200-22-2-1-1110000000000001-1−333−3−333−3000000
χ3522-2-22-111-1221-1222222-1-1-2-2-2-2-1-111111111-1-1-1-1-2-2002-2211-1-1000000000000-11−i3i3i3−i3i3−i3−i3i3000000
χ3622-2-22-111-1221-1222222-1-1-2-2-2-2-1-111111111-1-1-1-1-2-2002-2211-1-1000000000000-11i3−i3−i3i3−i3i3i3−i3000000
χ374444444441-2441-211-2-21-21-21-21-211-2-211-2-211-2-20044000000011-2-211-2-200000000000000000000
χ384444444441-2441-211-2-21-21-21-21-211-2-211-2-211-2-200-4-40000000-1-122-1-12200000000000000000000
χ39444444444-2144-21-2-211-21-21-21-21-2-211-2-211-2-21100440000000-2-211-2-21100000000000000000000
χ40444444444-2144-21-2-211-21-21-21-21-2-211-2-211-2-21100-4-4000000022-1-122-1-100000000000000000000
χ41444-4-44-4-441-24-41-2-1-1221-21-2-121-211-2-2-1-122-1-122004i−4i0000000ii−2i−2i−i−i2i2i00000000000000000000
χ42444-4-44-4-441-24-41-2-1-1221-21-2-121-211-2-2-1-122-1-12200−4i4i0000000−i−i2i2iii−2i−2i00000000000000000000
χ43444-4-44-4-44-214-4-2122-1-1-21-212-1-21-2-21122-1-122-1-1004i−4i0000000−2i−2iii2i2i−i−i00000000000000000000
χ44444-4-44-4-44-214-4-2122-1-1-21-212-1-21-2-21122-1-122-1-100−4i4i00000002i2i−i−i−2i−2iii00000000000000000000
χ4544-44-444441-2-4-41-2-1-1221-2-121-21-2-1-12211-2-2-1-122000000000003i−3i003i−3i0000000000000000000000
χ4644-44-444441-2-4-41-2-1-1221-2-121-21-2-1-12211-2-2-1-12200000000000−3i3i00−3i3i0000000000000000000000
χ4744-44-44444-21-4-4-2122-1-1-212-1-21-2122-1-1-2-21122-1-100000000000003i−3i003i−3i00000000000000000000
χ4844-44-44444-21-4-4-2122-1-1-212-1-21-2122-1-1-2-21122-1-10000000000000−3i3i00−3i3i00000000000000000000
χ4944-4-444-4-441-2-441-211-2-21-2-12-121-2-1-122-1-12211-2-2000000000003-300-330000000000000000000000
χ5044-4-444-4-441-2-441-211-2-21-2-12-121-2-1-122-1-12211-2-200000000000-33003-30000000000000000000000
χ5144-4-444-4-44-21-44-21-2-211-212-12-1-2122-1-122-1-1-2-21100000000000003-300-3300000000000000000000
χ5244-4-444-4-44-21-44-21-2-211-212-12-1-2122-1-122-1-1-2-2110000000000000-33003-300000000000000000000
χ534-4000400-44400-4-40000440000-4-40000000000004i−4i000004i−4i000000000000000000000000000000
χ544-4000400-44400-4-40000440000-4-4000000000000−4i4i00000−4i4i000000000000000000000000000000
χ554-4000-2−2i32i324400-4-40000-2-20000220000−2i32i3−2i32i300004i−4i00000−2i2i23−230000000000000000000000000000
χ564-4000-2−2i32i324400-4-40000-2-20000220000−2i32i3−2i32i30000−4i4i000002i−2i−23230000000000000000000000000000
χ574-4000-22i3−2i324400-4-40000-2-200002200002i3−2i32i3−2i300004i−4i00000−2i2i−23230000000000000000000000000000
χ584-4000-22i3−2i324400-4-40000-2-200002200002i3−2i32i3−2i30000−4i4i000002i−2i23−230000000000000000000000000000
χ5988888-4-4-4-42-4-4-42-422-4-4-122-42-4-12-1-122-1-122-1-122000000000000000000000000000000000000000
χ6088888-4-4-4-4-42-4-4-42-4-4222-1-42-422-122-1-122-1-122-1-1000000000000000000000000000000000000000
χ61888-8-8-444-42-4-442-4-2-244-122-4-24-12-1-12211-2-211-2-2000000000000000000000000000000000000000
χ62888-8-8-444-4-42-44-4244-2-22-1-424-22-122-1-1-2-211-2-211000000000000000000000000000000000000000
χ6388-88-8-4-4-4-42-4442-4-2-244-12-242-4-1211-2-2-1-12211-2-2000000000000000000000000000000000000000
χ6488-88-8-4-4-4-4-4244-4244-2-22-14-2-422-1-2-21122-1-1-2-211000000000000000000000000000000000000000
χ6588-8-88-444-42-44-42-422-4-4-12-24-24-1211-2-211-2-2-1-122000000000000000000000000000000000000000
χ6688-8-88-444-4-424-4-42-4-4222-14-24-22-1-2-211-2-21122-1-1000000000000000000000000000000000000000
χ678-8000800-82-400-246-6002-40000-24000000006-600000000000000000000000000000000000000000
χ688-8000800-82-400-24-66002-40000-2400000000-6600000000000000000000000000000000000000000
χ698-8000800-8-42004-2006-6-4200004-200000000006-6000000000000000000000000000000000000000
χ708-8000800-8-42004-200-66-4200004-20000000000-66000000000000000000000000000000000000000
χ718-8000-4−4i34i342-400-246-600-1200001-2−3i33i300−i3i32i3−2i3-3300000000000000000000000000000000000000000
χ728-8000-4−4i34i342-400-24-6600-1200001-23i3−3i300−i3i32i3−2i33-300000000000000000000000000000000000000000
χ738-8000-4−4i34i34-42004-2006-62-10000-2100−3i33i32i3−2i3−i3i300-33000000000000000000000000000000000000000
χ748-8000-4−4i34i34-42004-200-662-10000-21003i3−3i32i3−2i3−i3i3003-3000000000000000000000000000000000000000
χ758-8000-44i3−4i342-400-246-600-1200001-23i3−3i300i3−i3−2i32i3-3300000000000000000000000000000000000000000
χ768-8000-44i3−4i342-400-24-6600-1200001-2−3i33i300i3−i3−2i32i33-300000000000000000000000000000000000000000
χ778-8000-44i3−4i34-42004-2006-62-10000-21003i3−3i3−2i32i3i3−i300-33000000000000000000000000000000000000000
χ788-8000-44i3−4i34-42004-200-662-10000-2100−3i33i3−2i32i3i3−i3003-3000000000000000000000000000000000000000

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