Finite Group Databasebeta

← Group #10593505

Character table — Group #10593505

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1124444446666899121212121212182424363611244444466668991212121212121824243636
order1223366664444644241212121246128822266666644446442412121212461288
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111-1-111111-1-1-1-11111111111111111-1-111111-1-1-1-1
χ3111111111-1-1-1-111111-1-1-1-1111-1-1111111111-1-1-1-111111-1-1-1-1111-1-1
χ4111111111-1-1-1-1111-1-1-1-1-1-11-1-111111111111-1-1-1-1111-1-1-1-1-1-11-1-111
χ511-1111-11-1ii−i−i-1-1-11-1ii−i−i11-1i−i11-1111-11-1ii−i−i-1-1-11-1ii−i−i11-1i−i
χ611-1111-11-1ii−i−i-1-1-1-11ii−i−i1-11−ii11-1111-11-1ii−i−i-1-1-1-11ii−i−i1-11−ii
χ711-1111-11-1−i−iii-1-1-11-1−i−iii11-1−ii11-1111-11-1−i−iii-1-1-11-1−i−iii11-1−ii
χ811-1111-11-1−i−iii-1-1-1-11−i−iii1-11i−i11-1111-11-1−i−iii-1-1-1-11−i−iii1-11i−i
χ922222222200002-2-2000000-2000022222222200002-2-2000000-20000
χ1022-2222-22-20000-222000000-2000022-2222-22-20000-222000000-20000
χ112-2022-20-201+i−1−i1−i−1+i02i−2i001+i−1−i1−i−1+i000002-2022-20-201+i−1−i1−i−1+i02i−2i001+i−1−i1−i−1+i00000
χ122-2022-20-201−i−1+i1+i−1−i0−2i2i001−i−1+i1+i−1−i000002-2022-20-201−i−1+i1+i−1−i0−2i2i001−i−1+i1+i−1−i00000
χ132-2022-20-20−1+i1−i−1−i1+i0−2i2i00−1+i1−i−1−i1+i000002-2022-20-20−1+i1−i−1−i1+i0−2i2i00−1+i1−i−1−i1+i00000
χ142-2022-20-20−1−i1+i−1+i1−i02i−2i00−1−i1+i−1+i1−i000002-2022-20-20−1−i1+i−1+i1−i02i−2i00−1−i1+i−1+i1−i00000
χ154441-211-212222-20000-1-1-1-1000004441-211-212222-20000-1-1-1-100000
χ164441-211-21-2-2-2-2-200001111000004441-211-21-2-2-2-2-20000111100000
χ17444-21-2-21-200001002200000-1-100444-21-2-21-200001002200000-1-100
χ18444-21-2-21-20000100-2-2000001100444-21-2-21-20000100-2-2000001100
χ1944-41-21-1-2-12i2i−2i−2i20000−i−iii0000044-41-21-1-2-12i2i−2i−2i20000−i−iii00000
χ2044-41-21-1-2-1−2i−2i2i2i20000ii−i−i0000044-41-21-1-2-1−2i−2i2i2i20000ii−i−i00000
χ2144-4-21-22120000-1002-200000-110044-4-21-22120000-1002-200000-1100
χ2244-4-21-22120000-100-22000001-10044-4-21-22120000-100-22000001-100
χ234-401-2-132-32-22-200000-11-11000004-401-2-132-32-22-200000-11-1100000
χ244-401-2-132-3-22-22000001-11-1000004-401-2-132-3-22-22000001-11-100000
χ254-401-2-1-3232i−2i−2i2i00000−iii−i000004-401-2-1-3232i−2i−2i2i00000−iii−i00000
χ264-401-2-1-323−2i2i2i−2i00000i−i−ii000004-401-2-1-323−2i2i2i−2i00000i−i−ii00000
χ278-80-4240-200000000000000000008-80-4240-20000000000000000000
χ28111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ291111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111
χ30111111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-111
χ31111111111-1-1-1-1111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-11111-1-1-1111111-111-1-1
χ3211-1111-11-1ii−i−i-1-1-11-1ii−i−i11-1i−i-1-11-1-1-11-11−i−iii111-11−i−iii-1-11−ii
χ3311-1111-11-1ii−i−i-1-1-1-11ii−i−i1-11−ii-1-11-1-1-11-11−i−iii1111-1−i−iii-11-1i−i
χ3411-1111-11-1−i−iii-1-1-11-1−i−iii11-1−ii-1-11-1-1-11-11ii−i−i111-11ii−i−i-1-11i−i
χ3511-1111-11-1−i−iii-1-1-1-11−i−iii1-11i−i-1-11-1-1-11-11ii−i−i1111-1ii−i−i-11-1−ii
χ3622222222200002-2-2000000-20000-2-2-2-2-2-2-2-2-20000-22200000020000
χ3722-2222-22-20000-222000000-20000-2-22-2-2-22-2200002-2-200000020000
χ382-2022-20-201+i−1−i1−i−1+i02i−2i001+i−1−i1−i−1+i00000-220-2-22020−1−i1+i−1+i1−i0−2i2i00−1−i1+i−1+i1−i00000
χ392-2022-20-201−i−1+i1+i−1−i0−2i2i001−i−1+i1+i−1−i00000-220-2-22020−1+i1−i−1−i1+i02i−2i00−1+i1−i−1−i1+i00000
χ402-2022-20-20−1+i1−i−1−i1+i0−2i2i00−1+i1−i−1−i1+i00000-220-2-220201−i−1+i1+i−1−i02i−2i001−i−1+i1+i−1−i00000
χ412-2022-20-20−1−i1+i−1+i1−i02i−2i00−1−i1+i−1+i1−i00000-220-2-220201+i−1−i1−i−1+i0−2i2i001+i−1−i1−i−1+i00000
χ424441-211-212222-20000-1-1-1-100000-4-4-4-12-1-12-1-2-2-2-220000111100000
χ434441-211-21-2-2-2-2-20000111100000-4-4-4-12-1-12-1222220000-1-1-1-100000
χ44444-21-2-21-200001002200000-1-100-4-4-42-122-120000-100-2-2000001100
χ45444-21-2-21-20000100-2-2000001100-4-4-42-122-120000-1002200000-1-100
χ4644-41-21-1-2-12i2i−2i−2i20000−i−iii00000-4-44-12-1121−2i−2i2i2i-20000ii−i−i00000
χ4744-41-21-1-2-1−2i−2i2i2i20000ii−i−i00000-4-44-12-11212i2i−2i−2i-20000−i−iii00000
χ4844-4-21-22120000-1002-200000-1100-4-442-12-2-1-20000100-22000001-100
χ4944-4-21-22120000-100-22000001-100-4-442-12-2-1-200001002-200000-1100
χ504-401-2-132-32-22-200000-11-1100000-440-121-3-23-22-22000001-11-100000
χ514-401-2-132-3-22-22000001-11-100000-440-121-3-232-22-200000-11-1100000
χ524-401-2-1-3232i−2i−2i2i00000−iii−i00000-440-1213-2-3−2i2i2i−2i00000i−i−ii00000
χ534-401-2-1-323−2i2i2i−2i00000i−i−ii00000-440-1213-2-32i−2i−2i2i00000−iii−i00000
χ548-80-4240-20000000000000000000-8804-2-4020000000000000000000

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