Finite Group Databasebeta

← Group #10591582

Character table — Group #10591582

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222222222444444444488888888881212121212121212121212121212121218181818242424243636
order12223344666666344666121212121212121212121212121244448888242424242424242444441212121244
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ6111111111111111-1-11111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111
χ7111111111111111-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111
χ8111111111111111-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ911-1-1111-1-1-1-11-1111-1-1-111-1-111-11-11-111-1-11-1i−i1-1i−i11-1-1ii−i−ii−ii−ii−i1-1i−i
χ1011-1-1111-1-1-1-11-1111-1-1-111-1-111-11-11-111-1-11-1−ii1-1−ii11-1-1−i−iii−ii−ii−ii1-1−ii
χ1111-1-1111-1-1-1-11-1111-1-1-111-1-111-11-11-111-1-1-11i−i-11i−i-1-111ii−i−i−ii−iii−i-11−ii
χ1211-1-1111-1-1-1-11-1111-1-1-111-1-111-11-11-111-1-1-11−ii-11−ii-1-111−i−iiii−ii−i−ii-11i−i
χ1311-1-1111-1-1-1-11-111-11-1-111-1-11-11-111-1-1-1111-1i−i-11−ii-1-111−i−iiii−ii−ii−i1-1−ii
χ1411-1-1111-1-1-1-11-111-11-1-111-1-11-11-111-1-1-1111-1−ii-11i−i-1-111ii−i−i−ii−ii−ii1-1i−i
χ1511-1-1111-1-1-1-11-111-11-1-111-1-11-11-111-1-1-111-11i−i1-1−ii11-1-1−i−iii−ii−iii−i-11i−i
χ1611-1-1111-1-1-1-11-111-11-1-111-1-11-11-111-1-1-111-11−ii1-1i−i11-1-1ii−i−ii−ii−i−ii-11−ii
χ17222222-2-2222222200222-2-2-2-20000-2-20000000000000000000022-2-2000000
χ18222222-2-2222222200222-2-2-2-20000-2-200000000000000000000-2-222000000
χ1922222-12222-1-1-12-122-1-1-1-12-12-1-122-1-1-1-1-1-1002200220000-1-1-1-10000-1-10000
χ2022222-12222-1-1-12-122-1-1-1-12-12-1-122-1-1-1-1-1-100-2-200-2-2000011110000110000
χ2122222-12222-1-1-12-1-2-2-1-1-1-12-1211-2-2-1-11111002200-2-2000011110000-1-10000
χ2222222-12222-1-1-12-1-2-2-1-1-1-12-1211-2-2-1-1111100-2-200220000-1-1-1-10000110000
χ232222-1222-1-1222-1-122-1-1-12-12-122-1-1-1-1-1-1-1-122002200-1-1-1-10000000000-1-100
χ242222-1222-1-1222-1-122-1-1-12-12-122-1-1-1-1-1-1-1-1-2-200-2-200111100000000001100
χ252222-1222-1-1222-1-1-2-2-1-1-12-12-1-2-211-1-111112200-2-20011110000000000-1-100
χ262222-1222-1-1222-1-1-2-2-1-1-12-12-1-2-211-1-11111-2-2002200-1-1-1-100000000001100
χ2722-2-222-22-2-2-22-22200-2-22-222-20000-22000000000000000000002i−2i−2i2i000000
χ2822-2-222-22-2-2-22-22200-2-22-222-20000-2200000000000000000000−2i2i2i−2i000000
χ2922-2-22-12-2-2-21-112-12-211-1-1-212-112-2-11-1-111002i−2i002i−2i0000−i−iii0000−ii0000
χ3022-2-22-12-2-2-21-112-12-211-1-1-212-112-2-11-1-11100−2i2i00−2i2i0000ii−i−i0000i−i0000
χ3122-2-22-12-2-2-21-112-1-2211-1-1-2121-1-22-1111-1-1002i−2i00−2i2i0000ii−i−i0000−ii0000
χ3222-2-22-12-2-2-21-112-1-2211-1-1-2121-1-22-1111-1-100−2i2i002i−2i0000−i−iii0000i−i0000
χ3322-2-2-122-211-22-2-1-12-211-121-2-12-2-11-11-1-1112-2002-200-1-1110000000000-1100
χ3422-2-2-122-211-22-2-1-12-211-121-2-12-2-11-11-1-111-2200-220011-1-100000000001-100
χ3522-2-2-122-211-22-2-1-1-2211-121-2-1-221-1-1111-1-12-200-220011-1-10000000000-1100
χ3622-2-2-122-211-22-2-1-1-2211-121-2-1-221-1-1111-1-1-22002-200-1-11100000000001-100
χ3744444-2-4-444-2-2-24-200-2-2-22-42-4000022000000000000000000000000000000
χ384444-24-4-4-2-2444-2-200-2-2-2-42-42000022000000000000000000000000000000
χ394444-2-244-2-2-2-2-2-2144111-2-2-2-2-2-2-2-211111100000000000000000000000000
χ404444-2-244-2-2-2-2-2-21-4-4111-2-2-2-2222211-1-1-1-100000000000000000000000000
χ414444-2-2-4-4-2-2-2-2-2-210011122220000-1-13-33-300000000000000000000000000
χ424444-2-2-4-4-2-2-2-2-2-210011122220000-1-1-33-3300000000000000000000000000
χ4344-4-44-2-44-4-42-224-20022-224-2-400002-2000000000000000000000000000000
χ4444-4-4-24-4422-44-4-2-20022-2-4-24200002-2000000000000000000000000000000
χ4544-4-4-2-24-4222-22-214-4-1-11-222-2-22-221-111-1-100000000000000000000000000
χ4644-4-4-2-24-4222-22-21-44-1-11-222-22-22-21-1-1-11100000000000000000000000000
χ4744-4-4-2-2-44222-22-2100-1-112-2-220000-113-3-3300000000000000000000000000
χ4844-4-4-2-2-44222-22-2100-1-112-2-220000-11-333-300000000000000000000000000
χ494-44-444004-4-4-44-44004-4-40000000000000000000000000000000000000000
χ504-44-44-2004-422-2-4-200-222000000000000000000000000006−66−60000000000
χ514-44-44-2004-422-2-4-200-22200000000000000000000000000−66−660000000000
χ524-44-4-2400-22-4-442-200-2220000000000000000000000i6−i6i6−i600000000000000
χ534-44-4-2400-22-4-442-200-2220000000000000000000000−i6i6−i6i600000000000000
χ544-4-444400-444-4-4-4400-44-40000000000000000000000000000000000000000
χ554-4-444-200-44-222-4-2002-2200000000000000000000000000i6−i6−i6i60000000000
χ564-4-444-200-44-222-4-2002-2200000000000000000000000000−i6i6i6−i60000000000
χ574-4-44-24002-24-4-42-2002-220000000000000000000000i6−i6−i6i600000000000000
χ584-4-44-24002-24-4-42-2002-220000000000000000000000−i6i6i6−i600000000000000
χ598-88-8-4-400-4444-442002-2-20000000000000000000000000000000000000000
χ608-8-88-4-4004-4-4444200-22-20000000000000000000000000000000000000000

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