Finite Group Databasebeta

← Group #13180739

Character table — Group #13180739

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222223344446666666668812121212121212121616161616161616161616161616161616181824242424242424242424242424242424545454545454108108144144
order123333466662212121212466666666364444121212123333666612121212121212121222121212121212121212121212121212122244442466
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ5111111-1111111-1-1-1-1-111111111111-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-11-11111-1-11-1
χ6111111-1111111-1-1-1-1-111111111111-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-11
χ7111111-1111111-1-1-1-1-11111111111-11-11-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1111-1
χ8111111-1111111-1-1-1-1-11111111111-11-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-111111-1-1-11
χ922222222222222222222222222-1-100002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122000000000000000022000000-1-1
χ1022222222222222222222222222-1-100002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000000000000-2-200000011
χ11222222-2222222-2-2-2-2-222222222-1-10000-2-2-2-2-1-1-1-1-1-1-1-11111111112-200000000000000002-2000000-11
χ12222222-2222222-2-2-2-2-222222222-1-10000-2-2-2-2-1-1-1-1-1-1-1-1111111111-220000000000000000-220000001-1
χ13222-1-1-122-1-1-1222-1-1-122-1-1-12-1-1-12222222-1-1-12-1-1-12-1-1-1222-1-1-1-1-1-1002-1-1-12-1-1-12-1-1-12-1-1-10000000000
χ14222-1-1-122-1-1-1222-1-1-122-1-1-12-1-1-122-2-2-2-22-1-1-12-1-1-12-1-1-1222-1-1-1-1-1-100-2111-2111-2111-21110000000000
χ15222-1-1-1-22-1-1-122-2111-22-1-1-12-1-1-1222-22-2-21112-1-1-12-1-1-1-2-2-2111111002-1-1-1-21112-1-1-1-21110000000000
χ16222-1-1-1-22-1-1-122-2111-22-1-1-12-1-1-122-22-22-21112-1-1-12-1-1-1-2-2-211111100-21112-1-1-1-21112-1-1-10000000000
χ1722-12-1-12-12-1-122-12-1-12-12-1-1-12-1-1222222-12-1-1-12-1-1-12-1-12-1-122-1-1-1-100-12-1-1-12-1-1-12-1-1-12-1-10000000000
χ1822-12-1-12-12-1-122-12-1-12-12-1-1-12-1-122-2-2-2-2-12-1-1-12-1-1-12-1-12-1-122-1-1-1-1001-2111-2111-2111-2110000000000
χ1922-12-1-1-2-12-1-1221-211-2-12-1-1-12-1-1222-22-21-211-12-1-1-12-1-1-211-2-2111100-12-1-11-211-12-1-11-2110000000000
χ2022-12-1-1-2-12-1-1221-211-2-12-1-1-12-1-122-22-221-211-12-1-1-12-1-1-211-2-21111001-211-12-1-11-211-12-1-10000000000
χ2122-1-12-12-1-12-122-1-12-12-1-12-1-1-12-1222222-1-12-1-1-12-1-1-12-12-1-1-1-122-1-100-1-12-1-1-12-1-1-12-1-1-12-10000000000
χ2222-1-12-12-1-12-122-1-12-12-1-12-1-1-12-122-2-2-2-2-1-12-1-1-12-1-1-12-12-1-1-1-122-1-10011-2111-2111-2111-210000000000
χ2322-1-12-1-2-1-12-12211-21-2-1-12-1-1-12-1222-22-211-21-1-12-1-1-12-1-21111-2-21100-1-12-111-21-1-12-111-210000000000
χ2422-1-12-1-2-1-12-12211-21-2-1-12-1-1-12-122-22-2211-21-1-12-1-1-12-1-21111-2-2110011-21-1-12-111-21-1-12-10000000000
χ2522-1-1-122-1-1-1222-1-1-122-1-1-12-1-1-12222222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12200-1-1-12-1-1-12-1-1-12-1-1-120000000000
χ2622-1-1-122-1-1-1222-1-1-122-1-1-12-1-1-1222-2-2-2-2-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12200111-2111-2111-2111-20000000000
χ2722-1-1-12-2-1-1-1222111-2-2-1-1-12-1-1-12222-22-2111-2-1-1-12-1-1-12-2111111-2-200-1-1-12111-2-1-1-12111-20000000000
χ2822-1-1-12-2-1-1-1222111-2-2-1-1-12-1-1-1222-22-22111-2-1-1-12-1-1-12-2111111-2-200111-2-1-1-12111-2-1-1-120000000000
χ292-222220-2-2-2-22-2000002222-2-2-2-22-2000000002222-2-2-2-2000000000000000000000000000002i−2i2i−2i0000
χ302-222220-2-2-2-22-2000002222-2-2-2-22-2000000002222-2-2-2-200000000000000000000000000000−2i2i−2i2i0000
χ3133333333333-1-13333-1-1-1-1-1-1-1-1-10011-1-1-1-1-1-1000000000000000003311111111-1-1-1-1-1-1-1-1-1-111-1-11-100
χ3233333333333-1-13333-1-1-1-1-1-1-1-1-10011-1-1-1-1-1-100000000000000000-3-311111111-1-1-1-1-1-1-1-111-1-111-1100
χ3333333333333-1-13333-1-1-1-1-1-1-1-1-100-1-111-1-1-1-10000000000000000033-1-1-1-1-1-1-1-111111111-1-1-1-111-1100
χ3433333333333-1-13333-1-1-1-1-1-1-1-1-100-1-111-1-1-1-100000000000000000-3-3-1-1-1-1-1-1-1-1111111111111-1-11-100
χ35333333-33333-1-1-3-3-3-31-1-1-1-1-1-1-1-1001-1-111111000000000000000003-31111-1-1-1-1-1-1-1-11111-1111-1-1-1100
χ36333333-33333-1-1-3-3-3-31-1-1-1-1-1-1-1-1001-1-11111100000000000000000-331111-1-1-1-1-1-1-1-111111-1-1-1111-100
χ37333333-33333-1-1-3-3-3-31-1-1-1-1-1-1-1-100-111-11111000000000000000003-3-1-1-1-111111111-1-1-1-1-11-1-1111-100
χ38333333-33333-1-1-3-3-3-31-1-1-1-1-1-1-1-100-111-1111100000000000000000-33-1-1-1-111111111-1-1-1-11-111-1-1-1100
χ39444-2-2-244-2-2-2444-2-2-244-2-2-24-2-2-2-2-200004-2-2-2-2111-2111-2-2-21111110000000000000000000000000000
χ40444-2-2-2-44-2-2-244-4222-44-2-2-24-2-2-2-2-20000-4222-2111-2111222-1-1-1-1-1-10000000000000000000000000000
χ4144-24-2-24-24-2-244-24-2-24-24-2-2-24-2-2-2-20000-24-2-21-2111-211-211-2-211110000000000000000000000000000
χ4244-24-2-2-4-24-2-2442-422-4-24-2-2-24-2-2-2-200002-4221-2111-2112-1-122-1-1-1-10000000000000000000000000000
χ4344-2-24-24-2-24-244-2-24-24-2-24-2-2-24-2-2-20000-2-24-211-2111-21-21111-2-2110000000000000000000000000000
χ4444-2-24-2-4-2-24-24422-42-4-2-24-2-2-24-2-2-2000022-4211-2111-212-1-1-1-122-1-10000000000000000000000000000
χ4544-2-2-244-2-2-2444-2-2-244-2-2-24-2-2-24-2-20000-2-2-24111-2111-2-2111111-2-20000000000000000000000000000
χ4644-2-2-24-4-2-2-2444222-4-4-2-2-24-2-2-24-2-20000222-4111-2111-22-1-1-1-1-1-1220000000000000000000000000000
χ474-444440-4-4-4-44-4000004444-4-4-4-4-2200000000-2-2-2-222220000000000000000000000000000000000000
χ484-44-2-2-20-42224-4000004-2-2-2-42224-4000000004-2-2-2-42220000000000000000000000000000000000000
χ494-44-2-2-20-42224-4000004-2-2-2-4222-2200000000-21112-1-1-10003i−3i3i−3i3i−3i0000000000000000000000000000
χ504-44-2-2-20-42224-4000004-2-2-2-4222-2200000000-21112-1-1-1000−3i3i−3i3i−3i3i0000000000000000000000000000
χ514-4-24-2-202-4224-400000-24-2-22-4224-400000000-24-2-22-4220000000000000000000000000000000000000
χ524-4-24-2-202-4224-400000-24-2-22-422-22000000001-211-12-1-103i−3i003i−3i−3i3i0000000000000000000000000000
χ534-4-24-2-202-4224-400000-24-2-22-422-22000000001-211-12-1-10−3i3i00−3i3i3i−3i0000000000000000000000000000
χ544-4-2-24-2022-424-400000-2-24-222-424-400000000-2-24-222-420000000000000000000000000000000000000
χ554-4-2-24-2022-424-400000-2-24-222-42-220000000011-21-1-12-103i−3i−3i3i003i−3i0000000000000000000000000000
χ564-4-2-24-2022-424-400000-2-24-222-42-220000000011-21-1-12-10−3i3i3i−3i00−3i3i0000000000000000000000000000
χ574-4-2-2-240222-44-400000-2-2-24222-44-400000000-2-2-24222-40000000000000000000000000000000000000
χ584-4-2-2-240222-44-400000-2-2-24222-4-2200000000111-2-1-1-1203i−3i3i−3i−3i3i000000000000000000000000000000
χ594-4-2-2-240222-44-400000-2-2-24222-4-2200000000111-2-1-1-120−3i3i−3i3i3i−3i000000000000000000000000000000
χ60666-3-3-366-3-3-3-2-26-3-3-3-2-2111-21110022-2-2-211100000000000000000002-1-1-12-1-1-1-2111-21110000000000
χ61666-3-3-366-3-3-3-2-26-3-3-3-2-2111-211100-2-222-21110000000000000000000-2111-21112-1-1-12-1-1-10000000000
χ62666-3-3-3-66-3-3-3-2-2-63332-2111-2111002-2-222-1-1-100000000000000000002-1-1-1-2111-21112-1-1-10000000000
χ63666-3-3-3-66-3-3-3-2-2-63332-2111-211100-222-22-1-1-10000000000000000000-21112-1-1-12-1-1-1-21110000000000
χ6466-36-3-36-36-3-3-2-2-36-3-3-21-2111-2110022-2-21-2110000000000000000000-12-1-1-12-1-11-2111-2110000000000
χ6566-36-3-36-36-3-3-2-2-36-3-3-21-2111-21100-2-2221-21100000000000000000001-2111-211-12-1-1-12-1-10000000000
χ6666-36-3-3-6-36-3-3-2-23-63321-2111-211002-2-22-12-1-10000000000000000000-12-1-11-2111-211-12-1-10000000000
χ6766-36-3-3-6-36-3-3-2-23-63321-2111-21100-222-2-12-1-100000000000000000001-211-12-1-1-12-1-11-2110000000000
χ6866-3-36-36-3-36-3-2-2-3-36-3-211-2111-210022-2-211-210000000000000000000-1-12-1-1-12-111-2111-210000000000
χ6966-3-36-36-3-36-3-2-2-3-36-3-211-2111-2100-2-22211-21000000000000000000011-2111-21-1-12-1-1-12-10000000000
χ7066-3-36-3-6-3-36-3-2-233-63211-2111-21002-2-22-1-12-10000000000000000000-1-12-111-2111-21-1-12-10000000000
χ7166-3-36-3-6-3-36-3-2-233-63211-2111-2100-222-2-1-12-1000000000000000000011-21-1-12-1-1-12-111-210000000000
χ7266-3-3-366-3-3-36-2-2-3-3-36-2111-2111-20022-2-2111-20000000000000000000-1-1-12-1-1-12111-2111-20000000000
χ7366-3-3-366-3-3-36-2-2-3-3-36-2111-2111-200-2-222111-20000000000000000000111-2111-2-1-1-12-1-1-120000000000
χ7466-3-3-36-6-3-3-36-2-2333-62111-2111-2002-2-22-1-1-120000000000000000000-1-1-12111-2111-2-1-1-120000000000
χ7566-3-3-36-6-3-3-36-2-2333-62111-2111-200-222-2-1-1-120000000000000000000111-2-1-1-12-1-1-12111-20000000000
χ766-666660-6-6-6-6-2200000-2-2-2-22222000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ776-666660-6-6-6-6-2200000-2-2-2-2222200000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ7812-1212-6-6-60-12666-4400000-42224-2-2-20000000000000000000000000000000000000000000000000000000
χ7912-12-612-6-606-1266-44000002-422-24-2-20000000000000000000000000000000000000000000000000000000
χ8012-12-6-612-6066-126-440000022-42-2-24-20000000000000000000000000000000000000000000000000000000
χ8112-12-6-6-6120666-12-4400000222-4-2-2-240000000000000000000000000000000000000000000000000000000

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