Finite Group Databasebeta

← Group #13165979

Character table — Group #13165979

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11222222222444466881212121212121212161616161616161616161616161616161624242424242424242424242424242424242436108108108144144216
order1233334666612121212243666661212121233336666121212121212121212266666666824242424242424242444668
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11
χ522222222222222222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002200-1-10
χ622222222222222222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-200110
χ7222222-22222-2-2-2-2-2222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-20000000000000000000000000
χ8222222-22222-2-2-2-2-22-1-1-2-2-2-22222-1-1-1-1-1-1-1-11111111110000000000000000000000−i3i30
χ9222222-22222-2-2-2-2-22-1-1-2-2-2-22222-1-1-1-1-1-1-1-11111111110000000000000000000000i3−i30
χ10222-1-1-122-1-1-12-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-10000000
χ11222-1-1-122-1-1-12-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-1222-1-1-1-1-1-1-2-2-2111111-2-2-21111110000000
χ12222-1-1-1-22-1-1-1-2111-2222-21112-1-1-12-1-1-12-1-1-1-2-2-2111111000−i3−i3−i3i3i3i3000−i3−i3−i3i3i3i30000000
χ13222-1-1-1-22-1-1-1-2111-2222-21112-1-1-12-1-1-12-1-1-1-2-2-2111111000i3i3i3−i3−i3−i3000i3i3i3−i3−i3−i30000000
χ1422-12-1-12-12-1-1-12-1-12222-12-1-1-12-1-1-12-1-1-12-1-12-1-122-1-1-1-12-1-12-1-12-1-12-1-12-1-12-1-10000000
χ1522-12-1-12-12-1-1-12-1-12222-12-1-1-12-1-1-12-1-1-12-1-12-1-122-1-1-1-1-211-211-211-211-211-2110000000
χ1622-12-1-1-2-12-1-11-211-22221-211-12-1-1-12-1-1-12-1-1-211-2-211110−i3i30−i3i30−i3i30−i3i30−i3i30−i3i30000000
χ1722-12-1-1-2-12-1-11-211-22221-211-12-1-1-12-1-1-12-1-1-211-2-211110i3−i30i3−i30i3−i30i3−i30i3−i30i3−i30000000
χ1822-1-12-12-1-12-1-1-12-12222-1-12-1-1-12-1-1-12-1-1-12-12-1-1-1-122-1-12-1-1-12-1-1-122-1-1-12-1-1-120000000
χ1922-1-12-12-1-12-1-1-12-12222-1-12-1-1-12-1-1-12-1-1-12-12-1-1-1-122-1-1-2111-2111-2-2111-2111-20000000
χ2022-1-12-1-2-1-12-111-21-222211-21-1-12-1-1-12-1-1-12-1-21111-2-2110−i3i3i30−i3−i3i300−i3i3i30−i3−i3i300000000
χ2122-1-12-1-2-1-12-111-21-222211-21-1-12-1-1-12-1-1-12-1-21111-2-2110i3−i3−i30i3i3−i300i3−i3−i30i3i3−i300000000
χ2222-1-1-122-1-1-12-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1222-1-1-1-12-12-12-1-1-1-12-12-10000000
χ2322-1-1-122-1-1-12-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-21111-21-21-21111-21-210000000
χ2422-1-1-12-2-1-1-12111-2-2222111-2-1-1-12-1-1-12-1-1-12-2111111-2-20−i3i3−i3i30i30−i30−i3i3−i3i30i30−i30000000
χ2522-1-1-12-2-1-1-12111-2-2222111-2-1-1-12-1-1-12-1-1-12-2111111-2-20i3−i3i3−i30−i30i30i3−i3i3−i30−i30i30000000
χ26333333333333333-1-100-1-1-1-1-1-1-1-100000000000000000111111111-1-1-1-1-1-1-1-1-13-1-1-1001
χ27333333333333333-1-100-1-1-1-1-1-1-1-100000000000000000111111111-1-1-1-1-1-1-1-1-1-311100-1
χ28333333333333333-1-100-1-1-1-1-1-1-1-100000000000000000-1-1-1-1-1-1-1-1-11111111113-11100-1
χ29333333333333333-1-100-1-1-1-1-1-1-1-100000000000000000-1-1-1-1-1-1-1-1-1111111111-31-1-1001
χ30444-2-2-244-2-2-24-2-2-244-2-24-2-2-24-2-2-2-2111-2111-2-2-21111110000000000000000000000000
χ31444-2-2-2-44-2-2-2-4222-44-2-2-42224-2-2-2-2111-2111222-1-1-1-1-1-10000000000000000000000000
χ3244-24-2-24-24-2-2-24-2-244-2-2-24-2-2-24-2-21-2111-211-211-2-211110000000000000000000000000
χ3344-24-2-2-4-24-2-22-422-44-2-22-422-24-2-21-2111-2112-1-122-1-1-1-10000000000000000000000000
χ3444-2-24-24-2-24-2-2-24-244-2-2-2-24-2-2-24-211-2111-21-21111-2-2110000000000000000000000000
χ3544-2-24-2-4-2-24-222-42-44-2-222-42-2-24-211-2111-212-1-1-1-122-1-10000000000000000000000000
χ3644-2-2-244-2-2-24-2-2-2444-2-2-2-2-24-2-2-24111-2111-2-2111111-2-20000000000000000000000000
χ3744-2-2-24-4-2-2-24222-4-44-2-2222-4-2-2-24111-2111-22-1-1-1-1-1-1220000000000000000000000000
χ384-444440-4-4-4-4000000-2200000000-2-2-2-22222000000000000000000000000000002i−2i000
χ394-444440-4-4-4-4000000-2200000000-2-2-2-2222200000000000000000000000000000−2i2i000
χ40666666-66666-6-6-6-62-2002222-2-2-2-2000000000000000000000000000000000000000000
χ41666-3-3-366-3-3-36-3-3-3-2-200-2111-211100000000000000000222-1-1-1-1-1-1-2-2-21111110000000
χ42666-3-3-366-3-3-36-3-3-3-2-200-2111-211100000000000000000-2-2-2111111222-1-1-1-1-1-10000000
χ43666-3-3-3-66-3-3-3-63332-2002-1-1-1-211100000000000000000000−i3−i3−i3i3i3i3000i3i3i3−i3−i3−i30000000
χ44666-3-3-3-66-3-3-3-63332-2002-1-1-1-211100000000000000000000i3i3i3−i3−i3−i3000−i3−i3−i3i3i3i30000000
χ4566-36-3-36-36-3-3-36-3-3-2-2001-2111-211000000000000000002-1-12-1-12-1-1-211-211-2110000000
χ4666-36-3-36-36-3-3-36-3-3-2-2001-2111-21100000000000000000-211-211-2112-1-12-1-12-1-10000000
χ4766-36-3-3-6-36-3-33-6332-200-12-1-11-211000000000000000000−i3i30−i3i30−i3i30i3−i30i3−i30i3−i30000000
χ4866-36-3-3-6-36-3-33-6332-200-12-1-11-211000000000000000000i3−i30i3−i30i3−i30−i3i30−i3i30−i3i30000000
χ4966-3-36-36-3-36-3-3-36-3-2-20011-2111-21000000000000000002-1-1-12-1-1-12-2111-2111-20000000
χ5066-3-36-36-3-36-3-3-36-3-2-20011-2111-2100000000000000000-2111-2111-22-1-1-12-1-1-120000000
χ5166-3-36-3-6-3-36-333-632-200-1-12-111-21000000000000000000−i3i3i30−i3−i3i300i3−i3−i30i3i3−i300000000
χ5266-3-36-3-6-3-36-333-632-200-1-12-111-21000000000000000000i3−i3−i30i3i3−i300−i3i3i30−i3−i3i300000000
χ5366-3-3-366-3-3-36-3-3-36-2-200111-2111-2000000000000000002-1-1-1-12-12-1-21111-21-210000000
χ5466-3-3-366-3-3-36-3-3-36-2-200111-2111-200000000000000000-21111-21-212-1-1-1-12-12-10000000
χ5566-3-3-36-6-3-3-36333-62-200-1-1-12111-2000000000000000000−i3i3−i3i30i30−i30i3−i3i3−i30−i30i30000000
χ5666-3-3-36-6-3-3-36333-62-200-1-1-12111-2000000000000000000i3−i3i3−i30−i30i30−i3i3−i3i30i30−i30000000
χ578-888880-8-8-8-80000002-2000000002222-2-2-2-20000000000000000000000000000000000
χ588-88-4-4-40-84440000002-2000000002-1-1-1-21110003i−3i3i−3i3i−3i0000000000000000000000000
χ598-88-4-4-40-84440000002-2000000002-1-1-1-2111000−3i3i−3i3i−3i3i0000000000000000000000000
χ608-88-4-4-40-8444000000-4400000000-42224-2-2-20000000000000000000000000000000000
χ618-8-48-4-404-8440000002-200000000-12-1-11-21103i−3i003i−3i−3i3i0000000000000000000000000
χ628-8-48-4-404-8440000002-200000000-12-1-11-2110−3i3i00−3i3i3i−3i0000000000000000000000000
χ638-8-48-4-404-844000000-44000000002-422-24-2-20000000000000000000000000000000000
χ648-8-4-48-4044-840000002-200000000-1-12-111-2103i−3i−3i3i003i−3i0000000000000000000000000
χ658-8-4-48-4044-840000002-200000000-1-12-111-210−3i3i3i−3i00−3i3i0000000000000000000000000
χ668-8-4-48-4044-84000000-440000000022-42-2-24-20000000000000000000000000000000000
χ678-8-4-4-480444-80000002-200000000-1-1-12111-203i−3i3i−3i−3i3i000000000000000000000000000
χ688-8-4-4-480444-80000002-200000000-1-1-12111-20−3i3i−3i3i3i−3i000000000000000000000000000
χ698-8-4-4-480444-8000000-4400000000222-4-2-2-240000000000000000000000000000000000

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