Finite Group Databasebeta

← Group #13165976

Character table — Group #13165976

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222222224444668888121212121212121216161616161616161616161616161616181824242424242424242424242424242424242472727272108216216
order12333346666121212122436121266661212121233336666121212121212121288481212121212121212242424242424242424242424848
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1
χ3111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ522222222222222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122000000000000000000-1-1-1-1200
χ622222222222222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000000000000001111-200
χ7222222-22222-2-2-2-2-2222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2000000000000000000000000000
χ8222222-22222-2-2-2-2-22-1-111-2-2-2-22222-1-1-1-1-1-1-1-1111111110000000000000000000033−3−3000
χ9222222-22222-2-2-2-2-22-1-111-2-2-2-22222-1-1-1-1-1-1-1-11111111100000000000000000000−3−333000
χ10222-1-1-122-1-1-12-1-1-12222222-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1002222-1-1-1-1-1-122-1-1-1-1-1-10000000
χ11222-1-1-122-1-1-12-1-1-12222222-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-100-2-2-2-2111111-2-21111110000000
χ12222-1-1-1-22-1-1-1-2111-2222-2-2-21112-1-1-12-1-1-12-1-1-1-2-2111111000000−i3−i3−i3i3i3i300−i3−i3−i3i3i3i30000000
χ13222-1-1-1-22-1-1-1-2111-2222-2-2-21112-1-1-12-1-1-12-1-1-1-2-2111111000000i3i3i3−i3−i3−i300i3i3i3−i3−i3−i30000000
χ1422-12-1-12-12-1-1-12-1-1222222-12-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-10022-1-12-1-12-1-1-1-12-1-12-1-10000000
χ1522-12-1-12-12-1-1-12-1-1222222-12-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-100-2-211-211-21111-211-2110000000
χ1622-12-1-1-2-12-1-11-211-2222-2-21-211-12-1-1-12-1-1-12-1-111-2-211110000−i3i30−i3i30−i3i3−i3i30−i3i30−i3i30000000
χ1722-12-1-1-2-12-1-11-211-2222-2-21-211-12-1-1-12-1-1-12-1-111-2-211110000i3−i30i3−i30i3−i3i3−i30i3−i30i3−i30000000
χ1822-1-12-12-1-12-1-1-12-1222222-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-10022-1-1-12-1-1-12-1-1-12-1-1-120000000
χ1922-1-12-12-1-12-1-1-12-1222222-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-100-2-2111-2111-2111-2111-20000000
χ2022-1-12-1-2-1-12-111-21-2222-2-211-21-1-12-1-1-12-1-1-12-11111-2-2110000−i3i3i30−i3−i3i30−i3i3i30−i3−i3i300000000
χ2122-1-12-1-2-1-12-111-21-2222-2-211-21-1-12-1-1-12-1-1-12-11111-2-2110000i3−i3−i30i3i3−i30i3−i3−i30i3i3−i300000000
χ2222-1-1-122-1-1-12-1-1-12222222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-1-1220022-1-1-1-12-12-1-1-1-1-12-12-10000000
χ2322-1-1-122-1-1-12-1-1-12222222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-1-12200-2-21111-21-211111-21-210000000
χ2422-1-1-12-2-1-1-12111-2-2222-2-2111-2-1-1-12-1-1-12-1-1-12111111-2-20000−i3i3−i3i30i30−i3−i3i3−i3i30i30−i30000000
χ2522-1-1-12-2-1-1-12111-2-2222-2-2111-2-1-1-12-1-1-12-1-1-12111111-2-20000i3−i3i3−i30−i30i3i3−i3i3−i30−i30i30000000
χ26333333333333333-1-10000-1-1-1-1-1-1-1-10000000000000000331-111111111-1-1-1-1-1-1-1-10000-11-1
χ27333333333333333-1-10000-1-1-1-1-1-1-1-1000000000000000033-11-1-1-1-1-1-1-1-1111111110000-1-11
χ28333333333333333-1-10000-1-1-1-1-1-1-1-10000000000000000-3-31-111111111-1-1-1-1-1-1-1-100001-11
χ29333333333333333-1-10000-1-1-1-1-1-1-1-10000000000000000-3-3-11-1-1-1-1-1-1-1-111111111000011-1
χ30444-2-2-244-2-2-24-2-2-244-2-2-2-24-2-2-24-2-2-2-2111-2111-2-2111111000000000000000000000000000
χ31444-2-2-2-44-2-2-2-4222-44-2-222-42224-2-2-2-2111-211122-1-1-1-1-1-1000000000000000000000000000
χ3244-24-2-24-24-2-2-24-2-244-2-2-2-2-24-2-2-24-2-21-2111-21111-2-21111000000000000000000000000000
χ3344-24-2-2-4-24-2-22-422-44-2-2222-422-24-2-21-2111-211-1-122-1-1-1-1000000000000000000000000000
χ3444-2-24-24-2-24-2-2-24-244-2-2-2-2-2-24-2-2-24-211-2111-211111-2-211000000000000000000000000000
χ3544-2-24-2-4-2-24-222-42-44-2-22222-42-2-24-211-2111-21-1-1-1-122-1-1000000000000000000000000000
χ3644-2-2-244-2-2-24-2-2-2444-2-2-2-2-2-2-24-2-2-24111-2111-2111111-2-2000000000000000000000000000
χ3744-2-2-24-4-2-2-24222-4-44-2-222222-4-2-2-24111-2111-2-1-1-1-1-1-122000000000000000000000000000
χ384-444440-4-4-4-40000001-13−3000000001111-1-1-1-13−33−33−33−322−22000000000000000000ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23000
χ394-444440-4-4-4-40000001-13−3000000001111-1-1-1-13−33−33−33−3−2222000000000000000000−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23000
χ404-444440-4-4-4-40000001-1−33000000001111-1-1-1-1−33−33−33−3322−22000000000000000000ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7000
χ414-444440-4-4-4-40000001-1−33000000001111-1-1-1-1−33−33−33−33−2222000000000000000000−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7000
χ424-444440-4-4-4-4000000-220000000000-2-2-2-222220000000022−220000000000000000002−2−22000
χ434-444440-4-4-4-4000000-220000000000-2-2-2-2222200000000−2222000000000000000000−222−2000
χ44666666-66666-6-6-6-62-200002222-2-2-2-20000000000000000000000000000000000000000000
χ45666-3-3-366-3-3-36-3-3-3-2-20000-2111-21110000000000000000002-222-1-1-1-1-1-1-2-21111110000000
χ46666-3-3-366-3-3-36-3-3-3-2-20000-2111-2111000000000000000000-22-2-211111122-1-1-1-1-1-10000000
χ47666-3-3-3-66-3-3-3-63332-200002-1-1-1-21110000000000000000000000−i3−i3−i3i3i3i300i3i3i3−i3−i3−i30000000
χ48666-3-3-3-66-3-3-3-63332-200002-1-1-1-21110000000000000000000000i3i3i3−i3−i3−i300−i3−i3−i3i3i3i30000000
χ4966-36-3-36-36-3-3-36-3-3-2-200001-2111-2110000000000000000002-2-1-12-1-12-1-111-211-2110000000
χ5066-36-3-36-36-3-3-36-3-3-2-200001-2111-211000000000000000000-2211-211-211-1-12-1-12-1-10000000
χ5166-36-3-3-6-36-3-33-6332-20000-12-1-11-21100000000000000000000−i3i30−i3i30−i3i3i3−i30i3−i30i3−i30000000
χ5266-36-3-3-6-36-3-33-6332-20000-12-1-11-21100000000000000000000i3−i30i3−i30i3−i3−i3i30−i3i30−i3i30000000
χ5366-3-36-36-3-36-3-3-36-3-2-2000011-2111-210000000000000000002-2-1-1-12-1-1-12111-2111-20000000
χ5466-3-36-36-3-36-3-3-36-3-2-2000011-2111-21000000000000000000-22111-2111-2-1-1-12-1-1-120000000
χ5566-3-36-3-6-3-36-333-632-20000-1-12-111-2100000000000000000000−i3i3i30−i3−i3i30i3−i3−i30i3i3−i300000000
χ5666-3-36-3-6-3-36-333-632-20000-1-12-111-2100000000000000000000i3−i3−i30i3i3−i30−i3i3i30−i3−i3i300000000
χ5766-3-3-366-3-3-36-3-3-36-2-20000111-2111-20000000000000000002-2-1-1-1-12-12-11111-21-210000000
χ5866-3-3-366-3-3-36-3-3-36-2-20000111-2111-2000000000000000000-221111-21-21-1-1-1-12-12-10000000
χ5966-3-3-36-6-3-3-36333-62-20000-1-1-12111-200000000000000000000−i3i3−i3i30i30−i3i3−i3i3−i30−i30i30000000
χ6066-3-3-36-6-3-3-36333-62-20000-1-1-12111-200000000000000000000i3−i3i3−i30−i30i3−i3i3−i3i30i30−i30000000
χ618-88-4-4-40-84440000002-223−23000000002-1-1-1-211123−23−33−33−33000000000000000000000000000
χ628-88-4-4-40-84440000002-2−2323000000002-1-1-1-2111−23233−33−33−3000000000000000000000000000
χ638-88-4-4-40-8444000000-440000000000-42224-2-2-200000000000000000000000000000000000
χ648-8-48-4-404-8440000002-223−2300000000-12-1-11-211−3323−23−33−33000000000000000000000000000
χ658-8-48-4-404-8440000002-2−232300000000-12-1-11-2113−3−23233−33−3000000000000000000000000000
χ668-8-48-4-404-844000000-4400000000002-422-24-2-200000000000000000000000000000000000
χ678-8-4-48-4044-840000002-223−2300000000-1-12-111-21−33−3323−23−33000000000000000000000000000
χ688-8-4-48-4044-840000002-2−232300000000-1-12-111-213−33−3−23233−3000000000000000000000000000
χ698-8-4-48-4044-84000000-44000000000022-42-2-24-200000000000000000000000000000000000
χ708-8-4-4-480444-80000002-223−2300000000-1-1-12111-2−33−33−3323−23000000000000000000000000000
χ718-8-4-4-480444-80000002-2−232300000000-1-1-12111-23−33−33−3−2323000000000000000000000000000
χ728-8-4-4-480444-8000000-440000000000222-4-2-2-2400000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.