Finite Group Databasebeta

← Group #13151923

Character table — Group #13151923

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11222222222224444446666121212121212121212121212121212121212181818181818242424242424363636363636363636363636363636363636363636363636363636363636363636
order1222234444612126661212123366366666661212121212121212121288242424246661212122222224466666666666688812121212242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111
χ311111111111111111111111111111111111111111-1-1-1-1-1-1111111111-1-1-11-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1111-11-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-1
χ5111-1-111-1-111111-1-11-1-11111111-1-1-1-111111-1-1-1-1111111111-1-11-1-111-111-1-1-11111-1-11111-1-11-1-1-1-1-1-111-1-1-1-1
χ6111-1-111-1-111111-1-11-1-11111111-1-1-1-111111-1-1-1-1111111111-1-11-1-1-1-11-1-1111-1-1-1-111-1-1-1-1111-1-1111111-1-1-1-1
χ7111-1-111-1-111111-1-11-1-11111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11-1-11-1-111-1-1-11-111111-1-1-1-1-1-111-111-1-111-1-11111
χ8111-1-111-1-111111-1-11-1-11111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11-1-11-1-1-1-1111-11-1-1-1-1-1111111-1-1-11111-1-1-1-11111
χ911-11-11-11-11111-11-1-11-111111-1-111-1-1111-1-111-1-111111111-11-1-11-11-111-11-1-111-1-11111-1-111-11-1-1-1-1-1-1-111-1-1
χ1011-11-11-11-11111-11-1-11-111111-1-111-1-1111-1-111-1-111111111-11-1-11-1-11-1-11-111-1-111-1-1-1-111-1-1-11-11111-1-111-1-1
χ1111-11-11-11-11111-11-1-11-111111-1-111-1-1111-1-111-1-111-1-1-1-1-1-1-11-1-11-11-11-11-1-1111-1-111-1-111-1-11-11-1-11111-1-111
χ1211-11-11-11-11111-11-1-11-111111-1-111-1-1111-1-111-1-111-1-1-1-1-1-1-11-1-11-1-11-11-111-1-1-111-1-111-1-1111-1111-1-111-1-111
χ1311-1-111-1-111111-1-11-1-1111111-1-1-1-111111-1-1-1-11111111111-1-11-1-111-1-11-1-11111-1-1-1-111-1-1-1-1-1-111111-1-1-1-111
χ1411-1-111-1-111111-1-11-1-1111111-1-1-1-111111-1-1-1-11111111111-1-11-1-11-111-111-1-1-1-11111-1-11111-1-11-1-1-1-1-1-1-1-111
χ1511-1-111-1-111111-1-11-1-1111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1111-111-1-1-1-1-1-1111111-111-1-11111-1-1
χ1611-1-111-1-111111-1-11-1-1111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1111-1-1-11-1-1111111-1-1-1-111-1-1-1111111-1-1
χ1722222222222222222222-12-1-12-12-12-1-12-12-12-12-1-1-1000000-1-1-1-1-1-100022202000000-1-1-1-1-1-100000-1-1000000
χ1822222222222222222222-12-1-12-12-12-1-12-12-12-12-1-1-1000000-1-1-1-1-1-1000-2-2-20-20000001111110000011000000
χ192222222222222222222-12-12-1-12-12-12-1-12-12-12-12-1-1000000-1-1-1-1-1-122200020-1-1-1-1-1-1000000000-1-100000000
χ202222222222222222222-12-12-1-12-12-12-1-12-12-12-12-1-1000000-1-1-1-1-1-1-2-2-2000-201111110000000001100000000
χ212222-22-2-22-22-2-222-2-2-22222222222-2-22-2-2-2-2-2-222-2-200000022-2-2-22000000000000000000000000000000000
χ222222-22-2-22-22-2-222-2-2-222-12-1-12-12-1-21-1-21-21-212-111000000-1-1111-100000000000000−i3i3−i3i3−i3i300000−i3i3000000
χ232222-22-2-22-22-2-222-2-2-222-12-1-12-12-1-21-1-21-21-212-111000000-1-1111-100000000000000i3−i3i3−i3i3−i300000i3−i3000000
χ242222-22-2-22-22-2-222-2-2-22-12-12-1-12-121-2-11-21-21-2-1211000000-1-1111-100000000−i3i3−i3i3−i3i3000000000−i3i300000000
χ252222-22-2-22-22-2-222-2-2-22-12-12-1-12-121-2-11-21-21-2-1211000000-1-1111-100000000i3−i3i3−i3i3−i3000000000i3−i300000000
χ26222-222-22-2-22-2-22-22-22-22222222-2-2222-2-2-2-222-2-2-2-20000002-22-22-2000000000000000000000000000000000
χ27222-222-22-2-22-2-22-22-22-22-12-1-12-1-212-1-1-21-212-1-2111000000-11-11-1100000000000000−i3i3−i3i3i3−i300000i3−i3000000
χ28222-222-22-2-22-2-22-22-22-22-12-1-12-1-212-1-1-21-212-1-2111000000-11-11-1100000000000000i3−i3i3−i3−i3i300000−i3i3000000
χ29222-222-22-2-22-2-22-22-22-2-12-12-1-121-2-12-11-21-2-121-211000000-11-11-1100000000−i3i3−i3i3i3−i3000000000i3−i300000000
χ30222-222-22-2-22-2-22-22-22-2-12-12-1-121-2-12-11-21-2-121-211000000-11-11-1100000000i3−i3i3−i3−i3i3000000000−i3i300000000
χ31222-2-222-2-222222-2-22-2-22-12-1-12-1-21-21-12-12-1-21-21-1-1000000-111-11100022-20-2000000-1-1-1-1110000011000000
χ32222-2-222-2-222222-2-22-2-22-12-1-12-1-21-21-12-12-1-21-21-1-1000000-111-111000-2-22020000001111-1-100000-1-1000000
χ33222-2-222-2-222222-2-22-2-2-12-12-1-121-21-2-1-12-121-21-2-1-1000000-111-11122-2000-20-1-1-1-1110000000001100000000
χ34222-2-222-2-222222-2-22-2-2-12-12-1-121-21-2-1-12-121-21-2-1-1000000-111-111-2-22000201111-1-1000000000-1-100000000
χ3522-22222-2-2-22-2-2-2222-2-222222-2-222222-2-222-2-2-2-2-2-2000000-2222-2-2000000000000000000000000000000000
χ3622-22222-2-2-22-2-2-2222-2-22-12-1-1-212-12-1-1-212-1-21-21110000001-1-1-11100000000000000−i3i3i3−i3−i3i300000i3−i3000000
χ3722-22222-2-2-22-2-2-2222-2-22-12-1-1-212-12-1-1-212-1-21-21110000001-1-1-11100000000000000i3−i3−i3i3i3−i300000−i3i3000000
χ3822-22222-2-2-22-2-2-2222-2-2-12-12-11-2-12-12-11-2-121-21-2110000001-1-1-11100000000−i3i3i3−i3−i3i3000000000i3−i300000000
χ3922-22222-2-2-22-2-2-2222-2-2-12-12-11-2-12-12-11-2-121-21-2110000001-1-1-11100000000i3−i3−i3i3i3−i3000000000−i3i300000000
χ4022-22-22-22-22222-22-2-22-22-12-1-1-212-1-21-12-1-212-1-21-1-10000001-111-110002-220-2000000-1-111-1-10000011000000
χ4122-22-22-22-22222-22-2-22-22-12-1-1-212-1-21-12-1-212-1-21-1-10000001-111-11000-22-20200000011-1-11100000-1-1000000
χ4222-22-22-22-22222-22-2-22-2-12-12-11-2-121-2-1-121-2-121-2-1-10000001-111-112-22000-20-1-111-1-10000000001100000000
χ4322-22-22-22-22222-22-2-22-2-12-12-11-2-121-2-1-121-2-121-2-1-10000001-111-11-22-20002011-1-111000000000-1-100000000
χ4422-2-222-2-222222-2-22-2-222-12-1-1-21-212-1-12-1-21-212-1-1-100000011-111-10002-2-202000000-1-1111100000-1-1000000
χ4522-2-222-2-222222-2-22-2-222-12-1-1-21-212-1-12-1-21-212-1-1-100000011-111-1000-2220-200000011-1-1-1-10000011000000
χ4622-2-222-2-222222-2-22-2-22-12-12-11-21-2-12-1-121-21-2-12-1-100000011-111-12-2-200020-1-11111000000000-1-100000000
χ4722-2-222-2-222222-2-22-2-22-12-12-11-21-2-12-1-121-21-2-12-1-100000011-111-1-222000-2011-1-1-1-10000000001100000000
χ4822-2-2-22222-22-2-2-2-2-222222222-2-2-2-2-2-22-2-2222222-2-2000000-2-2-2222000000000000000000000000000000000
χ4922-2-2-22222-22-2-2-2-2-22222-12-1-1-21-21-21-1-212-12-12-111000000111-1-1-100000000000000−i3i3i3−i3i3−i300000−i3i3000000
χ5022-2-2-22222-22-2-2-2-2-22222-12-1-1-21-21-21-1-212-12-12-111000000111-1-1-100000000000000i3−i3−i3i3−i3i300000i3−i3000000
χ5122-2-2-22222-22-2-2-2-2-2222-12-12-11-21-21-2-11-2-12-12-1211000000111-1-1-100000000−i3i3i3−i3i3−i3000000000−i3i300000000
χ5222-2-2-22222-22-2-2-2-2-2222-12-12-11-21-21-2-11-2-12-12-1211000000111-1-1-100000000i3−i3−i3i3−i3i3000000000i3−i300000000
χ534444444444444444444-2-2-2-21-2-2-2-2-2-21-2-2-2-2-2-2-2-211000000111111000000000000000000000000000000000
χ544444-44-4-44-44-4-444-4-4-44-2-2-2-21-2-2-2-2221222222-2-2-1-100000011-1-1-11000000000000000000000000000000000
χ55444-444-44-4-44-4-44-44-44-4-2-2-2-21-2-222-2-212222-2-222-1-10000001-11-11-1000000000000000000000000000000000
χ56444-4-444-4-444444-4-44-4-4-2-2-2-21-2-222221-2-2-2-22222110000001-1-11-1-1000000000000000000000000000000000
χ5744-44444-4-4-44-4-4-4444-4-4-2-2-2-2122-2-2-2-2122-2-22222-1-1000000-1111-1-1000000000000000000000000000000000
χ5844-44-44-44-44444-44-4-44-4-2-2-2-2122-2-2221-2-222-2-22211000000-11-1-11-1000000000000000000000000000000000
χ5944-4-444-4-444444-4-44-4-44-2-2-2-212222-2-21-2-22222-2-211000000-1-11-1-11000000000000000000000000000000000
χ6044-4-4-44444-44-4-4-4-4-4444-2-2-2-21222222122-2-2-2-2-2-2-1-1000000-1-1-1111000000000000000000000000000000000
χ614-400040000-40000000044-4-44000000-4000000000022−222222−22−22000000000000000000000000000000000000000
χ624-400040000-40000000044-4-44000000-40000000000−2222−22−222222000000000000000000000000000000000000000
χ6366666-36666-3-3-3-3-3-3-3-3-3000000000000000000000022-1-1-1-1000000000000000000000000002220000-1-1-1-1-1-1
χ6466666-36666-3-3-3-3-3-3-3-3-30000000000000000000000-2-2111100000000000000000000000000-2-2-20000111111
χ656666-6-3-6-66-6-333-3-3333-30000000000000000000000003−33−30000000000000000000000000000000003−33−33−3
χ666666-6-3-6-66-6-333-3-3333-3000000000000000000000000−33−33000000000000000000000000000000000−33−33−33
χ67666-66-3-66-6-6-333-33-33-330000000000000000000000003−33−30000000000000000000000000000000003−3−33−33
χ68666-66-3-66-6-6-333-33-33-33000000000000000000000000−33−33000000000000000000000000000000000−333−33−3
χ69666-6-6-36-6-66-3-3-3-333-333000000000000000000000022-1-1-1-1000000000000000000000000002-2-20000-1-11111
χ70666-6-6-36-6-66-3-3-3-333-3330000000000000000000000-2-2111100000000000000000000000000-222000011-1-1-1-1
χ7166-666-36-6-6-6-3333-3-3-3330000000000000000000000003−33−3000000000000000000000000000000000−333−3−33
χ7266-666-36-6-6-6-3333-3-3-333000000000000000000000000−33−330000000000000000000000000000000003−3−333−3
χ7366-66-6-3-66-66-3-3-33-333-33000000000000000000000022-1-1-1-100000000000000000000000000-22-2000011-1-111
χ7466-66-6-3-66-66-3-3-33-333-330000000000000000000000-2-21111000000000000000000000000002-220000-1-111-1-1
χ7566-6-66-3-6-666-3-3-333-333-3000000000000000000000022-1-1-1-100000000000000000000000000-2-2200001111-1-1
χ7666-6-66-3-6-666-3-3-333-333-30000000000000000000000-2-211110000000000000000000000000022-20000-1-1-1-111
χ7766-6-6-6-3666-6-333333-3-3-30000000000000000000000003−33−3000000000000000000000000000000000−33−333−3
χ7866-6-6-6-3666-6-333333-3-3-3000000000000000000000000−33−330000000000000000000000000000000003−33−3−33
χ798-800080000-8000000008-4-84-400000040000000000000000000000000000000000000000000000000000000
χ808-800080000-800000000-484-8-400000040000000000000000000000000000000000000000000000000000000
χ818-800080000-800000000-4-4442000000-2000000006i−6i000000000000000000000000000000000000000000000
χ828-800080000-800000000-4-4442000000-200000000−6i6i000000000000000000000000000000000000000000000
χ8312-12000-60000663−63000000000000000000000000000022−222ζ5−2ζ72ζ13−2ζ23−2ζ5+2ζ7−2ζ13+2ζ23000000000000000000000000000000000000000
χ8412-12000-60000663−630000000000000000000000000000−2222−2ζ5+2ζ7−2ζ13+2ζ232ζ5−2ζ72ζ13−2ζ23000000000000000000000000000000000000000
χ8512-12000-600006−6363000000000000000000000000000022−222ζ13−2ζ232ζ5−2ζ7−2ζ13+2ζ23−2ζ5+2ζ7000000000000000000000000000000000000000
χ8612-12000-600006−63630000000000000000000000000000−2222−2ζ13+2ζ23−2ζ5+2ζ72ζ13−2ζ232ζ5−2ζ7000000000000000000000000000000000000000

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