Finite Group Databasebeta

← Group #13167591

Character table — Group #13167591

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size112224444444444888888888888888888888181836363636363636363672727272727272727272727272727272
order12236233666666633666666666666666666622224444466444661212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-111-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-11-1-111111-1-1-1-11-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-11-1-1-1-111-111-1-11-1-1-1-1-1-11111
χ511111-11111-1-111111-1-1-11-1111111-1-1-1-1-1-1-1-1111-1-11-11111-11-11-1-11-111-1-111-1-1
χ611111-11111-1-111111-1-1-11-1111111-1-1-1-1-1-1-1-1111-1-11-1-1-1111-111-1-11-1-1-111-1-111
χ711111-11111-1-111111-1-1-11-1111111-1-1-1-1-1-1-1-111-11-1-111111-1-11-11-1-1111-1-1-1-111
χ811111-11111-1-111111-1-1-11-1111111-1-1-1-1-1-1-1-111-11-1-11-1-11111-1-11-1-11-1-11111-1-1
χ9222222222222222222222222222222222222-2-200-20000-2-200000-20000000000
χ1022222-22222-2-222222-2-2-22-2222222-2-2-2-2-2-2-2-2-2-20020000-2-20000020000000000
χ11222-1-1222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1220020000-1-102200-1000000-1-1-1-1
χ12222-1-1222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1220020000-1-10-2-200-10000001111
χ13222-1-1222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-20000110000010000003−33−3
χ14222-1-1222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2000011000001000000−33−33
χ15222-1-1-222-12-2-2222-1-11-2-22-2-1-1-1-1-1-1111111112200-20000-1-102-2001000000-1-111
χ16222-1-1-222-12-2-2222-1-11-2-22-2-1-1-1-1-1-1111111112200-20000-1-10-2200100000011-1-1
χ17222-1-1-222-12-2-2222-1-11-2-22-2-1-1-1-1-1-111111111-2-200200001100000-10000003−3−33
χ18222-1-1-222-12-2-2222-1-11-2-22-2-1-1-1-1-1-111111111-2-200200001100000-1000000−333−3
χ1922-222022-2-2002-2222000-2022-2-2-2-2000000002-20200-2002-20000200-200000000
χ2022-222022-2-2002-2222000-2022-2-2-2-2000000002-20-2002002-20000-200200000000
χ2122-222022-2-2002-2222000-2022-2-2-2-200000000-22200-2000-22000200-2000000000
χ2222-222022-2-2002-2222000-2022-2-2-2-200000000-22-2002000-22000-2002000000000
χ234444441-241-2-211-21-2411-2-21-211-2-21111-2-2-2-20000000220020000000-1-1-1-10000
χ244444441-241-2-211-21-2411-2-21-211-2-21111-2-2-2-20000000-2-200-2000000011110000
χ25444444-214-211-2-21-214-2-211-21-2-211-2-2-2-2111100220220000000-1-10-1-100000000
χ26444444-214-211-2-21-214-2-211-21-2-211-2-2-2-2111100-2-20-2-200000001101100000000
χ2744444-41-2412211-21-2-4-1-1-221-211-2-2-1-1-1-1222200000002200-20000000-1-1110000
χ2844444-41-2412211-21-2-4-1-1-221-211-2-2-1-1-1-122220000000-2-2002000000011-1-10000
χ2944444-4-214-2-1-1-2-21-21-4221-1-21-2-2112222-1-1-1-1002-202-20000000-110-1100000000
χ3044444-4-214-2-1-1-2-21-21-4221-1-21-2-2112222-1-1-1-100-220-2200000001-101-100000000
χ3144-4440-21-4233-221-21000-1-3-2122-1-1000033-3-3002-20-220000000-1101-100000000
χ3244-4440-21-4233-221-21000-1-3-2122-1-1000033-3-300-2202-200000001-10-1100000000
χ3344-4440-21-42-3-3-221-21000-13-2122-1-10000-3-33300220-2-20000000-1-101100000000
χ3444-4440-21-42-3-3-221-21000-13-2122-1-10000-3-33300-2-20220000000110-1-100000000
χ3544-4-2-20442-4004-44-2-2000-40-2-22222000000004-40000000-220000000000000000
χ3644-4-2-20442-4004-44-2-2000-40-2-2222200000000-4400000002-20000000000000000
χ374-404-401-20-3−2i32i3-1321-20−i3i300-123-300−i3−i3i3i3−2i32i30000000002i−2i0000000000i−i3−30000
χ384-404-401-20-3−2i32i3-1321-20−i3i300-123-300−i3−i3i3i3−2i32i3000000000−2i2i0000000000−ii−330000
χ394-404-401-20-32i3−2i3-1321-20i3−i300-123-300i3i3−i3−i32i3−2i30000000002i−2i0000000000i−i−330000
χ404-404-401-20-32i3−2i3-1321-20i3−i300-123-300i3i3−i3−i32i3−2i3000000000−2i2i0000000000−ii3−30000
χ414-404-40440000-40-44400000-4-400000000000000000002i−2i0000000000−2i2i000000
χ424-404-40440000-40-44400000-4-40000000000000000000−2i2i00000000002i−2i000000
χ43888-4-482-4-42-4-422-4-12-422-4-4-12-1-122-1-1-1-12222000000000000000000000000000
χ44888-4-48-42-4-422-4-422-1-4-4-4222-122-1-12222-1-1-1-1000000000000000000000000000
χ45888-4-4-82-4-424422-4-124-2-2-44-12-1-1221111-2-2-2-2000000000000000000000000000
χ46888-4-4-8-42-4-4-2-2-4-422-14442-22-122-1-1-2-2-2-21111000000000000000000000000000
χ4788-88802-4-8-2002-2-42-4000402-4-2-24400000000000000000000000000000000000
χ4888-8-4-402-44-2002-2-4-1200040-1211-2-2−3i33i3−3i33i30000000000000000000000000000000
χ4988-8-4-402-44-2002-2-4-1200040-1211-2-23i3−3i33i3−3i30000000000000000000000000000000
χ5088-8-4-40-424466-4422-1000-2-62-1-2-2110000-3-333000000000000000000000000000
χ5188-8-4-40-4244-6-6-4422-1000-262-1-2-211000033-3-3000000000000000000000000000
χ528-808-802-40600-2-642-400000-24-660000000000000000000000000000000000000
χ538-808-80-4200−2i32i340-2-4202i3−2i3004-200002i32i3−2i3−2i3−2i32i300000000000000000000000000000
χ548-808-80-42002i3−2i340-2-420−2i32i3004-20000−2i3−2i32i32i32i3−2i300000000000000000000000000000
χ558-80-4402-40600-2-64-12000001-23-3003-3-33006-6000000000000000000000000000
χ568-80-4402-40600-2-64-12000001-23-300-333-300-66000000000000000000000000000
χ578-80-4402-40-6−4i34i3-264-120−2i32i3001-2-3300i3i3−i3−i32i3−2i300000000000000000000000000000
χ588-80-4402-40-64i3−4i3-264-1202i3−2i3001-2-3300−i3−i3i3i3−2i32i300000000000000000000000000000
χ598-80-440880000-80-8-4-40000044000000000000000000000000000000000000000
χ608-80-440-4200−2i32i340-22-102i3−2i300-2100−3i33i33−i3−3−i3−3+i33+i3i3−i3-33000000000000000000000000000
χ618-80-440-4200−2i32i340-22-102i3−2i300-21003i3−3i3−3−i33−i33+i3−3+i3i3−i33-3000000000000000000000000000
χ628-80-440-42002i3−2i340-22-10−2i32i300-2100−3i33i3−3+i33+i33−i3−3−i3−i3i33-3000000000000000000000000000
χ638-80-440-42002i3−2i340-22-10−2i32i300-21003i3−3i33+i3−3+i3−3−i33−i3−i3i3-33000000000000000000000000000

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