Finite Group Databasebeta

← Group #13167528

Character table — Group #13167528

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size112224444444444888888888888888888888181836363636363636363672727272727272727272727272727272
order122363346666612123366666661212121212121212121212124422444441212466881212121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-111-111-1-11-1-111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-11-1-111111-1-1-1-1111-1-111-1-1-1-1
χ411111111111111111111111111111111111111-1-11-1-1-1-111-1-1-1111-1-1-1-1-1-11111
χ51111111-111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-11111-11-11-1-1111-1-1-111-1-1
χ61111111-111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-11111-1-11-1-1-11-111-1-111
χ71111111-111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111-1-11-11-111-11-1-1-1-111
χ81111111-111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11-1-1111-111-1-1-1-1-111111-1-1
χ9222222222222222222222222222222222222-2-200-20000-2-200000-20000000000
χ102222222-222222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20020000-2-20000020000000000
χ11222-1-1222-1222222-1-12-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1220020000-1-100022-1000000-1-1-1-1
χ12222-1-1222-1222222-1-12-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1220020000-1-1000-2-2-10000001111
χ13222-1-1222-1222222-1-12-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-200-20000110000010000003−33−3
χ14222-1-1222-1222222-1-12-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-200-2000011000001000000−33−33
χ15222-1-122-2-12222-2-2-1-12-1-1-1-1-1-11-2-2-2111111112200-20000-1-10002-21000000-1-111
χ16222-1-122-2-12222-2-2-1-12-1-1-1-1-1-11-2-2-2111111112200-20000-1-1000-22100000011-1-1
χ17222-1-122-2-12222-2-2-1-12-1-1-1-1-1-11-2-2-211111111-2-200200001100000-10000003−3−33
χ18222-1-122-2-12222-2-2-1-12-1-1-1-1-1-11-2-2-211111111-2-200200001100000-1000000−333−3
χ1922-222220-2-2-2220022-2-2-2-2-2220000000000002-20200-2002-2002000000-2000000
χ2022-222220-2-2-2220022-2-2-2-2-2220000000000002-20-2002002-200-20000002000000
χ2122-222220-2-2-2220022-2-2-2-2-222000000000000-22200-2000-2202000000-20000000
χ2222-222220-2-2-2220022-2-2-2-2-222000000000000-22-2002000-220-200000020000000
χ23444441-244111-2-2-21-2-211-2-21-2411-21111-2-2-2-200000002200200000-1-100-1-10000
χ24444441-244111-2-2-21-2-211-2-21-2411-21111-2-2-2-20000000-2-200-2000001100110000
χ25444441-2-44111-2221-2-211-2-21-2-4-1-12-1-1-1-1222200000002200-200000-1-100110000
χ26444441-2-44111-2221-2-211-2-21-2-4-1-12-1-1-1-122220000000-2-2002000001100-1-10000
χ2744444-2144-2-2-2111-211-2-211-214-2-21-2-2-2-21111002202200000-1-100000-1-1000000
χ2844444-2144-2-2-2111-211-2-211-214-2-21-2-2-2-2111100-2-20-2-200000110000011000000
χ2944444-21-44-2-2-21-1-1-211-2-211-21-422-12222-1-1-1-1002-202-200000-1100000-11000000
χ3044444-21-44-2-2-21-1-1-211-2-211-21-422-12222-1-1-1-100-220-22000001-1000001-1000000
χ3144-444-210-422-2133-21-122-1-1-21000-3000033-3-300220-2-200000-1-10000011000000
χ3244-444-210-422-2133-21-122-1-1-21000-3000033-3-300-2-2022000001100000-1-1000000
χ3344-444-210-422-21-3-3-21-122-1-1-2100030000-3-333002-20-2200000-11000001-1000000
χ3444-444-210-422-21-3-3-21-122-1-1-2100030000-3-33300-2202-2000001-100000-11000000
χ3544-4-2-24402-4-44400-2-2-42222-2-20000000000004-40000000-220000000000000000
χ3644-4-2-24402-4-44400-2-2-42222-2-2000000000000-4400000002-20000000000000000
χ374-404-41-2003-3-1223−231-203-300-1203−3033−3−323−230000000002-2000000001-1003−30000
χ384-404-41-2003-3-1223−231-203-300-1203−3033−3−323−23000000000-2200000000-1100−330000
χ394-404-41-2003-3-12−23231-203-300-120−330−3−333−23230000000002-2000000001-100−330000
χ404-404-41-2003-3-12−23231-203-300-120−330−3−333−2323000000000-2200000000-11003−30000
χ414-404-4440000-4-4004400000-4-400000000000000000002-200000000-2200000000
χ424-404-4440000-4-4004400000-4-40000000000000000000-22000000002-200000000
χ43888-4-42-48-4222-4-4-4-12-4-1-122-12-422-4-1-1-1-12222000000000000000000000000000
χ44888-4-42-4-8-4222-444-12-4-1-122-124-2-241111-2-2-2-2000000000000000000000000000
χ45888-4-4-428-4-4-4-42222-1222-1-12-1-4-4-422222-1-1-1-1000000000000000000000000000
χ46888-4-4-42-8-4-4-4-42-2-22-1222-1-12-1444-2-2-2-2-21111000000000000000000000000000
χ4788-8882-40-8-2-22-4002-44-2-2442-4000000000000000000000000000000000000000
χ4888-8-4-42-404-2-22-400-12411-2-2-120000−3i33i3−3i33i30000000000000000000000000000000
χ4988-8-4-42-404-2-22-400-12411-2-2-1200003i3−3i33i3−3i30000000000000000000000000000000
χ5088-8-4-4-420444-42662-1-2-2-2112-1000-60000-3-333000000000000000000000000000
χ5188-8-4-4-420444-42-6-62-1-2-2-2112-10006000033-3-3000000000000000000000000000
χ528-808-82-400-66-24002-40-6600-24000000000000000000000000000000000000000
χ538-808-8-4200004-223−23-42000004-20−23230−23−23232323−2300000000000000000000000000000
χ548-808-8-4200004-2−2323-42000004-2023−2302323−23−23−232300000000000000000000000000000
χ558-80-442-4006-6-2443−43-120-33001-2023−230−3−333−232300000000000000000000000000000
χ568-80-442-4006-6-24−4343-120-33001-20−2323033−3−323−2300000000000000000000000000000
χ578-80-442-400-66-2400-1203-3001-200003i−3i−3i3i006i−6i000000000000000000000000000
χ588-80-442-400-66-2400-1203-3001-20000−3i3i3i−3i00−6i6i000000000000000000000000000
χ598-80-44880000-8-800-4-40000044000000000000000000000000000000000000000
χ608-80-44-4200004-223−232-1000−3i33i3-210−23230−4ζ7−2ζ112ζ7+4ζ114ζ7+2ζ11−2ζ7−4ζ11−33−3i3i000000000000000000000000000
χ618-80-44-4200004-223−232-10003i3−3i3-210−232302ζ7+4ζ11−4ζ7−2ζ11−2ζ7−4ζ114ζ7+2ζ11−333i−3i000000000000000000000000000
χ628-80-44-4200004-2−23232-1000−3i33i3-21023−2304ζ7+2ζ11−2ζ7−4ζ11−4ζ7−2ζ112ζ7+4ζ113−33i−3i000000000000000000000000000
χ638-80-44-4200004-2−23232-10003i3−3i3-21023−230−2ζ7−4ζ114ζ7+2ζ112ζ7+4ζ11−4ζ7−2ζ113−3−3i3i000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.