Finite Group Databasebeta

← Group #13167015

Character table — Group #13167015

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122224444444444444444444888888888888888818181818242424242424242424242424242424242424363636363636363672727272108108108108
order122236663333466666666666612123666121212121212121212121212444444121212121212121212121212121212122244121212126612128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11-1-111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1
χ92222222222222222222222222222222222222222222-2-2-2-20000000000000000000000-2-2-2-200000000
χ10222222222222-2222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-222-20000000000000000000000-2-22200000000
χ112222-1-1-1-12-1-1222-1-122-1-122-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-122-1-1-1-10000-1-1-1-100000000
χ122222-1-1-1-12-1-1222-1-122-1-122-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-21111-2-21111-2-211110000-1-1-1-100000000
χ132222-1-1-1-12-1-1222-1-122-1-122-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i30000111100000000
χ142222-1-1-1-12-1-1222-1-122-1-122-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i30000111100000000
χ152222-1-1-1-12-1-12-22-1-122-1-122-1-1211-1-1-1-1-2-2-2-2111111112-2-222-2-1-11122-1-1-1-1-2-211110000-1-11100000000
χ162222-1-1-1-12-1-12-22-1-122-1-122-1-1211-1-1-1-1-2-2-2-2111111112-2-22-2211-1-1-2-2111122-1-1-1-10000-1-11100000000
χ172222-1-1-1-12-1-12-22-1-122-1-122-1-1211-1-1-1-1-2-2-2-211111111-222-200−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3000011-1-100000000
χ182222-1-1-1-12-1-12-22-1-122-1-122-1-1211-1-1-1-1-2-2-2-211111111-222-200i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3000011-1-100000000
χ192-22-22-22-2222202222-2-2-2-2-2-2-2-20022-2-2000000000000200-20000000000000000002-2002-2002-2000000
χ202-22-22-22-2222202222-2-2-2-2-2-2-2-20022-2-2000000000000200-2000000000000000000-22002-200-22000000
χ212-22-22-22-2222202222-2-2-2-2-2-2-2-20022-2-2000000000000-2002000000000000000000002i−2i-2200002i−2i0000
χ222-22-22-22-2222202222-2-2-2-2-2-2-2-20022-2-2000000000000-200200000000000000000000−2i2i-220000−2i2i0000
χ232-2-222-2-2222220-2-2-2-2-2-2-2-22222002-22-200000000000002-200000000000000000000000002-200002−22−2
χ242-2-222-2-2222220-2-2-2-2-2-2-2-22222002-22-200000000000002-200000000000000000000000002-20000−22−22
χ252-2-222-2-2222220-2-2-2-2-2-2-2-22222002-22-20000000000000-220000000000000000000000000-2200002−2−22
χ262-2-222-2-2222220-2-2-2-2-2-2-2-22222002-22-20000000000000-220000000000000000000000000-220000−222−2
χ2744444444111-24111-2111-2111-244-2-2-2-211-2-21111-2-2-2-20000222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2844444444111-24111-2111-2111-244-2-2-2-211-2-21111-2-2-2-20000-2-2-2-2-2-21111111111110000000000000000
χ2944444444111-2-4111-2111-2111-2-4-4-2-2-2-2-1-122-1-1-1-1222200002-222-2-2-1-1-1-1-1-11111110000000000000000
χ3044444444111-2-4111-2111-2111-2-4-4-2-2-2-2-1-122-1-1-1-122220000-22-2-222111111-1-1-1-1-1-10000000000000000
χ3144444444-2-2-214-2-2-21-2-2-21-2-2-21441111-2-211-2-2-2-21111000000000000000000000022220000-1-1-1-10000
χ3244444444-2-2-214-2-2-21-2-2-21-2-2-21441111-2-211-2-2-2-211110000000000000000000000-2-2-2-2000011110000
χ3344444444-2-2-21-4-2-2-21-2-2-21-2-2-21-4-4111122-1-12222-1-1-1-1000000000000000000000022-2-20000-1-1110000
χ3444444444-2-2-21-4-2-2-21-2-2-21-2-2-21-4-4111122-1-12222-1-1-1-10000000000000000000000-2-222000011-1-10000
χ354444-2-2-2-21−1−3i32−1+3i32-241−1−3i32−1+3i32-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2111111-2-2−1−3i32−1−3i32−1+3i32−1+3i321111000022−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i320000000000000000
χ364444-2-2-2-21−1−3i32−1+3i32-241−1−3i32−1+3i32-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2111111-2-2−1−3i32−1−3i32−1+3i32−1+3i3211110000-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000000000000000
χ374444-2-2-2-21−1−3i32−1+3i32-2-41−1−3i32−1+3i32-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2221111-1-1221+3i321+3i321−3i321−3i32-1-1-1-100002-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i320000000000000000
χ384444-2-2-2-21−1−3i32−1+3i32-2-41−1−3i32−1+3i32-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2221111-1-1221+3i321+3i321−3i321−3i32-1-1-1-10000-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i320000000000000000
χ394444-2-2-2-21−1+3i32−1−3i32-241−1+3i32−1−3i32-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-2111111-2-2−1+3i32−1+3i32−1−3i32−1−3i321111000022−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i320000000000000000
χ404444-2-2-2-21−1+3i32−1−3i32-241−1+3i32−1−3i32-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-2111111-2-2−1+3i32−1+3i32−1−3i32−1−3i3211110000-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i320000000000000000
χ414444-2-2-2-21−1+3i32−1−3i32-2-41−1+3i32−1−3i32-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2221111-1-1221−3i321−3i321+3i321+3i32-1-1-1-100002-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i320000000000000000
χ424444-2-2-2-21−1+3i32−1−3i32-2-41−1+3i32−1−3i32-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2221111-1-1221−3i321−3i321+3i321+3i32-1-1-1-10000-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i320000000000000000
χ4344-4-444-4-4111-20-1-1-12111-2-1-1-1200-222-23-3003-33-3000000000000003−33−33−33−33−33−30000000000000000
χ4444-4-444-4-4111-20-1-1-12111-2-1-1-1200-222-23-3003-33-300000000000000−33−33−33−33−33−330000000000000000
χ4544-4-444-4-4111-20-1-1-12111-2-1-1-1200-222-2-3300-33-33000000000000003−33−33−3−33−33−330000000000000000
χ4644-4-444-4-4111-20-1-1-12111-2-1-1-1200-222-2-3300-33-3300000000000000−33−33−333−33−33−30000000000000000
χ4744-4-444-4-444440-4-4-4-44444-4-4-4-4004-4-4400000000000000000000000000000000000000000000000000
χ4844-4-4-2-2221−1−3i32−1+3i32-20-11+3i321−3i3221−1−3i32−1+3i32-2-11+3i321−3i322−2i32i31-1-113-300−3−i323+i32−3+i323−i32−i3−i3i3i300000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000000000000
χ4944-4-4-2-2221−1−3i32−1+3i32-20-11+3i321−3i3221−1−3i32−1+3i32-2-11+3i321−3i322−2i32i31-1-113-300−3−i323+i32−3+i323−i32−i3−i3i3i30000000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000000000000
χ5044-4-4-2-2221−1−3i32−1+3i32-20-11+3i321−3i3221−1−3i32−1+3i32-2-11+3i321−3i3222i3−2i31-1-11-33003+i32−3−i323−i32−3+i32i3i3−i3−i300000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000000000000
χ5144-4-4-2-2221−1−3i32−1+3i32-20-11+3i321−3i3221−1−3i32−1+3i32-2-11+3i321−3i3222i3−2i31-1-11-33003+i32−3−i323−i32−3+i32i3i3−i3−i30000000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000000000000
χ5244-4-4-2-2221−1+3i32−1−3i32-20-11−3i321+3i3221−1+3i32−1−3i32-2-11−3i321+3i322−2i32i31-1-11-33003−i32−3+i323+i32−3−i32−i3−i3i3i300000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000000000000
χ5344-4-4-2-2221−1+3i32−1−3i32-20-11−3i321+3i3221−1+3i32−1−3i32-2-11−3i321+3i322−2i32i31-1-11-33003−i32−3+i323+i32−3−i32−i3−i3i3i30000000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000000000000
χ5444-4-4-2-2221−1+3i32−1−3i32-20-11−3i321+3i3221−1+3i32−1−3i32-2-11−3i321+3i3222i3−2i31-1-113-300−3+i323−i32−3−i323+i32i3i3−i3−i300000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000000000000
χ5544-4-4-2-2221−1+3i32−1−3i32-20-11−3i321+3i3221−1+3i32−1−3i32-2-11−3i321+3i3222i3−2i31-1-113-300−3+i323−i32−3−i323+i32i3i3−i3−i30000000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000000000000
χ5644-4-4-2-2224-2-240-422-44-2-24-422-4−2i32i3-222-20000−2i32i32i3−2i32i32i3−2i3−2i300000000000000000000000000000000000000
χ5744-4-4-2-2224-2-240-422-44-2-24-422-42i3−2i3-222-200002i3−2i3−2i32i3−2i3−2i32i32i300000000000000000000000000000000000000
χ584-44-44-44-4-2-2-210-2-2-21222-1222-10011-1-1003i−3i00003i−3i3i−3i00000000000000000000002-22i−2i0000-11−ii0000
χ594-44-44-44-4-2-2-210-2-2-21222-1222-10011-1-1003i−3i00003i−3i3i−3i0000000000000000000000-22−2i2i00001-1i−i0000
χ604-44-44-44-4-2-2-210-2-2-21222-1222-10011-1-100−3i3i0000−3i3i−3i3i00000000000000000000002-2−2i2i0000-11i−i0000
χ614-44-44-44-4-2-2-210-2-2-21222-1222-10011-1-100−3i3i0000−3i3i−3i3i0000000000000000000000-222i−2i00001-1−ii0000
χ624-44-4-22-224-2-2404-2-24-422-4-422-400-2-222000000000000400-40000000000000000000000-220000000000
χ634-44-4-22-224-2-2404-2-24-422-4-422-400-2-222000000000000-400400000000000000000000002-20000000000
χ644-4-44-222-24-2-240-422-4-422-44-2-2400-22-2200000000000004-40000000000000000000000000-2200000000
χ654-4-44-222-24-2-240-422-4-422-44-2-2400-22-220000000000000-4400000000000000000000000002-200000000
χ668888-4-4-4-4-42228-4222-4222-4222-4-4-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000
χ678888-4-4-4-4-4222-8-4222-4222-422244-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000
χ6888-8-888-8-8-4-4-420444-2-4-4-42444-2002-2-2200000000000000000000000000000000000000000000000000
χ6988-8-8-4-444-422204-2-2-2-42224-2-2-2−4i34i3-111-100002i3−2i3−2i32i3i3i3−i3−i300000000000000000000000000000000000000
χ7088-8-8-4-444-422204-2-2-2-42224-2-2-24i3−4i3-111-10000−2i32i32i3−2i3−i3−i3i3i300000000000000000000000000000000000000
χ718-88-88-88-8222-40222-4-2-2-24-2-2-2400-4-44400000000000000000000000000000000000000000000000000
χ728-88-8-44-442−1−3i3−1+3i3-402−1−3i3−1+3i3-4-21+3i31−3i34-21+3i31−3i340022-2-200000000000000000000000000000000000000000000000000
χ738-88-8-44-442−1+3i3−1−3i3-402−1+3i3−1−3i3-4-21−3i31+3i34-21−3i31+3i340022-2-200000000000000000000000000000000000000000000000000
χ748-88-8-44-44-42220-42224-2-2-24-2-2-200-1-111006i−6i0000−3i3i−3i3i00000000000000000000000000000000000000
χ758-88-8-44-44-42220-42224-2-2-24-2-2-200-1-11100−6i6i00003i−3i3i−3i00000000000000000000000000000000000000
χ768-8-888-8-88222-40-2-2-24-2-2-24222-400-44-4400000000000000000000000000000000000000000000000000
χ778-8-888-8-88-4-4-420444-2444-2-4-4-42002-22-200000000000000000000000000000000000000000000000000
χ788-8-88-444-42−1−3i3−1+3i3-40-21+3i31−3i34-21+3i31−3i342−1−3i3−1+3i3-4002-22-200000000000000000000000000000000000000000000000000
χ798-8-88-444-42−1+3i3−1−3i3-40-21−3i31+3i34-21−3i31+3i342−1+3i3−1−3i3-4002-22-200000000000000000000000000000000000000000000000000
χ808-8-88-444-4-422204-2-2-24-2-2-2-422200-11-110000000033−33−333300000000000000000000000000000000000000
χ818-8-88-444-4-422204-2-2-24-2-2-2-422200-11-1100000000−333333−3300000000000000000000000000000000000000

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