Finite Group Databasebeta

← Group #13167215

Character table — Group #13167215

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112224444444444444444444488888888888888881212121212121212121212121818242424242424242424242424363636363636367272727272216216
order12236333346666666121212121212121236666661212121212121212122244666612121212446666661212121212124441212121241212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-111
χ5111111111-11111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111111-1-1-1111-1-1-1-11111-1-1-111-1-11-1
χ6111111111-11111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111111-1-1-1111-1-1-1-1-1-111-1-11-1-111-11
χ7111111111-11111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1-1111-1-1-1111-11111-1-1-111-1-1-11
χ8111111111-11111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1-1111-1-1-1111-1-1-111-1-11-1-1111-1
χ922222222222222222222222222222222222222222000000000000-2-2000000000000-200-2-2-2-20000000
χ10222222222-22222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2000000000000-2-2000000000000200-2-2220000000
χ11222-1-122-1-12-122-1-122-1-122-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-10000−i3i3−i3i3−i3i3−i3i3-2-20−i3i30−i3i30−i3i30−i3i3-20011110000000
χ12222-1-122-1-12-122-1-122-1-122-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-10000i3−i3i3−i3i3−i3i3−i3-2-20i3−i30i3−i30i3−i30i3−i3-20011110000000
χ13222-1-122-1-12-122-1-122-1-122-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-12-1-12-1-12-1-1200-1-1-1-10000000
χ14222-1-122-1-12-122-1-122-1-122-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-1-2-2-2-21111111122-211-211-211-211200-1-1-1-10000000
χ15222-1-122-1-1-2-122-1-12211-2-21111-12-1-1-1-1-1-211-2-211110000−i3i3i3−i3−i3i3i3−i3-2-20−i3i30i3−i30−i3i30i3−i320011-1-10000000
χ16222-1-122-1-1-2-122-1-12211-2-21111-12-1-1-1-1-1-211-2-211110000i3−i3−i3i3i3−i3−i3i3-2-20i3−i30−i3i30i3−i30−i3i320011-1-10000000
χ17222-1-122-1-1-2-122-1-12211-2-21111-12-1-1-1-1-1-211-2-211112-22-2-1-111-1-111222-1-1-2112-1-1-211-200-1-1110000000
χ18222-1-122-1-1-2-122-1-12211-2-21111-12-1-1-1-1-1-211-2-21111-22-2211-1-111-1-122-2112-1-1-2112-1-1-200-1-1110000000
χ1922-22222220-2-2222-22000000002-2-2-2-2-22000000000020-2002200-2-22-2000222000-2-2-20002-2000000000
χ2022-22222220-2-2222-22000000002-2-2-2-2-220000000000-20200-2-200222-2000-2-2-20002220002-2000000000
χ2122-22222220-2-2222-22000000002-2-2-2-2-2200000000020-202200-2-200-22222000-2-2-2000000-22000000000
χ2222-22222220-2-2222-22000000002-2-2-2-2-22000000000-2020-2-2002200-22-2-2-2000222000000-22000000000
χ2322-2-1-122-1-101-22-1-1-22−i3i300−i3−i3i3i3-1-21111-10−i3i300−i3−i3i3i3020-2−i3i3-1-1i3−i3112-20−i3i32-1-10i3−i3-211000-11−i3i30000000
χ2422-2-1-122-1-101-22-1-1-22−i3i300−i3−i3i3i3-1-21111-10−i3i300−i3−i3i3i30-202i3−i311−i3i3-1-12-20i3−i3-2110−i3i32-1-1000-11−i3i30000000
χ2522-2-1-122-1-101-22-1-1-22−i3i300−i3−i3i3i3-1-21111-10−i3i300−i3−i3i3i320-20-1-1−i3i311i3−i3-222-1-10−i3i3-2110i3−i30001-1i3−i30000000
χ2622-2-1-122-1-101-22-1-1-22−i3i300−i3−i3i3i3-1-21111-10−i3i300−i3−i3i3i3-202011i3−i3-1-1−i3i3-22-2110i3−i32-1-10−i3i30001-1i3−i30000000
χ2722-2-1-122-1-101-22-1-1-22i3−i300i3i3−i3−i3-1-21111-10i3−i300i3i3−i3−i3020-2i3−i3-1-1−i3i3112-20i3−i32-1-10−i3i3-211000-11i3−i30000000
χ2822-2-1-122-1-101-22-1-1-22i3−i300i3i3−i3−i3-1-21111-10i3−i300i3i3−i3−i30-202−i3i311i3−i3-1-12-20−i3i3-2110i3−i32-1-1000-11i3−i30000000
χ2922-2-1-122-1-101-22-1-1-22i3−i300i3i3−i3−i3-1-21111-10i3−i300i3i3−i3−i320-20-1-1i3−i311−i3i3-222-1-10i3−i3-2110−i3i30001-1−i3i30000000
χ3022-2-1-122-1-101-22-1-1-22i3−i300i3i3−i3−i3-1-21111-10i3−i300i3i3−i3−i3-202011−i3i3-1-1i3−i3-22-2110−i3i32-1-10i3−i30001-1−i3i30000000
χ31444441-2-2-2441-2-2-21144-2-2-2-2-2-21-2-2-2111-2-2-21111110000000000000000000000000002200002-1-1-1-100
χ32444441-2-2-2441-2-2-21144-2-2-2-2-2-21-2-2-2111-2-2-2111111000000000000000000000000000-2-20000-2111100
χ33444441-2-2-2-441-2-2-211-4-42222221-2-2-2111222-1-1-1-1-1-1000000000000000000000000000220000-2-1-11100
χ34444441-2-2-2-441-2-2-211-4-42222221-2-2-2111222-1-1-1-1-1-1000000000000000000000000000-2-20000211-1-100
χ3544444-211144-2111-2-244111111-2111-2-2-2111-2-2-2-2-2-222222222222200-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ3644444-211144-2111-2-244111111-2111-2-2-2111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20011111111111100000000000000
χ3744444-2111-44-2111-2-2-4-4-1-1-1-1-1-1-2111-2-2-2-1-1-12222222-22-222-2-222-2-200-1-1-1111-1-1-111100000000000000
χ3844444-2111-44-2111-2-2-4-4-1-1-1-1-1-1-2111-2-2-2-1-1-1222222-22-22-2-222-2-22200111-1-1-1111-1-1-100000000000000
χ39444-2-2-21−1−3i32−1+3i324-2-21−1−3i32−1+3i32-2-2-2-211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1+3i321111−1+3i32−1−3i32-2-211112222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i300-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i3200000000000000
χ40444-2-2-21−1−3i32−1+3i324-2-21−1−3i32−1+3i32-2-2-2-211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1+3i321111−1+3i32−1−3i32-2-21111-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i3001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ41444-2-2-21−1−3i32−1+3i32-4-2-21−1−3i32−1+3i32-2-222-1-11+3i321+3i321−3i321−3i3211−1−3i32−1+3i32111-11−3i321+3i3222-1-1-1-12-22-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i300-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i3200000000000000
χ42444-2-2-21−1−3i32−1+3i32-4-2-21−1−3i32−1+3i32-2-222-1-11+3i321+3i321−3i321−3i3211−1−3i32−1+3i32111-11−3i321+3i3222-1-1-1-1-22-221+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3001−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i3200000000000000
χ43444-2-2-21−1+3i32−1−3i324-2-21−1+3i32−1−3i32-2-2-2-211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1−3i321111−1−3i32−1+3i32-2-211112222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i300-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i3200000000000000
χ44444-2-2-21−1+3i32−1−3i324-2-21−1+3i32−1−3i32-2-2-2-211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1−3i321111−1−3i32−1+3i32-2-21111-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i3001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ45444-2-2-21−1+3i32−1−3i32-4-2-21−1+3i32−1−3i32-2-222-1-11−3i321−3i321+3i321+3i3211−1+3i32−1−3i32111-11+3i321−3i3222-1-1-1-12-22-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i300-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i3200000000000000
χ46444-2-2-21−1+3i32−1−3i32-4-2-21−1+3i32−1−3i32-2-222-1-11−3i321−3i321+3i321+3i3211−1+3i32−1−3i32111-11+3i321−3i3222-1-1-1-1-22-221−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3001−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i3200000000000000
χ4744-444-21110-421112-200333333-2-1-1-122-2-3-3-300000022-2-22222-2-2-2-200-1-1-1-1-1-111111100000000000000
χ4844-444-21110-421112-200333333-2-1-1-122-2-3-3-3000000-2-222-2-2-2-2222200111111-1-1-1-1-1-100000000000000
χ4944-444-21110-421112-200-3-3-3-3-3-3-2-1-1-122-23330000002-2-2222-2-2-2-22200-1-1-1111111-1-1-100000000000000
χ5044-444-21110-421112-200-3-3-3-3-3-3-2-1-1-122-2333000000-222-2-2-22222-2-200111-1-1-1-1-1-111100000000000000
χ5144-4-2-2-21−1−3i32−1+3i320221−1−3i32−1+3i322-2−2i32i333−3−i32−3−i32−3+i32−3+i321-11+3i321−3i32-1-11-33−i323+i3200i3i3−i3−i322-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ5244-4-2-2-21−1−3i32−1+3i320221−1−3i32−1+3i322-2−2i32i333−3−i32−3−i32−3+i32−3+i321-11+3i321−3i32-1-11-33−i323+i3200i3i3−i3−i3-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i3200000000000000
χ5344-4-2-2-21−1−3i32−1+3i320221−1−3i32−1+3i322-22i3−2i3-3-33+i323+i323−i323−i321-11+3i321−3i32-1-113−3+i32−3−i3200−i3−i3i3i32-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i300-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i3200000000000000
χ5444-4-2-2-21−1−3i32−1+3i320221−1−3i32−1+3i322-22i3−2i3-3-33+i323+i323−i323−i321-11+3i321−3i32-1-113−3+i32−3−i3200−i3−i3i3i3-222-21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i3001−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i3200000000000000
χ5544-4-2-2-21−1+3i32−1−3i320221−1+3i32−1−3i322-2−2i32i3-3-33−i323−i323+i323+i321-11−3i321+3i32-1-113−3−i32−3+i3200i3i3−i3−i32-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i300-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i3200000000000000
χ5644-4-2-2-21−1+3i32−1−3i320221−1+3i32−1−3i322-2−2i32i3-3-33−i323−i323+i323+i321-11−3i321+3i32-1-113−3−i32−3+i3200i3i3−i3−i3-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i3001−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i3200000000000000
χ5744-4-2-2-21−1+3i32−1−3i320221−1+3i32−1−3i322-22i3−2i333−3+i32−3+i32−3−i32−3−i321-11−3i321+3i32-1-11-33+i323−i3200−i3−i3i3i322-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ5844-4-2-2-21−1+3i32−1−3i320221−1+3i32−1−3i322-22i3−2i333−3+i32−3+i32−3−i32−3−i321-11−3i321+3i32-1-11-33+i323−i3200−i3−i3i3i3-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i3001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i3200000000000000
χ594-404-41-2-2-2003222-3-10023−2323−2323−2310003-3-10003−33−33−30000000000000000000000000002-2000001-13−300
χ604-404-41-2-2-2003222-3-10023−2323−2323−2310003-3-10003−33−33−3000000000000000000000000000-2200000-11−3300
χ614-404-41-2-2-2003222-3-100−2323−2323−232310003-3-1000−33−33−330000000000000000000000000002-2000001-1−3300
χ624-404-41-2-2-2003222-3-100−2323−2323−232310003-3-1000−33−33−33000000000000000000000000000-2200000-113−300
χ634-404-44444000-4-4-40-400000000400000-40000000000000000000000000000000000002-200000-220000
χ644-404-44444000-4-4-40-400000000400000-4000000000000000000000000000000000000-22000002-20000
χ65888-4-42-4228-42-42222-4-4-4-42222-1-422-1-1-1-42222-1-1-1-10000000000000000000000000000000000000000
χ66888-4-42-422-8-42-422224444-2-2-2-2-1-422-1-1-14-2-2-2-211110000000000000000000000000000000000000000
χ6788-8882-4-4-40-8-2-4-4-4-22000000002444-2-220000000000000000000000000000000000000000000000000
χ6888-8-4-42-42204-2-422-22−4i34i3002i32i3−2i3−2i3-14-2-211-102i3−2i300−i3−i3i3i30000000000000000000000000000000000000000
χ6988-8-4-42-42204-2-422-224i3−4i300−2i3−2i32i32i3-14-2-211-10−2i32i300i3i3−i3−i30000000000000000000000000000000000000000
χ708-808-82-4-4-400-64446-2000000002000-66-20000000000000000000000000000000000000000000000000
χ718-808-8-4222000-2-2-2040023−2323−2323−23-4000004000−2323−2323−23230000000000000000000000000000000000000000
χ728-808-8-4222000-2-2-20400−2323−2323−2323-400000400023−2323−2323−230000000000000000000000000000000000000000
χ738-80-442-4220064-2-2-6-20043−43−2323−2323-1000-33100023−23−33−330000000000000000000000000000000000000000
χ748-80-442-4220064-2-2-6-200−434323−2323−23-1000-331000−23233−33−30000000000000000000000000000000000000000
χ758-80-442-42200-64-2-26-200006i−6i−6i6i-10003-31000003i−3i−3i3i0000000000000000000000000000000000000000
χ768-80-442-42200-64-2-26-20000−6i6i6i−6i-10003-3100000−3i3i3i−3i0000000000000000000000000000000000000000
χ778-80-4488-4-4000-8440-800000000-40000040000000000000000000000000000000000000000000000000
χ788-80-44-42−1−3i3−1+3i3000-21+3i31−3i3040023−23−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ11200000-2000−23232ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ110000000000000000000000000000000000000000
χ798-80-44-42−1−3i3−1+3i3000-21+3i31−3i30400−23232ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ11200000-200023−23−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ110000000000000000000000000000000000000000
χ808-80-44-42−1+3i3−1−3i3000-21−3i31+3i3040023−234ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ11200000-2000−2323−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ110000000000000000000000000000000000000000
χ818-80-44-42−1+3i3−1−3i3000-21−3i31+3i30400−2323−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ11200000-200023−234ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ110000000000000000000000000000000000000000

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