Finite Group Databasebeta

← Group #13167292

Character table — Group #13167292

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444444448888888888888812121212121212121212121218181818181818182424242424242424242424243636363636363636363636363636108108108108
order1222223666333366666666666666666636666666666666444412121212121212124444121212121212121212121212121212124444121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111-1-111111111-1-111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1
χ61111-1-111111111-1-111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ71111-1-111111111-1-111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111
χ81111-1-111111111-1-111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1
χ91-1-111-11-1-1111111-1111-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-111-1-1i−ii−iii−i−iii−i−i11-1-111-1-1iii−i−i−iiii−i−i−i1-11-11-111-1-111-1-1i−ii−i
χ101-1-111-11-1-1111111-1111-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-111-1-1i−ii−iii−i−iii−i−i11-1-111-1-1iii−i−i−iiii−i−i−i-11-111-1-1-111-1-111−ii−ii
χ111-1-111-11-1-1111111-1111-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-111-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−i−iiii−i−i−iiii1-11-11-111-1-111-1-1−ii−ii
χ121-1-111-11-1-1111111-1111-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-111-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−i−iiii−i−i−iiii-11-111-1-1-111-1-111i−ii−i
χ131-1-11-111-1-111111-11111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-1-111i−i−iiii−i−i−i−iii1-11-1-1-111iii−i−i−i−i−i−iiii1-1-111-111-1-1-1-111i−i−ii
χ141-1-11-111-1-111111-11111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-1-111i−i−iiii−i−i−i−iii1-11-1-1-111iii−i−i−i−i−i−iiii-111-11-1-1-11111-1-1−iii−i
χ151-1-11-111-1-111111-11111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-1-111−iii−i−i−iiiii−i−i1-11-1-1-111−i−i−iiiiiii−i−i−i1-1-111-111-1-1-1-111−iii−i
χ161-1-11-111-1-111111-11111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-1-111−iii−i−i−iiiii−i−i1-11-1-1-111−i−i−iiiiiii−i−i−i-111-11-1-1-11111-1-1i−i−ii
χ172222222222222222222222222222222222222222222222000000000000-2-2-2-2-2-2-2-20000000000000000-2-2000000000000
χ18222222-1-1-1-122-1-1-1-12-1-122222222-1-1-1-12-12-1-12-1-1-1-1-1-1-1-1-10000−i3i3−i3i3−i3i3−i3i3-2-2-2-211110−i3i30−i3i30−i3i30−i3i3000011000000000000
χ19222222-1-1-1-122-1-1-1-12-1-122222222-1-1-1-12-12-1-12-1-1-1-1-1-1-1-1-10000i3−i3i3−i3i3−i3i3−i3-2-2-2-211110i3−i30i3−i30i3−i30i3−i3000011000000000000
χ20222222-1-1-1-122-1-1-1-12-1-122222222-1-1-1-12-12-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-12-1-12-1-12-1-12-1-10000-1-1000000000000
χ21222222-1-1-1-122-1-1-1-12-1-122222222-1-1-1-12-12-1-12-1-1-1-1-1-1-1-1-1-2-2-2-2111111112222-1-1-1-1-211-211-211-2110000-1-1000000000000
χ222222-2-222222222-2-222222-2-2-2-222222222-2-2-2-2-2-2222-2-2-2-2000000000000-222-222220000000000000000-2-2000000000000
χ232222-2-2-1-1-1-122-1-1112-1-122-2-2-2-222-1-1-1-12-1-211-211-1-1-111110000−i3i3−i3i3i3−i3i3−i3-222-2-1-1-1-10−i3i30−i3i30i3−i30i3−i3000011000000000000
χ242222-2-2-1-1-1-122-1-1112-1-122-2-2-2-222-1-1-1-12-1-211-211-1-1-111110000i3−i3i3−i3−i3i3−i3i3-222-2-1-1-1-10i3−i30i3−i30−i3i30−i3i3000011000000000000
χ252222-2-2-1-1-1-122-1-1112-1-122-2-2-2-222-1-1-1-12-1-211-211-1-1-1111122-2-2-1-1-1-111112-2-2211112-1-12-1-1-211-2110000-1-1000000000000
χ262222-2-2-1-1-1-122-1-1112-1-122-2-2-2-222-1-1-1-12-1-211-211-1-1-11111-2-2221111-1-1-1-12-2-221111-211-2112-1-12-1-10000-1-1000000000000
χ272-2-222-22-2-2222222-2222-2-222-2-2-2-2-2-2-2-222222-2-2-22-2-222-2-2000000000000-2-222-2-2220000000000000000-22000000000000
χ282-2-222-2-111-122-1-1-112-1-1-2-222-2-2-2-211112-12-1-1-211-111-1-11100003−3−333−3−33-2-22211-1-103−30−3303−30−3300001-1000000000000
χ292-2-222-2-111-122-1-1-112-1-1-2-222-2-2-2-211112-12-1-1-211-111-1-1110000−333−3−333−3-2-22211-1-10−3303−30−3303−300001-1000000000000
χ302-2-222-2-111-122-1-1-112-1-1-2-222-2-2-2-211112-12-1-1-211-111-1-1112i−2i2i−2i−i−iii−i−iii22-2-2-1-1112i−i−i−2iii2i−i−i−2iii0000-11000000000000
χ312-2-222-2-111-122-1-1-112-1-1-2-222-2-2-2-211112-12-1-1-211-111-1-111−2i2i−2i2iii−i−iii−i−i22-2-2-1-111−2iii2i−i−i−2iii2i−i−i0000-11000000000000
χ322-2-22-222-2-222222-22222-2-2-2-222-2-2-2-2-2-222-2-2-22222-2-2-2-222000000000000-22-2222-2-20000000000000000-22000000000000
χ332-2-22-22-111-122-1-11-12-1-1-2-2-2-222-2-211112-1-2112-1-1-11111-1-100003−3−33−333−3-22-22-1-11103−30−330−3303−300001-1000000000000
χ342-2-22-22-111-122-1-11-12-1-1-2-2-2-222-2-211112-1-2112-1-1-11111-1-10000−333−33−3−33-22-22-1-1110−3303−303−30−3300001-1000000000000
χ352-2-22-22-111-122-1-11-12-1-1-2-2-2-222-2-211112-1-2112-1-1-11111-1-12i−2i−2i2i−i−iiiii−i−i2-22-211-1-12i−i−i−2iii−2iii2i−i−i0000-11000000000000
χ362-2-22-22-111-122-1-11-12-1-1-2-2-2-222-2-211112-1-2112-1-1-11111-1-1−2i2i2i−2iii−i−i−i−iii2-22-211-1-1−2iii2i−i−i2i−i−i−2iii0000-11000000000000
χ3744444444441-21144111-2-2-2-2-2-2111111-2-2111111-2-2-2-2-2-2-222222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3844444444441-21144111-2-2-2-2-2-2111111-2-2111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000111111111111000000000000000000
χ394444444444-21-2-244-2-2-2111111-2-2-2-2-2-211-2-2-2-2-2-2111111100000000000000000000000000000000222200-1-1-1-1-1-1-1-10000
χ404444444444-21-2-244-2-2-2111111-2-2-2-2-2-211-2-2-2-2-2-2111111100000000000000000000000000000000-2-2-2-200111111110000
χ41444444-2-2-2-21-2−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-2-2-2-2-211−1−3i32−1−3i32−1+3i32−1+3i32-211−1−3i32−1+3i321−1−3i32−1+3i3211111112222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i300000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32000000000000000000
χ42444444-2-2-2-21-2−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-2-2-2-2-211−1−3i32−1−3i32−1+3i32−1+3i32-211−1−3i32−1+3i321−1−3i32−1+3i321111111-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i3000000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ43444444-2-2-2-21-2−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-2-2-2-2-211−1+3i32−1+3i32−1−3i32−1−3i32-211−1+3i32−1−3i321−1+3i32−1−3i3211111112222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i300000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32000000000000000000
χ44444444-2-2-2-21-2−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-2-2-2-2-211−1+3i32−1+3i32−1−3i32−1−3i32-211−1+3i32−1−3i321−1+3i32−1−3i321111111-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i3000000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ454444-4-444441-211-4-4111-2-22222111111-2-2-1-1-1-1-1-1-2-2-2222222-2-22222-2-2-2-200000000-1-1-1-1-1-1111111000000000000000000
χ464444-4-444441-211-4-4111-2-22222111111-2-2-1-1-1-1-1-1-2-2-22222-2-222-2-2-2-2222200000000111111-1-1-1-1-1-1000000000000000000
χ474444-4-44444-21-2-2-4-4-2-2-211-1-1-1-1-2-2-2-2-2-211222222111-1-1-1-10000000000000000000000000000000022-2-200-1-1-1-111110000
χ484444-4-44444-21-2-2-4-4-2-2-211-1-1-1-1-2-2-2-2-2-211222222111-1-1-1-100000000000000000000000000000000-2-222001111-1-1-1-10000
χ494444-4-4-2-2-2-21-2−1−3i32−1+3i32221−1−3i32−1+3i32-2-2222211−1−3i32−1−3i32−1+3i32−1+3i32-21-11+3i321−3i32-11+3i321−3i32111-1-1-1-122-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ504444-4-4-2-2-2-21-2−1−3i32−1+3i32221−1−3i32−1+3i32-2-2222211−1−3i32−1−3i32−1+3i32−1+3i32-21-11+3i321−3i32-11+3i321−3i32111-1-1-1-1-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3000000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32000000000000000000
χ514444-4-4-2-2-2-21-2−1+3i32−1−3i32221−1+3i32−1−3i32-2-2222211−1+3i32−1+3i32−1−3i32−1−3i32-21-11−3i321+3i32-11−3i321+3i32111-1-1-1-122-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ524444-4-4-2-2-2-21-2−1+3i32−1−3i32221−1+3i32−1−3i32-2-2222211−1+3i32−1+3i32−1−3i32−1−3i32-21-11−3i321+3i32-11−3i321+3i32111-1-1-1-1-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i3000000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32000000000000000000
χ5344-4-40044-4-4444400-4-4-44-400004-44-44-4-44000000-44-4000000000000000000000000000000000000000000000000000000
χ5444-4-40044-4-4-21-2-2002221-13-33-3-22-22-22-11000000-11-13-33-3000000000000000000000000000000000000003−33−33−33−30000
χ5544-4-40044-4-4-21-2-2002221-13-33-3-22-22-22-11000000-11-13-33-300000000000000000000000000000000000000−33−33−33−330000
χ5644-4-40044-4-4-21-2-2002221-1-33-33-22-22-22-11000000-11-1-33-33000000000000000000000000000000000000003−33−3−33−330000
χ5744-4-40044-4-4-21-2-2002221-1-33-33-22-22-22-11000000-11-1-33-3300000000000000000000000000000000000000−33−333−33−30000
χ5844-4-400-2-22244-2-200-4224-400004-4-22-22-4-20000002-220000000000000000000023−2323−23000000000000000000000000000000
χ5944-4-400-2-22244-2-200-4224-400004-4-22-22-4-20000002-2200000000000000000000−2323−2323000000000000000000000000000000
χ604-44-4004-44-4444400-4-4-4-440000-44-44-44-44000000-4-44000000000000000000000000000000000000000000000000000000
χ614-44-4004-44-4-21-2-200222-113-3-332-22-22-2-11000000-1-113-3-33000000000000000000000000000000000000003−3−333−3−330000
χ624-44-4004-44-4-21-2-200222-113-3-332-22-22-2-11000000-1-113-3-3300000000000000000000000000000000000000−333−3−333−30000
χ634-44-4004-44-4-21-2-200222-11-333-32-22-22-2-11000000-1-11-333-3000000000000000000000000000000000000003−3−33−333−30000
χ644-44-4004-44-4-21-2-200222-11-333-32-22-22-2-11000000-1-11-333-300000000000000000000000000000000000000−333−33−3−330000
χ654-44-400-22-2244-2-200-422-440000-442-22-2-4-200000022-20000000000000000000023−23−2323000000000000000000000000000000
χ664-44-400-22-2244-2-200-422-440000-442-22-2-4-200000022-200000000000000000000−232323−23000000000000000000000000000000
χ674-4-444-44-4-441-2114-411122-2-222-1-1-1-1-1-1-2-2111-1-1-1-222-2-2222i−2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000−i−i−iiii−i−i−iiii000000000000000000
χ684-4-444-44-4-441-2114-411122-2-222-1-1-1-1-1-1-2-2111-1-1-1-222-2-222−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000iii−i−i−iiii−i−i−i000000000000000000
χ694-4-444-44-4-44-21-2-24-4-2-2-2-1-111-1-122222211-2-2-22221-1-111-1-1000000000000000000000000000000002-22-200-1-111-1-1110000
χ704-4-444-44-4-44-21-2-24-4-2-2-2-1-111-1-122222211-2-2-22221-1-111-1-100000000000000000000000000000000-22-220011-1-111-1-10000
χ714-4-444-4-222-21-2−1−3i32−1+3i32-221−1−3i32−1+3i3222-2-222-1-11+3i321+3i321−3i321−3i32-211−1−3i32−1+3i32-11+3i321−3i321-1-111-1-12i−2i2i−2i2ζ112ζ7−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ700000000−i−ζ11−ζ7iζ11ζ7−i−ζ11−ζ7iζ11ζ7000000000000000000
χ724-4-444-4-222-21-2−1−3i32−1+3i32-221−1−3i32−1+3i3222-2-222-1-11+3i321+3i321−3i321−3i32-211−1−3i32−1+3i32-11+3i321−3i321-1-111-1-1−2i2i−2i2i−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ72ζ112ζ700000000iζ11ζ7−i−ζ11−ζ7iζ11ζ7−i−ζ11−ζ7000000000000000000
χ734-4-444-4-222-21-2−1+3i32−1−3i32-221−1+3i32−1−3i3222-2-222-1-11−3i321−3i321+3i321+3i32-211−1+3i32−1−3i32-11−3i321+3i321-1-111-1-12i−2i2i−2i2ζ72ζ11−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ1100000000−i−ζ7−ζ11iζ7ζ11−i−ζ7−ζ11iζ7ζ11000000000000000000
χ744-4-444-4-222-21-2−1+3i32−1−3i32-221−1+3i32−1−3i3222-2-222-1-11−3i321−3i321+3i321+3i32-211−1+3i32−1−3i32-11−3i321+3i321-1-111-1-1−2i2i−2i2i−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ112ζ72ζ1100000000iζ7ζ11−i−ζ7−ζ11iζ7ζ11−i−ζ7−ζ11000000000000000000
χ754-4-44-444-4-441-211-441112222-2-2-1-1-1-1-1-1-2-2-1-1-1111-22222-2-22i−2i−2i2i2i2i−2i−2i−2i−2i2i2i00000000−i−i−iiiiiii−i−i−i000000000000000000
χ764-4-44-444-4-441-211-441112222-2-2-1-1-1-1-1-1-2-2-1-1-1111-22222-2-2−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i00000000iii−i−i−i−i−i−iiii000000000000000000
χ774-4-44-444-4-44-21-2-2-44-2-2-2-1-1-1-11122222211222-2-2-21-1-1-1-111000000000000000000000000000000002-2-2200-1-11111-1-10000
χ784-4-44-444-4-44-21-2-2-44-2-2-2-1-1-1-11122222211222-2-2-21-1-1-1-11100000000000000000000000000000000-222-20011-1-1-1-1110000
χ794-4-44-44-222-21-2−1−3i32−1+3i322-21−1−3i32−1+3i322222-2-2-1-11+3i321+3i321−3i321−3i32-21-11+3i321−3i321−1−3i32−1+3i321-1-1-1-1112i−2i−2i2i2ζ112ζ7−2ζ11−2ζ7−2ζ11−2ζ72ζ112ζ700000000−i−ζ11−ζ7iζ11ζ7iζ11ζ7−i−ζ11−ζ7000000000000000000
χ804-4-44-44-222-21-2−1−3i32−1+3i322-21−1−3i32−1+3i322222-2-2-1-11+3i321+3i321−3i321−3i32-21-11+3i321−3i321−1−3i32−1+3i321-1-1-1-111−2i2i2i−2i−2ζ11−2ζ72ζ112ζ72ζ112ζ7−2ζ11−2ζ700000000iζ11ζ7−i−ζ11−ζ7−i−ζ11−ζ7iζ11ζ7000000000000000000
χ814-4-44-44-222-21-2−1+3i32−1−3i322-21−1+3i32−1−3i322222-2-2-1-11−3i321−3i321+3i321+3i32-21-11−3i321+3i321−1+3i32−1−3i321-1-1-1-1112i−2i−2i2i2ζ72ζ11−2ζ7−2ζ11−2ζ7−2ζ112ζ72ζ1100000000−i−ζ7−ζ11iζ7ζ11iζ7ζ11−i−ζ7−ζ11000000000000000000
χ824-4-44-44-222-21-2−1+3i32−1−3i322-21−1+3i32−1−3i322222-2-2-1-11−3i321−3i321+3i321+3i32-21-11−3i321+3i321−1+3i32−1−3i321-1-1-1-111−2i2i2i−2i−2ζ7−2ζ112ζ72ζ112ζ72ζ11−2ζ7−2ζ1100000000iζ7ζ11−i−ζ7−ζ11−i−ζ7−ζ11iζ7ζ11000000000000000000
χ83888888-4-4-4-4-4222-4-4-422222222-4-422222-1-422-422-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000
χ848888-8-8-4-4-4-4-422244-42222-2-2-2-2-4-422222-14-2-24-2-2-1-1-1111100000000000000000000000000000000000000000000000000
χ8588-8-80088-8-82-42200-2-2-2-4400002-22-22-24-40000004-44000000000000000000000000000000000000000000000000000000
χ8688-8-800-4-4442-4−1−3i3−1+3i300-21+3i31−3i3-4400002-2−1−3i31+3i3−1+3i31−3i342000000-22-2000000000000000000000000000000000000000000000000000000
χ8788-8-800-4-4442-4−1+3i3−1−3i300-21−3i31+3i3-4400002-2−1+3i31−3i3−1−3i31+3i342000000-22-2000000000000000000000000000000000000000000000000000000
χ8888-8-800-4-444-4222004-2-22-26-66-6-442-22-2-2-10000001-11-33-3300000000000000000000000000000000000000000000000000
χ8988-8-800-4-444-4222004-2-22-2-66-66-442-22-2-2-10000001-113-33-300000000000000000000000000000000000000000000000000
χ908-88-8008-88-82-42200-2-2-24-40000-22-22-224-400000044-4000000000000000000000000000000000000000000000000000000
χ918-88-800-44-442-4−1−3i3−1+3i300-21+3i31−3i34-40000-221+3i3−1−3i31−3i3−1+3i342000000-2-22000000000000000000000000000000000000000000000000000000
χ928-88-800-44-442-4−1+3i3−1−3i300-21−3i31+3i34-40000-221−3i3−1+3i31+3i3−1−3i342000000-2-22000000000000000000000000000000000000000000000000000000
χ938-88-800-44-44-4222004-2-2-226-6-664-4-22-22-2-100000011-1-333-300000000000000000000000000000000000000000000000000
χ948-88-800-44-44-4222004-2-2-22-666-64-4-22-22-2-100000011-13-3-3300000000000000000000000000000000000000000000000000
χ958-8-888-8-444-4-4222-44-422-2-222-2-244-2-2-2-22-1-4224-2-2-111-1-11100000000000000000000000000000000000000000000000000
χ968-8-88-88-444-4-42224-4-422-2-2-2-22244-2-2-2-22-14-2-2-422-11111-1-100000000000000000000000000000000000000000000000000

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