Finite Group Databasebeta

← Group #13167298

Character table — Group #13167298

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222224444444444444444448888888888888888991212121212121212121212121818181818181824242424242424242424242436363636363672727272108108108108
order1222236663333666666666666663666666666666666444444121212121212121244412121212121212121212121212121212224412126612128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111-1-11-1-1111111-111111-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11-111-1-1iiiiii−i−i−i−i−i−i11-1-11-111-1-1ii−i−i
χ6111-1-11-1-1111111-111111-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11-111-1-1iiiiii−i−i−i−i−i−i-1-1111-1-1-111−i−iii
χ7111-1-11-1-1111111-111111-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-1−i−iii−i−i−i−iiiii11-111-1-1−i−i−i−i−i−iiiiiii11-1-11-111-1-1−i−iii
χ8111-1-11-1-1111111-111111-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-1−i−iii−i−i−i−iiiii11-111-1-1−i−i−i−i−i−iiiiiii-1-1111-1-1-111ii−i−i
χ911-11-11-1-111111-11111-1-1-1-1-1-1-1-111-1-1-11111-11-1-111-1-1-1-1i−ii−iii−i−iii−i−i1-1111-1-1iii−i−i−iiii−i−i−i1-11-1-111-11-1i−ii−i
χ1011-11-11-1-111111-11111-1-1-1-1-1-1-1-111-1-1-11111-11-1-111-1-1-1-1i−ii−iii−i−iii−i−i1-1111-1-1iii−i−i−iiii−i−i−i-11-11-11-11-11−ii−ii
χ1111-11-11-1-111111-11111-1-1-1-1-1-1-1-111-1-1-11111-11-1-111-1-1-1-1−ii−ii−i−iii−i−iii1-1111-1-1−i−i−iiii−i−i−iiii1-11-1-111-11-1−ii−ii
χ1211-11-11-1-111111-11111-1-1-1-1-1-1-1-111-1-1-11111-11-1-111-1-1-1-1−ii−ii−i−iii−i−iii1-1111-1-1−i−i−iiii−i−i−iiii-11-11-11-11-11i−ii−i
χ1311-1-1111111111-1-1111-1-111111111-1-1-1-1-1-1-111-1-1-1-111111-1-1111-1-1-1-1111-1-11111111-1-1-1-1-1-11111-1-11-1-11-1-111-1-11
χ1411-1-1111111111-1-1111-1-111111111-1-1-1-1-1-1-111-1-1-1-111111-1-1111-1-1-1-1111-1-11111111-1-1-1-1-1-1111-111-1-1-1-111-1-111-1
χ1511-1-1111111111-1-1111-1-111111111-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-11111-1-11-1-11111-1-1-1111111-1-1-11-1-11-1-11-1-11-111-1
χ1611-1-1111111111-1-1111-1-111111111-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-11111-1-11-1-11111-1-1-1111111-1-1-1-111-1-1-1-111-11-1-11
χ172222222222222222222222222222222222222222222-2-2000000000000-2-2-2-2-2-2-20000000000000000-2-200000000
χ1822222-1-1-1-12-1-12-1-12-1-12222-1-1-1-12-12-1-12-1-122-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-12-1-12-1-10000-1-100000000
χ1922222-1-1-1-12-1-12-1-12-1-12222-1-1-1-12-12-1-12-1-122-1-1-1-1-1-1-122-2-2-2-211111111222-1-1-1-1-211-211-211-2110000-1-100000000
χ2022222-1-1-1-12-1-12-1-12-1-12222-1-1-1-12-12-1-12-1-122-1-1-1-1-1-1-1-2-20000−i3i3−i3i3−i3i3−i3i3-2-2-211110−i3i30−i3i30−i3i30−i3i300001100000000
χ2122222-1-1-1-12-1-12-1-12-1-12222-1-1-1-12-12-1-12-1-122-1-1-1-1-1-1-1-2-20000i3−i3i3−i3i3−i3i3−i3-2-2-211110i3−i30i3−i30i3−i30i3−i300001100000000
χ22222-2-22-2-2222222-222222-2-2-2-2-2-222222-2-2-2-2-2222-2-2-2-222000000000000-2-22-2-2220000000000000000-2200000000
χ23222-2-2-111-12-1-12-112-1-122-2-211112-12-1-1-211-2-2-1-1-111112200003−33−3−33−33-2-2211-1-103−303−30−330−3300001-100000000
χ24222-2-2-111-12-1-12-112-1-122-2-211112-12-1-1-211-2-2-1-1-11111220000−33−333−33−3-2-2211-1-10−330−3303−303−300001-100000000
χ25222-2-2-111-12-1-12-112-1-122-2-211112-12-1-1-211-2-2-1-1-11111-2-22i2i−2i−2i−i−i−i−iiiii22-2-1-1112i−i−i2i−i−i−2iii−2iii0000-1100000000
χ26222-2-2-111-12-1-12-112-1-122-2-211112-12-1-1-211-2-2-1-1-11111-2-2−2i−2i2i2iiiii−i−i−i−i22-2-1-111−2iii−2iii2i−i−i2i−i−i0000-1100000000
χ2722-22-22-2-222222-22222-2-2-2-2-2-2-2-222-2-2-22222-22-2-222-2-222000000000000-22-2-2-22200000000000000002-200000000
χ2822-22-2-111-12-1-121-12-1-1-2-2-2-211112-1-2112-1-12-2-111-1-1112200003−3−333−3−33-22-211-1-103−30−3303−30−330000-1100000000
χ2922-22-2-111-12-1-121-12-1-1-2-2-2-211112-1-2112-1-12-2-111-1-111220000−333−3−333−3-22-211-1-10−3303−30−3303−30000-1100000000
χ3022-22-2-111-12-1-121-12-1-1-2-2-2-211112-1-2112-1-12-2-111-1-111-2-22i−2i2i−2i−i−iii−i−iii2-22-1-1112i−i−i−2iii2i−i−i−2iii00001-100000000
χ3122-22-2-111-12-1-121-12-1-1-2-2-2-211112-1-2112-1-12-2-111-1-111-2-2−2i2i−2i2iii−i−iii−i−i2-22-1-111−2iii2i−i−i−2iii2i−i−i00001-100000000
χ3222-2-2222222222-2-2222-2-222222222-2-2-2-2-2-2-222-2-2-2-222-2-2000000000000-222-2-2-2-200000000000000002200000000
χ3322-2-22-1-1-1-12-1-12112-1-1-2-222-1-1-1-12-1-211-211-22-11111-1-1222-2-22-1-11111-1-12-2-2-1-1-1-12-1-1-211-2112-1-100001100000000
χ3422-2-22-1-1-1-12-1-12112-1-1-2-222-1-1-1-12-1-211-211-22-11111-1-122-222-211-1-1-1-1112-2-2-1-1-1-1-2112-1-12-1-1-21100001100000000
χ3522-2-22-1-1-1-12-1-12112-1-1-2-222-1-1-1-12-1-211-211-22-11111-1-1-2-20000−i3i3i3−i3i3−i3−i3i3-22211110−i3i30i3−i30i3−i30−i3i30000-1-100000000
χ3622-2-22-1-1-1-12-1-12112-1-1-2-222-1-1-1-12-1-211-211-22-11111-1-1-2-20000i3−i3−i3i3−i3i3i3−i3-22211110i3−i30−i3i30−i3i30i3−i30000-1-100000000
χ37444444444111-244111-2-2111111-2-2111111-2-2-2-2-2-2-2-2-2002222222222220000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ38444444444111-244111-2-2111111-2-2111111-2-2-2-2-2-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2000000011111111111100000000000000
χ39444444444-2-2-2144-2-2-211-2-2-2-2-2-211-2-2-2-2-2-2111111111000000000000000000000000000000000222200-1-1-1-10000
χ40444444444-2-2-2144-2-2-211-2-2-2-2-2-211-2-2-2-2-2-2111111111000000000000000000000000000000000-2-2-2-20011110000
χ4144444-2-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1−3i32−1+3i32−1+3i32-211−1−3i32−1+3i321−1−3i32−1+3i32-2-21111111002222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i3200000000000000
χ4244444-2-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1−3i32−1+3i32−1+3i32-211−1−3i32−1+3i321−1−3i32−1+3i32-2-2111111100-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i300000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ4344444-2-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1+3i32−1−3i32−1−3i32-211−1+3i32−1−3i321−1+3i32−1−3i32-2-21111111002222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i30000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i3200000000000000
χ4444444-2-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1+3i32−1−3i32−1−3i32-211−1+3i32−1−3i321−1+3i32−1−3i32-2-2111111100-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i300000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ45444-4-44-4-44111-24-4111-2-2-1-1-1-1-1-1-2-2111-1-1-122-2-2-22222002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000−i−i−i−i−i−iiiiiii00000000000000
χ46444-4-44-4-44111-24-4111-2-2-1-1-1-1-1-1-2-2111-1-1-122-2-2-2222200−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000iiiiii−i−i−i−i−i−i00000000000000
χ47444-4-44-4-44-2-2-214-4-2-2-21122222211-2-2-2222-1-1111-1-1-1-100000000000000000000000000000000022-2-200-1-1110000
χ48444-4-44-4-44-2-2-214-4-2-2-21122222211-2-2-2222-1-1111-1-1-1-1000000000000000000000000000000000-2-2220011-1-10000
χ49444-4-4-222-21−1−3i32−1+3i32-2-221−1−3i32−1+3i32-2-2-1-11+3i321+3i321−3i321−3i32-211−1−3i32−1+3i32-11+3i321−3i3222111-1-1-1-1002i2i−2i−2i2ζ112ζ72ζ112ζ7−2ζ11−2ζ7−2ζ11−2ζ70000000−i−ζ11−ζ7−i−ζ11−ζ7iζ11ζ7iζ11ζ700000000000000
χ50444-4-4-222-21−1−3i32−1+3i32-2-221−1−3i32−1+3i32-2-2-1-11+3i321+3i321−3i321−3i32-211−1−3i32−1+3i32-11+3i321−3i3222111-1-1-1-100−2i−2i2i2i−2ζ11−2ζ7−2ζ11−2ζ72ζ112ζ72ζ112ζ70000000iζ11ζ7iζ11ζ7−i−ζ11−ζ7−i−ζ11−ζ700000000000000
χ51444-4-4-222-21−1+3i32−1−3i32-2-221−1+3i32−1−3i32-2-2-1-11−3i321−3i321+3i321+3i32-211−1+3i32−1−3i32-11−3i321+3i3222111-1-1-1-1002i2i−2i−2i2ζ72ζ112ζ72ζ11−2ζ7−2ζ11−2ζ7−2ζ110000000−i−ζ7−ζ11−i−ζ7−ζ11iζ7ζ11iζ7ζ1100000000000000
χ52444-4-4-222-21−1+3i32−1−3i32-2-221−1+3i32−1−3i32-2-2-1-11−3i321−3i321+3i321+3i32-211−1+3i32−1−3i32-11−3i321+3i3222111-1-1-1-100−2i−2i2i2i−2ζ7−2ζ11−2ζ7−2ζ112ζ72ζ112ζ72ζ110000000iζ7ζ11iζ7ζ11−i−ζ7−ζ11−i−ζ7−ζ1100000000000000
χ5344-44-44-4-44111-2-4411122-1-1-1-1-1-1-2-2-1-1-1111-22-222-2-222002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000−i−i−iiii−i−i−iiii00000000000000
χ5444-44-44-4-44111-2-4411122-1-1-1-1-1-1-2-2-1-1-1111-22-222-2-22200−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000iii−i−i−iiii−i−i−i00000000000000
χ5544-44-44-4-44-2-2-21-44-2-2-2-1-122222211222-2-2-21-11-1-111-1-10000000000000000000000000000000002-22-200-11-110000
χ5644-44-44-4-44-2-2-21-44-2-2-2-1-122222211222-2-2-21-11-1-111-1-1000000000000000000000000000000000-22-22001-11-10000
χ5744-44-4-222-21−1−3i32−1+3i32-22-21−1−3i32−1+3i3222-1-11+3i321+3i321−3i321−3i32-21-11+3i321−3i321−1−3i32−1+3i32-221-1-111-1-1002i−2i2i−2i2ζ112ζ7−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ70000000−i−ζ11−ζ7iζ11ζ7−i−ζ11−ζ7iζ11ζ700000000000000
χ5844-44-4-222-21−1−3i32−1+3i32-22-21−1−3i32−1+3i3222-1-11+3i321+3i321−3i321−3i32-21-11+3i321−3i321−1−3i32−1+3i32-221-1-111-1-100−2i2i−2i2i−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ72ζ112ζ70000000iζ11ζ7−i−ζ11−ζ7iζ11ζ7−i−ζ11−ζ700000000000000
χ5944-44-4-222-21−1+3i32−1−3i32-22-21−1+3i32−1−3i3222-1-11−3i321−3i321+3i321+3i32-21-11−3i321+3i321−1+3i32−1−3i32-221-1-111-1-1002i−2i2i−2i2ζ72ζ11−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ110000000−i−ζ7−ζ11iζ7ζ11−i−ζ7−ζ11iζ7ζ1100000000000000
χ6044-44-4-222-21−1+3i32−1−3i32-22-21−1+3i32−1−3i3222-1-11−3i321−3i321+3i321+3i32-21-11−3i321+3i321−1+3i32−1−3i32-221-1-111-1-100−2i2i−2i2i−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ112ζ72ζ110000000iζ7ζ11−i−ζ7−ζ11iζ7ζ11−i−ζ7−ζ1100000000000000
χ6144-4-444444111-2-4-411122111111-2-2-1-1-1-1-1-12-2-22222-2-2002-2-2222-2-2-2-2220000000-1-1-1111111-1-1-100000000000000
χ6244-4-444444111-2-4-411122111111-2-2-1-1-1-1-1-12-2-22222-2-200-222-2-2-22222-2-20000000111-1-1-1-1-1-111100000000000000
χ6344-4-444444-2-2-21-4-4-2-2-2-1-1-2-2-2-2-2-211222222-111-1-1-1-1110000000000000000000000000000000002-2-2200-111-10000
χ6444-4-444444-2-2-21-4-4-2-2-2-1-1-2-2-2-2-2-211222222-111-1-1-1-111000000000000000000000000000000000-222-2001-1-110000
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χ6644-4-44-2-2-2-21−1−3i32−1+3i32-2221−1−3i32−1+3i322211−1−3i32−1−3i32−1+3i32−1+3i32-21-11+3i321−3i32-11+3i321−3i322-21-1-1-1-11100-222-21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i300000001−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i3200000000000000
χ6744-4-44-2-2-2-21−1+3i32−1−3i32-2221−1+3i32−1−3i322211−1+3i32−1+3i32−1−3i32−1−3i32-21-11−3i321+3i32-11−3i321+3i322-21-1-1-1-111002-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i30000000-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i3200000000000000
χ6844-4-44-2-2-2-21−1+3i32−1−3i32-2221−1+3i32−1−3i322211−1+3i32−1+3i32−1−3i32−1−3i32-21-11−3i321+3i32-11−3i321+3i322-21-1-1-1-11100-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000001−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i3200000000000000
χ694-4000400-4444400-4-4-400000000-4400000000-40000004i−4i000000000000000004i−4i00000000000000000000000000
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χ7588888-4-4-4-4-4222-4-4-42222-4-422222-1-422-42222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000
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χ828-8000800-8-4-4-4200444-66000000-2200000000-2-66000000000000000000000000000000000000000000000000000
χ838-8000-4−4i34i342−1−3i3−1+3i3-400-21+3i31−3i3006-6−3−i33+i33−i3−3+i34200000000-200002i3−2i300000000000000000000000000000000000000000000000
χ848-8000-4−4i34i342−1+3i3−1−3i3-400-21−3i31+3i300-663−i3−3+i3−3−i33+i34200000000-200002i3−2i300000000000000000000000000000000000000000000000
χ858-8000-4−4i34i34-4222004-2-26-6002i3−2i32i3−2i3-2-1000000001-33−3i33i3−i3i300000000000000000000000000000000000000000000000
χ868-8000-4−4i34i34-4222004-2-2-66002i3−2i32i3−2i3-2-10000000013-33i3−3i3−i3i300000000000000000000000000000000000000000000000
χ878-8000-44i3−4i342−1−3i3−1+3i3-400-21+3i31−3i300-663+i3−3−i3−3+i33−i34200000000-20000−2i32i300000000000000000000000000000000000000000000000
χ888-8000-44i3−4i342−1+3i3−1−3i3-400-21−3i31+3i3006-6−3+i33−i33+i3−3−i34200000000-20000−2i32i300000000000000000000000000000000000000000000000
χ898-8000-44i3−4i34-4222004-2-26-600−2i32i3−2i32i3-2-1000000001-333i3−3i3i3−i300000000000000000000000000000000000000000000000
χ908-8000-44i3−4i34-4222004-2-2-6600−2i32i3−2i32i3-2-10000000013-3−3i33i3i3−i300000000000000000000000000000000000000000000000

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