Finite Group Databasebeta

← Group #13155005

Character table — Group #13155005

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222224444444444444444448888888888888888991212121212121212121212121818181818181824242424242424242424242436363636363672727272108108108108
order1223446121233336666612121212121212121236666666121212121212121222888824242424242424242446612122424242424242424242424246888812242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111
χ51111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111ii−i−iiiii−i−i−i−i1-1-111-1-1iiiiii−i−i−i−i−i−i1ii−i−i-1ii−i−i11-1-1
χ61111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111ii−i−iiiii−i−i−i−i1-1-111-1-1iiiiii−i−i−i−i−i−i1−i−iii-1−i−iii-1-111
χ71111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111−i−iii−i−i−i−iiiii1-1-111-1-1−i−i−i−i−i−iiiiiii1ii−i−i-1ii−i−i-1-111
χ81111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111−i−iii−i−i−i−iiiii1-1-111-1-1−i−i−i−i−i−iiiiiii1−i−iii-1−i−iii11-1-1
χ911-111-11111111-11111-1111111-1-11-1-1-1-1-1-111-1-1-111-1-1-1-11-11-111-1-111-1-111-1-1-1-1-1111-1-1-1111-1-1-11i−ii−i1i−ii−ii−ii−i
χ1011-111-11111111-11111-1111111-1-11-1-1-1-1-1-111-1-1-111-1-1-1-11-11-111-1-111-1-111-1-1-1-1-1111-1-1-1111-1-1-11−ii−ii1−ii−ii−ii−ii
χ1111-111-11111111-11111-1111111-1-11-1-1-1-1-1-111-1-1-111-1-1-1-1-11-11-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-11111i−ii−i1i−ii−i−ii−ii
χ1211-111-11111111-11111-1111111-1-11-1-1-1-1-1-111-1-1-111-1-1-1-1-11-11-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-11111−ii−ii1−ii−iii−ii−i
χ1311-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11-1111-1-111-1-1i−i−iiii−i−i−i−iii1-11-1-111iii−i−i−i−i−i−iiii11-1-11-11-1-11−iii−i
χ1411-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11-1111-1-111-1-1i−i−iiii−i−i−i−iii1-11-1-111iii−i−i−i−i−i−iiii1-111-1-1-111-1i−i−ii
χ1511-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11-1111-1-111-1-1−iii−i−i−iiiii−i−i1-11-1-111−i−i−iiiiiii−i−i−i11-1-11-11-1-11i−i−ii
χ1611-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11-1111-1-111-1-1−iii−i−i−iiiii−i−i1-11-1-111−i−i−iiiiiii−i−i−i1-111-1-1-111-1−iii−i
χ172222222222222222222222222222222222222222222-2-2000000000000-2-2-2-2-2-2-2000000000000-20000-200000000
χ182222-2-22-2-2222222222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2000000000000-222-2-222000000000000-20000200000000
χ19222-122-1-1-122-1-1-122-1-1-122-1-1-1-122-122-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-12-1-12-1-1-10000-100000000
χ20222-122-1-1-122-1-1-122-1-1-122-1-1-1-122-122-1-1-1-1-122-1-1-1-1-1-122-2-2-2-211111111222-1-1-1-1-211-211-211-211-10000-100000000
χ21222-122-1-1-122-1-1-122-1-1-122-1-1-1-122-122-1-1-1-1-122-1-1-1-1-1-1-2-20000−i3i3−i3i3−i3i3−i3i3-2-2-211110−i3i30−i3i30−i3i30−i3i310000100000000
χ22222-122-1-1-122-1-1-122-1-1-122-1-1-1-122-122-1-1-1-1-122-1-1-1-1-1-1-2-20000i3−i3i3−i3i3−i3i3−i3-2-2-211110i3−i30i3−i30i3−i30i3−i310000100000000
χ23222-1-2-2-11122-1-1-122-1-11-2-21111-2-2-122-1-1-1-1-1-2-2111111222i2i−2i−2i−i−i−i−iiiii2-2-2-1-1112i−i−i2i−i−i−2iii−2iii-10000100000000
χ24222-1-2-2-11122-1-1-122-1-11-2-21111-2-2-122-1-1-1-1-1-2-211111122−2i−2i2i2iiiii−i−i−i−i2-2-2-1-111−2iii−2iii2i−i−i2i−i−i-10000100000000
χ25222-1-2-2-11122-1-1-122-1-11-2-21111-2-2-122-1-1-1-1-1-2-2111111-2-200003−33−3−33−33-22211-1-103−303−30−330−3310000-100000000
χ26222-1-2-2-11122-1-1-122-1-11-2-21111-2-2-122-1-1-1-1-1-2-2111111-2-20000−33−333−33−3-22211-1-10−330−3303−303−310000-100000000
χ2722-222-22222222-22222-2222222-2-22-2-2-2-2-2-222-2-2-222-2-222000000000000-2-222222000000000000-20000-200000000
χ2822-22-222-2-22222-222222-2-2-2-2-2-2222-2-2-2-2-2-22-2222-2-22222000000000000-22-222-2-2000000000000-20000200000000
χ2922-2-12-2-1-1-122-1-1122-1-1122-1-1-1-1-2-2-1-2-21111-12-211-1-111220000−i3i3i3−i3−i3i3i3−i3-2-22-1-1-1-10−i3i30i3−i30−i3i30i3−i310000100000000
χ3022-2-12-2-1-1-122-1-1122-1-1122-1-1-1-1-2-2-1-2-21111-12-211-1-111220000i3−i3−i3i3i3−i3−i3i3-2-22-1-1-1-10i3−i30−i3i30i3−i30−i3i310000100000000
χ3122-2-12-2-1-1-122-1-1122-1-1122-1-1-1-1-2-2-1-2-21111-12-211-1-111-2-22-22-2-1-111-1-11122-211112-1-1-2112-1-1-211-10000-100000000
χ3222-2-12-2-1-1-122-1-1122-1-1122-1-1-1-1-2-2-1-2-21111-12-211-1-111-2-2-22-2211-1-111-1-122-21111-2112-1-1-2112-1-1-10000-100000000
χ3322-2-1-22-11122-1-1122-1-1-1-2-2111122-1-2-21111-1-22-1-111-1-12200003−3−33−333−3-22-2-1-11103−30−330−3303−310000-100000000
χ3422-2-1-22-11122-1-1122-1-1-1-2-2111122-1-2-21111-1-22-1-111-1-1220000−333−33−3−33-22-2-1-1110−3303−303−30−3310000-100000000
χ3522-2-1-22-11122-1-1122-1-1-1-2-2111122-1-2-21111-1-22-1-111-1-1-2-22i−2i−2i2i−i−iiiii−i−i2-2211-1-12i−i−i−2iii−2iii2i−i−i-10000100000000
χ3622-2-1-22-11122-1-1122-1-1-1-2-2111122-1-2-21111-1-22-1-111-1-1-2-2−2i2i2i−2iii−i−i−i−iii2-2211-1-1−2iii2i−i−i2i−i−i−2iii-10000100000000
χ374444444441-21141-2114111111-2-2-21-211-2-2-2-2111-2-2-2-2002222222222220000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ384444444441-21141-2114111111-2-2-21-211-2-2-2-2111-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2000000011111111111100000000000000
χ39444444444-21-2-24-21-2-24-2-2-2-2-2-2111-21-2-21111-2-2-21111000000000000000000000000000000000022220-1-1-1-10000
χ40444444444-21-2-24-21-2-24-2-2-2-2-2-2111-21-2-21111-2-2-211110000000000000000000000000000000000-2-2-2-2011110000
χ414444-4-44-4-41-21141-211-4-1-1-1-1-1-122-21-211-2-2-22-1-1-12222002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000−i−i−i−i−i−iiiiiii00000000000000
χ424444-4-44-4-41-21141-211-4-1-1-1-1-1-122-21-211-2-2-22-1-1-1222200−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000iiiiii−i−i−i−i−i−i00000000000000
χ434444-4-44-4-4-21-2-24-21-2-2-4222222-1-11-21-2-2111-1222-1-1-1-100000000000000000000000000000000002i2i−2i−2i0−i−iii0000
χ444444-4-44-4-4-21-2-24-21-2-2-4222222-1-11-21-2-2111-1222-1-1-1-10000000000000000000000000000000000−2i−2i2i2i0ii−i−i0000
χ45444-244-2-2-21-2−1−3i32−1+3i32-21-2−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i32-2-211-2−1−3i32−1+3i32111-21−1−3i32−1+3i321111002222−1−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
χ46444-244-2-2-21-2−1−3i32−1+3i32-21-2−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i32-2-211-2−1−3i32−1+3i32111-21−1−3i32−1+3i32111100-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i300000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ47444-244-2-2-21-2−1+3i32−1−3i32-21-2−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i32-2-211-2−1+3i32−1−3i32111-21−1+3i32−1−3i321111002222−1+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
χ48444-244-2-2-21-2−1+3i32−1−3i32-21-2−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i32-2-211-2−1+3i32−1−3i32111-21−1+3i32−1−3i32111100-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i300000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ49444-2-4-4-2221-2−1−3i32−1+3i32-21-2−1−3i32−1+3i322-1-11+3i321+3i321−3i321−3i322211-2−1−3i32−1+3i321112-11+3i321−3i32-1-1-1-1002i2i−2i−2i2ζ112ζ72ζ112ζ7−2ζ11−2ζ7−2ζ11−2ζ70000000−i−ζ11−ζ7−i−ζ11−ζ7iζ11ζ7iζ11ζ700000000000000
χ50444-2-4-4-2221-2−1−3i32−1+3i32-21-2−1−3i32−1+3i322-1-11+3i321+3i321−3i321−3i322211-2−1−3i32−1+3i321112-11+3i321−3i32-1-1-1-100−2i−2i2i2i−2ζ11−2ζ7−2ζ11−2ζ72ζ112ζ72ζ112ζ70000000iζ11ζ7iζ11ζ7−i−ζ11−ζ7−i−ζ11−ζ700000000000000
χ51444-2-4-4-2221-2−1+3i32−1−3i32-21-2−1+3i32−1−3i322-1-11−3i321−3i321+3i321+3i322211-2−1+3i32−1−3i321112-11−3i321+3i32-1-1-1-1002i2i−2i−2i2ζ72ζ112ζ72ζ11−2ζ7−2ζ11−2ζ7−2ζ110000000−i−ζ7−ζ11−i−ζ7−ζ11iζ7ζ11iζ7ζ1100000000000000
χ52444-2-4-4-2221-2−1+3i32−1−3i32-21-2−1+3i32−1−3i322-1-11−3i321−3i321+3i321+3i322211-2−1+3i32−1−3i321112-11−3i321+3i32-1-1-1-100−2i−2i2i2i−2ζ7−2ζ11−2ζ7−2ζ112ζ72ζ112ζ72ζ110000000iζ7ζ11iζ7ζ11−i−ζ7−ζ11−i−ζ7−ζ1100000000000000
χ5344-444-44441-211-41-211-411111122-2-12-1-122-2-2-1-1-1-2-222002-22-222-2-222-2-20000000-1-1-1111-1-1-111100000000000000
χ5444-444-44441-211-41-211-411111122-2-12-1-122-2-2-1-1-1-2-22200-22-22-2-222-2-2220000000111-1-1-1111-1-1-100000000000000
χ5544-444-4444-21-2-2-4-21-2-2-4-2-2-2-2-2-2-1-112-122-1-11122211-1-100000000000000000000000000000000002i−2i2i−2i0−ii−ii0000
χ5644-444-4444-21-2-2-4-21-2-2-4-2-2-2-2-2-2-1-112-122-1-11122211-1-10000000000000000000000000000000000−2i2i−2i2i0i−ii−i0000
χ5744-44-444-4-41-211-41-2114-1-1-1-1-1-1-2-2-2-12-1-122-2211122-2-2002i−2i−2i2i2i2i−2i−2i−2i−2i2i2i0000000−i−i−iiiiiii−i−i−i00000000000000
χ5844-44-444-4-41-211-41-2114-1-1-1-1-1-1-2-2-2-12-1-122-2211122-2-200−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i0000000iii−i−i−i−i−i−iiii00000000000000
χ5944-44-444-4-4-21-2-2-4-21-2-242222221112-122-1-11-1-2-2-2-1-11100000000000000000000000000000000002-2-220-111-10000
χ6044-44-444-4-4-21-2-2-4-21-2-242222221112-122-1-11-1-2-2-2-1-1110000000000000000000000000000000000-222-201-1-110000
χ6144-4-24-4-2-2-21-2−1−3i32−1+3i3221-2−1−3i32−1+3i32211−1−3i32−1−3i32−1+3i32−1+3i32221-121+3i321−3i32-1-11-2-11+3i321−3i3211-1-1002-22-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i30000000-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i3200000000000000
χ6244-4-24-4-2-2-21-2−1−3i32−1+3i3221-2−1−3i32−1+3i32211−1−3i32−1−3i32−1+3i32−1+3i32221-121+3i321−3i32-1-11-2-11+3i321−3i3211-1-100-22-221+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i300000001−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i3200000000000000
χ6344-4-24-4-2-2-21-2−1+3i32−1−3i3221-2−1+3i32−1−3i32211−1+3i32−1+3i32−1−3i32−1−3i32221-121−3i321+3i32-1-11-2-11−3i321+3i3211-1-1002-22-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i30000000-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i3200000000000000
χ6444-4-24-4-2-2-21-2−1+3i32−1−3i3221-2−1+3i32−1−3i32211−1+3i32−1+3i32−1−3i32−1−3i32221-121−3i321+3i32-1-11-2-11−3i321+3i3211-1-100-22-221−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i300000001−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i3200000000000000
χ6544-4-2-44-2221-2−1−3i32−1+3i3221-2−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32-2-21-121+3i321−3i32-1-1121−1−3i32−1+3i32-1-111002i−2i−2i2i2ζ112ζ7−2ζ11−2ζ7−2ζ11−2ζ72ζ112ζ70000000−i−ζ11−ζ7iζ11ζ7iζ11ζ7−i−ζ11−ζ700000000000000
χ6644-4-2-44-2221-2−1−3i32−1+3i3221-2−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32-2-21-121+3i321−3i32-1-1121−1−3i32−1+3i32-1-11100−2i2i2i−2i−2ζ11−2ζ72ζ112ζ72ζ112ζ7−2ζ11−2ζ70000000iζ11ζ7−i−ζ11−ζ7−i−ζ11−ζ7iζ11ζ700000000000000
χ6744-4-2-44-2221-2−1+3i32−1−3i3221-2−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i32-2-21-121−3i321+3i32-1-1121−1+3i32−1−3i32-1-111002i−2i−2i2i2ζ72ζ11−2ζ7−2ζ11−2ζ7−2ζ112ζ72ζ110000000−i−ζ7−ζ11iζ7ζ11iζ7ζ11−i−ζ7−ζ1100000000000000
χ6844-4-2-44-2221-2−1+3i32−1−3i3221-2−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i32-2-21-121−3i321+3i32-1-1121−1+3i32−1−3i32-1-11100−2i2i2i−2i−2ζ7−2ζ112ζ72ζ112ζ72ζ11−2ζ7−2ζ110000000iζ7ζ11−i−ζ7−ζ11−i−ζ7−ζ11iζ7ζ1100000000000000
χ694-40400-40044440-4-4-4-40000000004000000-4000000004-40000000000000004-40000000000000000000000000000
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χ828-80800-800-42-4-404-2440000000−6i6i2000000-2000000−6i6i00000000000000000000000000000000000000000000000
χ838-80-400443−432-4−1−3i3−1+3i30-241+3i31−3i306i−6i2ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ11002000000-20000−23230000000000000000000000000000000000000000000000000
χ848-80-400443−432-4−1+3i3−1−3i30-241−3i31+3i30−6i6i−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ11002000000-20000−23230000000000000000000000000000000000000000000000000
χ858-80-400443−43-422204-2-2-2000−2323−23236i−6i-10000−3i33i3100003−3−3i3i00000000000000000000000000000000000000000000000
χ868-80-400443−43-422204-2-2-2000−2323−2323−6i6i-100003i3−3i3100003−33i−3i00000000000000000000000000000000000000000000000
χ878-80-4004−43432-4−1−3i3−1+3i30-241+3i31−3i30−6i6i−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ11002000000-2000023−230000000000000000000000000000000000000000000000000
χ888-80-4004−43432-4−1+3i3−1−3i30-241−3i31+3i306i−6i4ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ11002000000-2000023−230000000000000000000000000000000000000000000000000
χ898-80-4004−4343-422204-2-2-200023−2323−236i−6i-100003i3−3i310000−33−3i3i00000000000000000000000000000000000000000000000
χ908-80-4004−4343-422204-2-2-200023−2323−23−6i6i-10000−3i33i310000−333i−3i00000000000000000000000000000000000000000000000

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