Finite Group Databasebeta

← Group #13155010

Character table — Group #13155010

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222224444444444444444448888888888888888991212121212121212121212121818181818181824242424242424242424242436363636363672727272108108108108
order1223446663333666666666612121212366661212121212121212121212444444121212121212121222412121212121212121212121212121212668888242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-111ii−i−iii−i−iii−i−i
χ61111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-111−i−iii−i−iii−i−iii
χ71111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii
χ81111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−i
χ911-111-1-1-111111-1-1-11111-1-1-11-1-1-11-1-1-111111-1-1-111-1-111i−ii−iii−i−iii−i−i1-1-111-1-1iii−i−i−iiii−i−i−i1-1i−ii−ii−ii−i1-11-1
χ1011-111-1-1-111111-1-1-11111-1-1-11-1-1-11-1-1-111111-1-1-111-1-111i−ii−iii−i−iii−i−i1-1-111-1-1iii−i−i−iiii−i−i−i1-1−ii−ii−ii−ii-11-11
χ1111-111-1-1-111111-1-1-11111-1-1-11-1-1-11-1-1-111111-1-1-111-1-111−ii−ii−i−iii−i−iii1-1-111-1-1−i−i−iiii−i−i−iiii1-1i−ii−ii−ii−i-11-11
χ1211-111-1-1-111111-1-1-11111-1-1-11-1-1-11-1-1-111111-1-1-111-1-111−ii−ii−i−iii−i−iii1-1-111-1-1−i−i−iiii−i−i−iiii1-1−ii−ii−ii−ii1-11-1
χ1311-11-11-1-111111-1-1-11111-1-1-1-11111-1-1-11-1-1-1-1111-1-111-1-1i−i−iiii−i−i−i−iii1-11-1-111iii−i−i−i−i−i−iiii1-11-1-111-1-11−iii−i
χ1411-11-11-1-111111-1-1-11111-1-1-1-11111-1-1-11-1-1-1-1111-1-111-1-1i−i−iiii−i−i−i−iii1-11-1-111iii−i−i−i−i−i−iiii1-1-111-1-111-1i−i−ii
χ1511-11-11-1-111111-1-1-11111-1-1-1-11111-1-1-11-1-1-1-1111-1-111-1-1−iii−i−i−iiiii−i−i1-11-1-111−i−i−iiiiiii−i−i−i1-11-1-111-1-11i−i−ii
χ1611-11-11-1-111111-1-1-11111-1-1-1-11111-1-1-11-1-1-1-1111-1-111-1-1−iii−i−i−iiiii−i−i1-11-1-111−i−i−iiiiiii−i−i−i1-1-111-1-111-1−iii−i
χ172222222222222222222222222222222222222222222-2-2000000000000-2-2-2-2-2-2-2000000000000-2-2000000000000
χ182222-2-222222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-222000000000000-2-222222000000000000-2-2000000000000
χ19222-122-1-1-122-1-12-1-122-1-12-1-1-1-122-12-1-1-122-1-12-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-12-1-12-1-1-1-1000000000000
χ20222-122-1-1-122-1-12-1-122-1-12-1-1-1-122-12-1-1-122-1-12-1-1-1-1-1-122-2-2-2-211111111222-1-1-1-1-211-211-211-211-1-1000000000000
χ21222-122-1-1-122-1-12-1-122-1-12-1-1-1-122-12-1-1-122-1-12-1-1-1-1-1-1-2-20000−i3i3−i3i3−i3i3−i3i3-2-2-211110−i3i30−i3i30−i3i30−i3i311000000000000
χ22222-122-1-1-122-1-12-1-122-1-12-1-1-1-122-12-1-1-122-1-12-1-1-1-1-1-1-2-20000i3−i3i3−i3i3−i3i3−i3-2-2-211110i3−i30i3−i30i3−i30i3−i311000000000000
χ23222-1-2-2-1-1-122-1-12-1-122-1-12-1-111-2-2-12-1-1-1-2-211-2111111220000−i3i3−i3i3i3−i3i3−i3-2-22-1-1-1-10−i3i30−i3i30i3−i30i3−i311000000000000
χ24222-1-2-2-1-1-122-1-12-1-122-1-12-1-111-2-2-12-1-1-1-2-211-2111111220000i3−i3i3−i3−i3i3−i3i3-2-22-1-1-1-10i3−i30i3−i30−i3i30−i3i311000000000000
χ25222-1-2-2-1-1-122-1-12-1-122-1-12-1-111-2-2-12-1-1-1-2-211-2111111-2-222-2-2-1-1-1-1111122-211112-1-12-1-1-211-211-1-1000000000000
χ26222-1-2-2-1-1-122-1-12-1-122-1-12-1-111-2-2-12-1-1-1-2-211-2111111-2-2-2-2221111-1-1-1-122-21111-211-2112-1-12-1-1-1-1000000000000
χ2722-222-2-2-222222-2-2-22222-2-2-22-2-2-22-2-2-222222-2-2-222-2-2-2-2000000000000-222-2-222000000000000-22000000000000
χ2822-22-22-2-222222-2-2-22222-2-2-2-22222-2-2-22-2-2-2-2222-2-22222000000000000-22-222-2-2000000000000-22000000000000
χ2922-2-12-211-122-1-1-21122-1-1-211-11-2-2-1-211-122-1-1-211-1-111222i−2i2i−2i−i−iii−i−iii2-2-2-1-1112i−i−i−2iii2i−i−i−2iii-11000000000000
χ3022-2-12-211-122-1-1-21122-1-1-211-11-2-2-1-211-122-1-1-211-1-11122−2i2i−2i2iii−i−iii−i−i2-2-2-1-111−2iii2i−i−i−2iii2i−i−i-11000000000000
χ3122-2-12-211-122-1-1-21122-1-1-211-11-2-2-1-211-122-1-1-211-1-111-2-200003−3−333−3−33-22211-1-103−30−3303−30−331-1000000000000
χ3222-2-12-211-122-1-1-21122-1-1-211-11-2-2-1-211-122-1-1-211-1-111-2-20000−333−3−333−3-22211-1-10−3303−30−3303−31-1000000000000
χ3322-2-1-2211-122-1-1-21122-1-1-2111-122-1-211-1-2-2112-1-111-1-12200003−3−33−333−3-22-2-1-11103−30−330−3303−31-1000000000000
χ3422-2-1-2211-122-1-1-21122-1-1-2111-122-1-211-1-2-2112-1-111-1-1220000−333−33−3−33-22-2-1-1110−3303−303−30−331-1000000000000
χ3522-2-1-2211-122-1-1-21122-1-1-2111-122-1-211-1-2-2112-1-111-1-1-2-22i−2i−2i2i−i−iiiii−i−i2-2211-1-12i−i−i−2iii−2iii2i−i−i-11000000000000
χ3622-2-1-2211-122-1-1-21122-1-1-2111-122-1-211-1-2-2112-1-111-1-1-2-2−2i2i2i−2iii−i−i−i−iii2-2211-1-1−2iii2i−i−i2i−i−i−2iii-11000000000000
χ374444444441-2111111-21111144-2-2-2-2-2-2-21-211111-2-2-2-2002222222222220000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ384444444441-2111111-21111144-2-2-2-2-2-2-21-211111-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2000000011111111111100000000000000
χ39444444444-21-2-2-2-2-2-21-2-2-2-2-2441111111-21-2-2-2-2-21111000000000000000000000000000000000002222-1-1-1-10000
χ40444444444-21-2-2-2-2-2-21-2-2-2-2-2441111111-21-2-2-2-2-2111100000000000000000000000000000000000-2-2-2-211110000
χ414444-4-44441-2111111-211111-4-422-2-2-2-2-2-12-1-1-1-1-122220022-2-22222-2-2-2-20000000-1-1-1-1-1-111111100000000000000
χ424444-4-44441-2111111-211111-4-422-2-2-2-2-2-12-1-1-1-1-1222200-2-222-2-2-2-222220000000111111-1-1-1-1-1-100000000000000
χ434444-4-4444-21-2-2-2-2-2-21-2-2-2-2-2-4-4-1-1111112-122222-1-1-1-1000000000000000000000000000000000002i2i−2i−2i−i−iii0000
χ444444-4-4444-21-2-2-2-2-2-21-2-2-2-2-2-4-4-1-1111112-122222-1-1-1-100000000000000000000000000000000000−2i−2i2i2iii−i−i0000
χ45444-244-2-2-21-2−1−3i32−1+3i321−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-21-21111-2−1−3i32−1+3i321−1−3i32−1+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+3i321−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-21-21111-2−1−3i32−1+3i321−1−3i32−1+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+3i32−1−3i321−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-21-21111-2−1+3i32−1−3i321−1+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+3i32−1−3i321−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-21-21111-2−1+3i32−1−3i321−1+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
χ49444-2-4-4-2-2-21-2−1−3i32−1+3i321−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i3222221-2111-121+3i321−3i32-11+3i321−3i32-1-1-1-10022-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ50444-2-4-4-2-2-21-2−1−3i32−1+3i321−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i3222221-2111-121+3i321−3i32-11+3i321−3i32-1-1-1-100-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i300000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i3200000000000000
χ51444-2-4-4-2-2-21-2−1+3i32−1−3i321−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i3222221-2111-121−3i321+3i32-11−3i321+3i32-1-1-1-10022-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ52444-2-4-4-2-2-21-2−1+3i32−1−3i321−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i3222221-2111-121−3i321+3i32-11−3i321+3i32-1-1-1-100-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i300000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i3200000000000000
χ5344-444-4-4-441-211-1-1-11-211-1-1-14-422-2222-21-211-1-1-1-2-222002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000−i−i−iiii−i−i−iiii00000000000000
χ5444-444-4-4-441-211-1-1-11-211-1-1-14-422-2222-21-211-1-1-1-2-22200−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000iii−i−i−iiii−i−i−i00000000000000
χ5544-444-4-4-44-21-2-2222-21-2-22224-4-1-11-1-1-11-21-2-222211-1-1000000000000000000000000000000000002i−2i2i−2i−ii−ii0000
χ5644-444-4-4-44-21-2-2222-21-2-22224-4-1-11-1-1-11-21-2-222211-1-100000000000000000000000000000000000−2i2i−2i2ii−ii−i0000
χ5744-44-44-4-441-211-1-1-11-211-1-1-1-44-2-2-2222-2-12-1-111122-2-2002i−2i−2i2i2i2i−2i−2i−2i−2i2i2i0000000−i−i−iiiiiii−i−i−i00000000000000
χ5844-44-44-4-441-211-1-1-11-211-1-1-1-44-2-2-2222-2-12-1-111122-2-200−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i0000000iii−i−i−i−i−i−iiii00000000000000
χ5944-44-44-4-44-21-2-2222-21-2-2222-44111-1-1-112-122-2-2-2-1-111000000000000000000000000000000000002-2-22-111-10000
χ6044-44-44-4-44-21-2-2222-21-2-2222-44111-1-1-112-122-2-2-2-1-11100000000000000000000000000000000000-222-21-1-110000
χ6144-4-24-422-21-2−1−3i32−1+3i32-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i32-222212-1-111-2−1−3i32−1+3i32-11+3i321−3i3211-1-1002i−2i2i−2i2ζ112ζ7−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ70000000−i−ζ11−ζ7iζ11ζ7−i−ζ11−ζ7iζ11ζ700000000000000
χ6244-4-24-422-21-2−1−3i32−1+3i32-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i32-222212-1-111-2−1−3i32−1+3i32-11+3i321−3i3211-1-100−2i2i−2i2i−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ72ζ112ζ70000000iζ11ζ7−i−ζ11−ζ7iζ11ζ7−i−ζ11−ζ700000000000000
χ6344-4-24-422-21-2−1+3i32−1−3i32-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i32-222212-1-111-2−1+3i32−1−3i32-11−3i321+3i3211-1-1002i−2i2i−2i2ζ72ζ11−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ110000000−i−ζ7−ζ11iζ7ζ11−i−ζ7−ζ11iζ7ζ1100000000000000
χ6444-4-24-422-21-2−1+3i32−1−3i32-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i32-222212-1-111-2−1+3i32−1−3i32-11−3i321+3i3211-1-100−2i2i−2i2i−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ112ζ72ζ110000000iζ7ζ11−i−ζ7−ζ11iζ7ζ11−i−ζ7−ζ1100000000000000
χ6544-4-2-4422-21-2−1−3i32−1+3i32-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i322-2-2-212-1-11-121+3i321−3i321−1−3i32−1+3i32-1-111002i−2i−2i2i2ζ112ζ7−2ζ11−2ζ7−2ζ11−2ζ72ζ112ζ70000000−i−ζ11−ζ7iζ11ζ7iζ11ζ7−i−ζ11−ζ700000000000000
χ6644-4-2-4422-21-2−1−3i32−1+3i32-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i322-2-2-212-1-11-121+3i321−3i321−1−3i32−1+3i32-1-11100−2i2i2i−2i−2ζ11−2ζ72ζ112ζ72ζ112ζ7−2ζ11−2ζ70000000iζ11ζ7−i−ζ11−ζ7−i−ζ11−ζ7iζ11ζ700000000000000
χ6744-4-2-4422-21-2−1+3i32−1−3i32-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i322-2-2-212-1-11-121−3i321+3i321−1+3i32−1−3i32-1-111002i−2i−2i2i2ζ72ζ11−2ζ7−2ζ11−2ζ7−2ζ112ζ72ζ110000000−i−ζ7−ζ11iζ7ζ11iζ7ζ11−i−ζ7−ζ1100000000000000
χ6844-4-2-4422-21-2−1+3i32−1−3i32-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i322-2-2-212-1-11-121−3i321+3i321−1+3i32−1−3i32-1-11100−2i2i2i−2i−2ζ7−2ζ112ζ72ζ112ζ72ζ11−2ζ7−2ζ110000000iζ7ζ11−i−ζ7−ζ11−i−ζ7−ζ11iζ7ζ1100000000000000
χ694-4040000-44444000-4-4-4-400000004000-4000000000004i−4i0000000000000004i−4i0000000000000000000000000000
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χ734-40-2002i3−2i3244-2-202i3−2i3-4-4220−2i32i30000-202i3−2i32000000000004i−4i000000000000000−2i2i−232300000000000000000000000000
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χ75888-488-4-4-4-4222-422-4222-422-4-422-12-1-1-1-4222-422-1-1-1-100000000000000000000000000000000000000000000000
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χ798-8080000-82-422666-24-2-2-6-6-60000-400040000000000000000000000000000000000000000000000000000000000
χ808-8080000-82-422-6-6-6-24-2-26660000-400040000000000000000000000000000000000000000000000000000000000
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χ828-8080000-8-42-4-40004-24400000−6i6i2000-2000000000−6i6i00000000000000000000000000000000000000000000000
χ838-80-400−4i34i342-4−1−3i3−1+3i36−3−i3−3+i3-241+3i31−3i3-63+i33−i30000202i3−2i3-20000000000000000000000000000000000000000000000000000000000
χ848-80-400−4i34i342-4−1+3i3−1−3i3-63−i33+i3-241−3i31+3i36−3+i3−3−i30000202i3−2i3-20000000000000000000000000000000000000000000000000000000000
χ858-80-400−4i34i34-422202i3−2i34-2-2-20−2i32i3006i−6i-10−i3i31000000033−33−3i3i00000000000000000000000000000000000000000000000
χ868-80-400−4i34i34-422202i3−2i34-2-2-20−2i32i300−6i6i-10−i3i310000000−33333i−3i00000000000000000000000000000000000000000000000
χ878-80-4004i3−4i342-4−1−3i3−1+3i3-63+i33−i3-241+3i31−3i36−3−i3−3+i3000020−2i32i3-20000000000000000000000000000000000000000000000000000000000
χ888-80-4004i3−4i342-4−1+3i3−1−3i36−3+i3−3−i3-241−3i31+3i3-63−i33+i3000020−2i32i3-20000000000000000000000000000000000000000000000000000000000
χ898-80-4004i3−4i34-42220−2i32i34-2-2-202i3−2i3006i−6i-10i3−i310000000−3333−3i3i00000000000000000000000000000000000000000000000
χ908-80-4004i3−4i34-42220−2i32i34-2-2-202i3−2i300−6i6i-10i3−i31000000033−333i−3i00000000000000000000000000000000000000000000000

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