Finite Group Databasebeta

← Group #72220746

Character table — Group #72220746

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size112224444444444488888881212121212121818181824242424242436363636363636108108112224444444444488888881212121212121818181824242424242436363636363636108108112224444444444488888881212121212121818181824242424242436363636363636108108
order1223633336666666366666624661212226666612121244612121212443663633336666666366666661266121266666661212121212612121212121236636333366666663666666612661212666666612121212126121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-11-1-1-1-1-1-1111111111111111111111111111111111111111-1-11-1-1-1-1-1-1111111111111111111111111111111111111111-1-11-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1
χ411111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111
χ511-1111111-11-1111-11-1-1-11-1-11-111-1-11-111111-1-1-1i−i-1ii−i−ii−i11-1111111-11-1111-11-1-1-11-1-11-111-1-11-111111-1-1-1i−i-1ii−i−ii−i11-1111111-11-1111-11-1-1-11-1-11-111-1-11-111111-1-1-1i−i-1ii−i−ii−i
χ611-1111111-11-1111-11-1-1-11-1-11-111-1-11-111111-1-1-1−ii-1−i−iii−ii11-1111111-11-1111-11-1-1-11-1-11-111-1-11-111111-1-1-1−ii-1−i−iii−ii11-1111111-11-1111-11-1-1-11-1-11-111-1-11-111111-1-1-1−ii-1−i−iii−ii
χ711-1111111-11-1111-11-1-1-11-1-1-11-1-1111-111-1-1-1111i−i-1ii−i−i−ii11-1111111-11-1111-11-1-1-11-1-1-11-1-1111-111-1-1-1111i−i-1ii−i−i−ii11-1111111-11-1111-11-1-1-11-1-1-11-1-1111-111-1-1-1111i−i-1ii−i−i−ii
χ811-1111111-11-1111-11-1-1-11-1-1-11-1-1111-111-1-1-1111−ii-1−i−iiii−i11-1111111-11-1111-11-1-1-11-1-1-11-1-1111-111-1-1-1111−ii-1−i−iiii−i11-1111111-11-1111-11-1-1-11-1-1-11-1-1111-111-1-1-1111−ii-1−i−iiii−i
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χ11222-1-122-1-1-1222-1-12-12-1-1-1-1-100i3−i3i3−i3-2-2110i3−i30i3−i3001000000222-1-122-1-1-1222-1-12-12-1-1-1-1-100i3−i3i3−i3-2-2110i3−i30i3−i3001000000222-1-122-1-1-1222-1-12-12-1-1-1-1-100i3−i3i3−i3-2-2110i3−i30i3−i3001000000
χ12222-1-122-1-1-1222-1-12-12-1-1-1-1-122-1-1-1-122-1-12-1-12-1-100-1000000222-1-122-1-1-1222-1-12-12-1-1-1-1-122-1-1-1-122-1-12-1-12-1-100-1000000222-1-122-1-1-1222-1-12-12-1-1-1-1-122-1-1-1-122-1-12-1-12-1-100-1000000
χ13222-1-122-1-1-1222-1-12-12-1-1-1-1-1-2-2111122-1-1-211-21100-1000000222-1-122-1-1-1222-1-12-12-1-1-1-1-1-2-2111122-1-1-211-21100-1000000222-1-122-1-1-1222-1-12-12-1-1-1-1-1-2-2111122-1-1-211-21100-1000000
χ1422-2222222-22-2222-22-2-2-22-2-2000000-22-2-200000000200000022-2222222-22-2222-22-2-2-22-2-2000000-22-2-200000000200000022-2222222-22-2222-22-2-2-22-2-2000000-22-2-2000000002000000
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χ1622-2-1-122-1-112-22-1-1-2-1-211-11100i3−i3−i3i3-22110i3−i30−i3i300-100000022-2-1-122-1-112-22-1-1-2-1-211-11100i3−i3−i3i3-22110i3−i30−i3i300-100000022-2-1-122-1-112-22-1-1-2-1-211-11100i3−i3−i3i3-22110i3−i30−i3i300-1000000
χ1722-2-1-122-1-112-22-1-1-2-1-211-1112-2-1-1112-2-1-12-1-1-21100100000022-2-1-122-1-112-22-1-1-2-1-211-1112-2-1-1112-2-1-12-1-1-21100100000022-2-1-122-1-112-22-1-1-2-1-211-1112-2-1-1112-2-1-12-1-1-211001000000
χ1822-2-1-122-1-112-22-1-1-2-1-211-111-2211-1-12-2-1-1-2112-1-100100000022-2-1-122-1-112-22-1-1-2-1-211-111-2211-1-12-2-1-1-2112-1-100100000022-2-1-122-1-112-22-1-1-2-1-211-111-2211-1-12-2-1-1-2112-1-1001000000
χ19444441-2-2-2411-2-2-211-2-2-21110000000000000000220-1-1-1-100444441-2-2-2411-2-2-211-2-2-21110000000000000000220-1-1-1-100444441-2-2-2411-2-2-211-2-2-21110000000000000000220-1-1-1-100
χ20444441-2-2-2411-2-2-211-2-2-21110000000000000000-2-20111100444441-2-2-2411-2-2-211-2-2-21110000000000000000-2-20111100444441-2-2-2411-2-2-211-2-2-21110000000000000000-2-20111100
χ2144444-21114-2-2111-2-2111-2-2-22222220000-1-1-1-1-1-100000000044444-21114-2-2111-2-2111-2-2-22222220000-1-1-1-1-1-100000000044444-21114-2-2111-2-2111-2-2-22222220000-1-1-1-1-1-1000000000
χ2244444-21114-2-2111-2-2111-2-2-2-2-2-2-2-2-2000011111100000000044444-21114-2-2111-2-2111-2-2-2-2-2-2-2-2-2000011111100000000044444-21114-2-2111-2-2111-2-2-2-2-2-2-2-2-20000111111000000000
χ23444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i3211122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i32000000000444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i3211122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i32000000000444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i3211122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i32000000000
χ24444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32111-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i32000000000444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32111-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i32000000000444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32111-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i32000000000
χ25444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i3211122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i32000000000444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i3211122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i32000000000444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i3211122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i32000000000
χ26444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32111-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i32000000000444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32111-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i32000000000444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32111-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i32000000000
χ2744-4441-2-2-2-41-1-2-2-2-112221-1-100000000000000002i−2i0−i−iii0044-4441-2-2-2-41-1-2-2-2-112221-1-100000000000000002i−2i0−i−iii0044-4441-2-2-2-41-1-2-2-2-112221-1-100000000000000002i−2i0−i−iii00
χ2844-4441-2-2-2-41-1-2-2-2-112221-1-10000000000000000−2i2i0ii−i−i0044-4441-2-2-2-41-1-2-2-2-112221-1-10000000000000000−2i2i0ii−i−i0044-4441-2-2-2-41-1-2-2-2-112221-1-10000000000000000−2i2i0ii−i−i00
χ2944-444-2111-4-221112-2-1-1-1-2222-222-2-20000-1-1-111100000000044-444-2111-4-221112-2-1-1-1-2222-222-2-20000-1-1-111100000000044-444-2111-4-221112-2-1-1-1-2222-222-2-20000-1-1-1111000000000
χ3044-444-2111-4-221112-2-1-1-1-222-22-2-2220000111-1-1-100000000044-444-2111-4-221112-2-1-1-1-222-22-2-2220000111-1-1-100000000044-444-2111-4-221112-2-1-1-1-222-22-2-2220000111-1-1-1000000000
χ3144-4-2-2-21−1−3i32−1+3i322-221−1−3i32−1+3i3221-11+3i321−3i321-1-12-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i3200000000044-4-2-2-21−1−3i32−1+3i322-221−1−3i32−1+3i3221-11+3i321−3i321-1-12-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i3200000000044-4-2-2-21−1−3i32−1+3i322-221−1−3i32−1+3i3221-11+3i321−3i321-1-12-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i32000000000
χ3244-4-2-2-21−1−3i32−1+3i322-221−1−3i32−1+3i3221-11+3i321−3i321-1-1-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i3200000000044-4-2-2-21−1−3i32−1+3i322-221−1−3i32−1+3i3221-11+3i321−3i321-1-1-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i3200000000044-4-2-2-21−1−3i32−1+3i322-221−1−3i32−1+3i3221-11+3i321−3i321-1-1-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i32000000000
χ3344-4-2-2-21−1+3i32−1−3i322-221−1+3i32−1−3i3221-11−3i321+3i321-1-12-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i3200000000044-4-2-2-21−1+3i32−1−3i322-221−1+3i32−1−3i3221-11−3i321+3i321-1-12-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i3200000000044-4-2-2-21−1+3i32−1−3i322-221−1+3i32−1−3i3221-11−3i321+3i321-1-12-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i32000000000
χ3444-4-2-2-21−1+3i32−1−3i322-221−1+3i32−1−3i3221-11−3i321+3i321-1-1-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i3200000000044-4-2-2-21−1+3i32−1−3i322-221−1+3i32−1−3i3221-11−3i321+3i321-1-1-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i3200000000044-4-2-2-21−1+3i32−1−3i322-221−1+3i32−1−3i3221-11−3i321+3i321-1-1-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i32000000000
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χ374-404-41-2-2-20-1-322231000-1-3300000000000000000003−3−33004-404-41-2-2-20-1-322231000-1-3300000000000000000003−3−33004-404-41-2-2-20-1-322231000-1-3300000000000000000003−3−3300
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χ394-404-444440-40-4-4-404000-40000000000000000000000000004-404-444440-40-4-4-404000-40000000000000000000000000004-404-444440-40-4-4-404000-4000000000000000000000000000
χ404-40-2244-2-20-40-4220-200020000000000−2i32i30000000000000004-40-2244-2-20-40-4220-200020000000000−2i32i30000000000000004-40-2244-2-20-40-4220-200020000000000−2i32i3000000000000000
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χ42888-4-42-422-422-4222-1-422-1-1-10000000000000000000000000888-4-42-422-422-4222-1-422-1-1-10000000000000000000000000888-4-42-422-422-4222-1-422-1-1-10000000000000000000000000
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χ478-80-44-42−1−3i3−1+3i3040-21+3i31−3i302000-20000000000000000000000000008-80-44-42−1−3i3−1+3i3040-21+3i31−3i302000-20000000000000000000000000008-80-44-42−1−3i3−1+3i3040-21+3i31−3i302000-2000000000000000000000000000
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χ1428-80-442-4220-2-64-2-26-100013-30000000000000000000000000−4−4i34+4i302+2i3−2−2i3−1−i32+2i3−1−i3−1−i301+i33+3i3−2−2i31+i31+i3−3−3i31+i32000−1−i32−3−3i323+3i320000000000000000000000000−4+4i34−4i302−2i3−2+2i3−1+i32−2i3−1+i3−1+i301−i33−3i3−2+2i31−i31−i3−3+3i31−i32000−1+i32−3+3i323−3i320000000000000000000000000
χ1438-80-44-42−1−3i3−1+3i3040-21+3i31−3i302000-2000000000000000000000000000−4−4i34+4i302+2i3−2−2i32+2i3−1−i3−4+2i35−i30−2−2i301+i34−2i3−5+i30−1−i30001+i3000000000000000000000000000−4+4i34−4i302−2i3−2+2i32−2i3−1+i35+i3−4−2i30−2+2i301−i3−5−i34+2i30−1+i30001−i3000000000000000000000000000
χ1448-80-44-42−1+3i3−1−3i3040-21−3i31+3i302000-2000000000000000000000000000−4−4i34+4i302+2i3−2−2i32+2i3−1−i35−i3−4+2i30−2−2i301+i3−5+i34−2i30−1−i30001+i3000000000000000000000000000−4+4i34−4i302−2i3−2+2i32−2i3−1+i3−4−2i35+i30−2+2i301−i34+2i3−5−i30−1+i30001−i3000000000000000000000000000

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