Finite Group Databasebeta

← Group #11720561

Character table — Group #11720561

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size1111112222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636
order123366244661212121288242424243333666612121212121212126666121212122424242424242424242424242424242444881212121224242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ4111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111-1-111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i11-1-1ii−i−i
χ61111111-1-111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii-1-111−i−iii
χ71111111-1-111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii11-1-1−i−iii
χ81111111-1-111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i-1-111ii−i−i
χ92222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000
χ10222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000
χ11222222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000
χ12222222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000
χ13222222222222222-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1-2-2111111-2-2111111000000000000
χ14222222222222222-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-111-2-2111111-2-21111000000000000
χ15222222222222222-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-11111-2-2111111-2-211000000000000
χ16222222222222222-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12111111-2-2111111-2-2000000000000
χ172222222-2-222-2-2-2-22i−2i2i2i−2i−2i2-1-1-12-1-1-1-2-21111112-1-1-1-21112i2i−i−i−i−i−i−i−2i−2iiiiiii000000000000
χ182222222-2-222-2-2-2-22i−2i2i2i−2i−2i-12-1-1-12-1-111-2-21111-12-1-11-211−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000
χ192222222-2-222-2-2-2-22i−2i2i2i−2i−2i-1-12-1-1-12-11111-2-211-1-12-111-21−i−i−i−i2i2i−i−iiiii−2i−2iii000000000000
χ202222222-2-222-2-2-2-22i−2i2i2i−2i−2i-1-1-12-1-1-12111111-2-2-1-1-12111-2−i−i−i−i−i−i2i2iiiiiii−2i−2i000000000000
χ212222222-2-222-2-2-2-2−2i2i−2i−2i2i2i2-1-1-12-1-1-1-2-21111112-1-1-1-2111−2i−2iiiiiii2i2i−i−i−i−i−i−i000000000000
χ222222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-12-1-1-12-1-111-2-21111-12-1-11-211ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000
χ232222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-1-12-1-1-12-11111-2-211-1-12-111-21iiii−2i−2iii−i−i−i−i2i2i−i−i000000000000
χ242222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-1-1-12-1-1-12111111-2-2-1-1-12111-2iiiiii−2i−2i−i−i−i−i−i−i2i2i000000000000
χ25222222-22-2-2-222-2-20000002222222222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ26222222-22-2-2-222-2-20000002-1-1-12-1-1-122-1-1-1-1-1-1-2111-211100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000
χ27222222-22-2-2-222-2-20000002-1-1-12-1-1-122-1-1-1-1-1-1-2111-211100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000
χ28222222-22-2-2-222-2-2000000-12-1-1-12-1-1-1-122-1-1-1-11-2111-211−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000
χ29222222-22-2-2-222-2-2000000-12-1-1-12-1-1-1-122-1-1-1-11-2111-211i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000000000
χ30222222-22-2-2-222-2-2000000-1-12-1-1-12-1-1-1-1-122-1-111-2111-21−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000
χ31222222-22-2-2-222-2-2000000-1-12-1-1-12-1-1-1-1-122-1-111-2111-21i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000000000
χ32222222-22-2-2-222-2-2000000-1-1-12-1-1-12-1-1-1-1-1-122111-2111-2−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000000000
χ33222222-22-2-2-222-2-2000000-1-1-12-1-1-12-1-1-1-1-1-122111-2111-2i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000000000
χ34222222-2-22-2-2-2-22200000022222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ35222222-2-22-2-2-2-2220000002-1-1-12-1-1-1-2-2111111-21112-1-1-1003−33−33−300−33−33−33000000000000
χ36222222-2-22-2-2-2-2220000002-1-1-12-1-1-1-2-2111111-21112-1-1-100−33−33−33003−33−33−3000000000000
χ37222222-2-22-2-2-2-222000000-12-1-1-12-1-111-2-211111-211-12-1-13−3003−3−33−3300−333−3000000000000
χ38222222-2-22-2-2-2-222000000-12-1-1-12-1-111-2-211111-211-12-1-1−3300−333−33−3003−3−33000000000000
χ39222222-2-22-2-2-2-222000000-1-12-1-1-12-11111-2-21111-21-1-12-13−3−33003−3−333−300−33000000000000
χ40222222-2-22-2-2-2-222000000-1-12-1-1-12-11111-2-21111-21-1-12-1−333−300−333−3−33003−3000000000000
χ41222222-2-22-2-2-2-222000000-1-1-12-1-1-12111111-2-2111-2-1-1-123−33−3−3300−33−333−300000000000000
χ42222222-2-22-2-2-2-222000000-1-1-12-1-1-12111111-2-2111-2-1-1-12−33−333−3003−33−3−3300000000000000
χ4333−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ4433−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32
χ4533−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32000000000000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ4633−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320000000000000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ4733−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ700000000000000000000000000000000000000001-1i−i−1−i32−1+i321+i321−i32ζ11ζ7−ζ11−ζ7
χ4833−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ70000000000000000000000000000000000000000-11−ii1+i321−i32−1−i32−1+i32−ζ11−ζ7ζ11ζ7
χ4933−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ700000000000000000000000000000000000000001-1−ii−1−i32−1+i321+i321−i32−ζ11−ζ7ζ11ζ7
χ5033−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ70000000000000000000000000000000000000000-11i−i1+i321−i32−1−i32−1+i32ζ11ζ7−ζ11−ζ7
χ5133−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ5233−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32
χ5333−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32000000000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ5433−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320000000000000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ5533−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i323i−3i3ζ73ζ11−3ζ7−3ζ1100000000000000000000000000000000000000001-1i−i−1+i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ11
χ5633−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i323i−3i3ζ73ζ11−3ζ7−3ζ110000000000000000000000000000000000000000-11−ii1−i321+i32−1+i32−1−i32−ζ7−ζ11ζ7ζ11
χ5733−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32−3i3i−3ζ7−3ζ113ζ73ζ1100000000000000000000000000000000000000001-1−ii−1+i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ11
χ5833−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32−3i3i−3ζ7−3ζ113ζ73ζ110000000000000000000000000000000000000000-11i−i1−i321+i32−1+i32−1−i32ζ7ζ11−ζ7−ζ11
χ594-444-4-40000000000000004444-4-4-4-400000000000000000000000000000000000000000000
χ604-444-4-40000000000000004-2-2-2-42220023−2323−2323−23000000000000000000000000000000000000
χ614-444-4-40000000000000004-2-2-2-422200−2323−2323−2323000000000000000000000000000000000000
χ624-444-4-4000000000000000-24-2-22-42223−230023−23−2323000000000000000000000000000000000000
χ634-444-4-4000000000000000-24-2-22-422−232300−232323−23000000000000000000000000000000000000
χ644-444-4-4000000000000000-2-24-222-4223−23−23230023−23000000000000000000000000000000000000
χ654-444-4-4000000000000000-2-24-222-42−232323−2300−2323000000000000000000000000000000000000
χ664-444-4-4000000000000000-2-2-24222-423−2323−23−232300000000000000000000000000000000000000
χ674-444-4-4000000000000000-2-2-24222-4−2323−232323−2300000000000000000000000000000000000000
χ6866−3−3i3−3+3i3−3−3i3−3+3i3-66-63+3i33−3i3−3−3i3−3+3i33+3i33−3i30000000000000000000000000000000000000000000000000000000000
χ6966−3−3i3−3+3i3−3−3i3−3+3i3-6-663+3i33−3i33+3i33−3i3−3−3i3−3+3i30000000000000000000000000000000000000000000000000000000000
χ7066−3+3i3−3−3i3−3+3i3−3−3i3-66-63−3i33+3i3−3+3i3−3−3i33−3i33+3i30000000000000000000000000000000000000000000000000000000000
χ7166−3+3i3−3−3i3−3+3i3−3−3i3-6-663−3i33+3i33−3i33+3i3−3+3i3−3−3i30000000000000000000000000000000000000000000000000000000000
χ7212-12−6−6i3−6+6i36+6i36−6i30000000000000000000000000000000000000000000000000000000000000000000
χ7312-12−6+6i3−6−6i36−6i36+6i30000000000000000000000000000000000000000000000000000000000000000000

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