Finite Group Databasebeta

← Group #11722393

Character table — Group #11722393

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size1111111111116666666666121212121212181818181818181818181818242424242424242424242424363636363636
order1233446612121212234666121212126661212128888242424242424242433366612121212121224661212
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ31111-1-111-1-1-1-1-111-1-11-1-111-1-1-111111-1-11111-1-1-1-1111111-1-1-1-1-1-11-111-1-1
χ41111-1-111-1-1-1-1-111-1-11-1-111-1-1-1111-1-111-1-1-1-11111111111-1-1-1-1-1-1-11-1-111
χ52222222222222222222222222222000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000
χ62222222222222-1222-1-1-122-1-1-1-1-1-10000000000002-1-12-1-122-1-1-1-1000000
χ72222222222222-1222-1-1-122-1-1-1-1-1-1000000000000-12-1-12-1-1-122-1-1000000
χ82222222222222-1222-1-1-122-1-1-1-1-1-1000000000000-1-12-1-12-1-1-1-122000000
χ92222-2-222-2-2-2-2-222-2-22-2-222-2-2-2222000000000000-1-1-1-1-1-1111111000000
χ102222-2-222-2-2-2-2-2-12-2-2-11122111-1-1-10000000000002-1-12-1-1-2-21111000000
χ112222-2-222-2-2-2-2-2-12-2-2-11122111-1-1-1000000000000-12-1-12-111-2-211000000
χ122222-2-222-2-2-2-2-2-12-2-2-11122111-1-1-1000000000000-1-12-1-121111-2-2000000
χ132-2222i−2i-2-22i2i−2i−2i02000-22i−2i00000000−i2i22−2−i2−i2i2i222−2−2-1-1-1111i−ii−ii−i000000
χ142-2222i−2i-2-22i2i−2i−2i02000-22i−2i00000000i2−i2−22i2i2−i2−i2−2−222-1-1-1111i−ii−ii−i000000
χ152-222−2i2i-2-2−2i−2i2i2i02000-2−2i2i00000000−i2i2−22−i2−i2i2i2−2−222-1-1-1111−ii−ii−ii000000
χ162-222−2i2i-2-2−2i−2i2i2i02000-2−2i2i00000000i2−i22−2i2i2−i2−i222−2−2-1-1-1111−ii−ii−ii000000
χ17333333333333-13-1-1-1333-1-1-1-1-1-1-1-1111111111111000000000000-1-1-1-1-1-1
χ18333333333333-13-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111
χ193333-3-333-3-3-3-313-1113-3-3-1-1111-1-1-111-1-11111-1-1-1-1000000000000-11-1-111
χ203333-3-333-3-3-3-313-1113-3-3-1-1111-1-1-1-1-111-1-1-1-111110000000000001-111-1-1
χ2133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i320000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000011−1−i32−1+i32−1−i32−1+i32
χ2233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i32000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000-1-11+i321−i321+i321−i32
χ2333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-10-11+i321−i320001+i321−i322−1−i3−1+i32−1−i3−1+i31111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000-1-11+i321−i321+i321−i32
χ2433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-10-11+i321−i320001+i321−i322−1−i3−1+i32−1−i3−1+i3-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000011−1−i32−1+i32−1−i32−1+i32
χ2533−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3210-1−1−i32−1+i320001+i321−i32-21+i31−i32−1−i3−1+i311-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32000000000000-111+i321−i32−1−i32−1+i32
χ2633−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3210-1−1−i32−1+i320001+i321−i32-21+i31−i32−1−i3−1+i3-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000001-1−1−i32−1+i321+i321−i32
χ2733−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-3033+3i323−3i32000−3−3i32−3+3i3200000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000001-1−1−i32−1+i321+i321−i32
χ2833−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-3033+3i323−3i32000−3−3i32−3+3i32000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32000000000000-111+i321−i32−1−i32−1+i32
χ2933−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i320000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3200000000000011−1+i32−1−i32−1+i32−1−i32
χ3033−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i32000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32000000000000-1-11−i321+i321−i321+i32
χ3133−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-10-11−i321+i320001−i321+i322−1+i3−1−i32−1+i3−1−i31111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000-1-11−i321+i321−i321+i32
χ3233−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-10-11−i321+i320001−i321+i322−1+i3−1−i32−1+i3−1−i3-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000000011−1+i32−1−i32−1+i32−1−i32
χ3333−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3210-1−1+i32−1−i320001−i321+i32-21−i31+i32−1+i3−1−i311-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32000000000000-111−i321+i32−1+i32−1−i32
χ3433−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3210-1−1+i32−1−i320001−i321+i32-21−i31+i32−1+i3−1−i3-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i320000000000001-1−1+i32−1−i321−i321+i32
χ3533−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-3033−3i323+3i32000−3+3i32−3−3i3200000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i320000000000001-1−1+i32−1−i321−i321+i32
χ3633−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-3033−3i323+3i32000−3+3i32−3−3i32000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32000000000000-111−i321+i32−1+i32−1−i32
χ374-4444i−4i-4-44i4i−4i−4i04000-44i−4i00000000000000000000111-1-1-1−ii−ii−ii000000
χ384-4444i−4i-4-44i4i−4i−4i0-20002−2i2i0000000000000000000011-2-1-12−ii−ii2i−2i000000
χ394-4444i−4i-4-44i4i−4i−4i0-20002−2i2i000000000000000000001-21-12-1−ii2i−2i−ii000000
χ404-4444i−4i-4-44i4i−4i−4i0-20002−2i2i00000000000000000000-2112-1-12i−2i−ii−ii000000
χ414-444−4i4i-4-4−4i−4i4i4i04000-4−4i4i00000000000000000000111-1-1-1i−ii−ii−i000000
χ424-444−4i4i-4-4−4i−4i4i4i0-200022i−2i0000000000000000000011-2-1-12i−ii−i−2i2i000000
χ434-444−4i4i-4-4−4i−4i4i4i0-200022i−2i000000000000000000001-21-12-1i−i−2i2ii−i000000
χ444-444−4i4i-4-4−4i−4i4i4i0-200022i−2i00000000000000000000-2112-1-1−2i2ii−ii−i000000
χ45666666666666-2-3-2-2-2-3-3-3-2-2111111000000000000000000000000000000
χ466666-6-666-6-6-6-62-3-222-333-2-2-1-1-1111000000000000000000000000000000
χ4766−3−3i3−3+3i366−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3-20-21+i31−i30001+i31−i3-21+i31−i3-21+i31−i3000000000000000000000000000000
χ4866−3−3i3−3+3i3-6-6−3−3i3−3+3i33+3i33−3i33+3i33−3i320-2−1−i3−1+i30001+i31−i32−1−i3−1+i3-21+i31−i3000000000000000000000000000000
χ4966−3+3i3−3−3i366−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3-20-21−i31+i30001−i31+i3-21−i31+i3-21−i31+i3000000000000000000000000000000
χ5066−3+3i3−3−3i3-6-6−3+3i3−3−3i33−3i33+3i33−3i33+3i320-2−1+i3−1−i30001−i31+i32−1+i3−1−i3-21−i31+i3000000000000000000000000000000
χ516-6−3−3i3−3+3i36i−6i3+3i33−3i36ζ226ζ14−6ζ22−6ζ140000000000000000−i2i22−2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23000000000000000000
χ526-6−3−3i3−3+3i36i−6i3+3i33−3i36ζ226ζ14−6ζ22−6ζ140000000000000000i2−i2−22−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23000000000000000000
χ536-6−3−3i3−3+3i3−6i6i3+3i33−3i3−6ζ22−6ζ146ζ226ζ140000000000000000−i2i2−22ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23000000000000000000
χ546-6−3−3i3−3+3i3−6i6i3+3i33−3i3−6ζ22−6ζ146ζ226ζ140000000000000000i2−i22−2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23000000000000000000
χ556-6−3+3i3−3−3i36i−6i3−3i33+3i36ζ146ζ22−6ζ14−6ζ220000000000000000−i2i22−2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13000000000000000000
χ566-6−3+3i3−3−3i36i−6i3−3i33+3i36ζ146ζ22−6ζ14−6ζ220000000000000000i2−i2−22−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13000000000000000000
χ576-6−3+3i3−3−3i3−6i6i3−3i33+3i3−6ζ14−6ζ226ζ146ζ220000000000000000−i2i2−22ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13000000000000000000
χ586-6−3+3i3−3−3i3−6i6i3−3i33+3i3−6ζ14−6ζ226ζ146ζ220000000000000000i2−i22−2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.