Finite Group Databasebeta

← Group #11720559

Character table — Group #11720559

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size1111111111112222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636
order123344661212121224661212882424242433336666121212121212121266661212121224242424242424242424242424242424888824242424242424248824242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-111-1-1-1-1-11-1-111i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1i−iii−i−i
χ61111-1-111-1-1-1-1-11-1-111i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-11111−ii−i−iii
χ71111-1-111-1-1-1-1-11-1-111−ii−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−ii−i−iii
χ81111-1-111-1-1-1-1-11-1-111−ii−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-11111i−iii−i−i
χ92222222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000
χ10222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000
χ11222222222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000
χ12222222222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000
χ13222222222222222222-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1-2-2111111-2-2111111000000000000000000
χ14222222222222222222-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-111-2-2111111-2-21111000000000000000000
χ15222222222222222222-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-11111-2-2111111-2-211000000000000000000
χ16222222222222222222-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12111111-2-2111111-2-2000000000000000000
χ17222222222222-2-2-2-2-2-20000002222222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000
χ18222222222222-2-2-2-2-2-20000002-1-1-12-1-1-122-1-1-1-1-1-1-2111-211100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000
χ19222222222222-2-2-2-2-2-20000002-1-1-12-1-1-122-1-1-1-1-1-1-2111-211100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000
χ20222222222222-2-2-2-2-2-2000000-12-1-1-12-1-1-1-122-1-1-1-11-2111-211−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000
χ21222222222222-2-2-2-2-2-2000000-12-1-1-12-1-1-1-122-1-1-1-11-2111-211i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000000000000000
χ22222222222222-2-2-2-2-2-2000000-1-12-1-1-12-1-1-1-1-122-1-111-2111-21−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000000000
χ23222222222222-2-2-2-2-2-2000000-1-12-1-1-12-1-1-1-1-122-1-111-2111-21i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000000000000000
χ24222222222222-2-2-2-2-2-2000000-1-1-12-1-1-12-1-1-1-1-1-122111-2111-2−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000000000000000
χ25222222222222-2-2-2-2-2-2000000-1-1-12-1-1-12-1-1-1-1-1-122111-2111-2i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000000000000000
χ262222-2-222-2-2-2-22-222-2-200000022222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000000000
χ272222-2-222-2-2-2-22-222-2-20000002-1-1-12-1-1-1-2-21111112-1-1-1-2111003−33−33−300−33−33−33000000000000000000
χ282222-2-222-2-2-2-22-222-2-20000002-1-1-12-1-1-1-2-21111112-1-1-1-211100−33−33−33003−33−33−3000000000000000000
χ292222-2-222-2-2-2-22-222-2-2000000-12-1-1-12-1-111-2-21111-12-1-11-2113−3003−3−33−3300−333−3000000000000000000
χ302222-2-222-2-2-2-22-222-2-2000000-12-1-1-12-1-111-2-21111-12-1-11-211−3300−333−33−3003−3−33000000000000000000
χ312222-2-222-2-2-2-22-222-2-2000000-1-12-1-1-12-11111-2-211-1-12-111-213−3−33003−3−333−300−33000000000000000000
χ322222-2-222-2-2-2-22-222-2-2000000-1-12-1-1-12-11111-2-211-1-12-111-21−333−300−333−3−33003−3000000000000000000
χ332222-2-222-2-2-2-22-222-2-2000000-1-1-12-1-1-12111111-2-2-1-1-12111-23−33−3−3300−33−333−300000000000000000000
χ342222-2-222-2-2-2-22-222-2-2000000-1-1-12-1-1-12111111-2-2-1-1-12111-2−33−333−3003−33−3−3300000000000000000000
χ352222-2-222-2-2-2-2-22-2-2222i−2i2i2i−2i−2i2-1-1-12-1-1-1-2-2111111-21112-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii000000000000000000
χ362222-2-222-2-2-2-2-22-2-2222i−2i2i2i−2i−2i-12-1-1-12-1-111-2-211111-211-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000000000
χ372222-2-222-2-2-2-2-22-2-2222i−2i2i2i−2i−2i-1-12-1-1-12-11111-2-21111-21-1-12-1−i−i−i−i2i2i−i−iiiii−2i−2iii000000000000000000
χ382222-2-222-2-2-2-2-22-2-2222i−2i2i2i−2i−2i-1-1-12-1-1-12111111-2-2111-2-1-1-12−i−i−i−i−i−i2i2iiiiiii−2i−2i000000000000000000
χ392222-2-222-2-2-2-2-22-2-222−2i2i−2i−2i2i2i2-1-1-12-1-1-1-2-2111111-21112-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i000000000000000000
χ402222-2-222-2-2-2-2-22-2-222−2i2i−2i−2i2i2i-12-1-1-12-1-111-2-211111-211-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000000000
χ412222-2-222-2-2-2-2-22-2-222−2i2i−2i−2i2i2i-1-12-1-1-12-11111-2-21111-21-1-12-1iiii−2i−2iii−i−i−i−i2i2i−i−i000000000000000000
χ422222-2-222-2-2-2-2-22-2-222−2i2i−2i−2i2i2i-1-1-12-1-1-12111111-2-2111-2-1-1-12iiiiii−2i−2i−i−i−i−i−i−i2i2i000000000000000000
χ432-2222i−2i-2-22i2i−2i−2i0000000000002222-2-2-2-22i−2i2i−2i2i−2i2i−2i0000000000000000000000002−2−i2i222−2−2−i2−i2i2i2000000
χ442-2222i−2i-2-22i2i−2i−2i0000000000002222-2-2-2-22i−2i2i−2i2i−2i2i−2i000000000000000000000000−22i2−i2−2−222i2i2−i2−i2000000
χ452-222−2i2i-2-2−2i−2i2i2i0000000000002222-2-2-2-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000002−2i2−i222−2−2i2i2−i2−i2000000
χ462-222−2i2i-2-2−2i−2i2i2i0000000000002222-2-2-2-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000−22−i2i2−2−222−i2−i2i2i2000000
χ4733−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+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+i3211−1−i32−1+i32−1−i32−1+i32
χ4833−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i321+i321−i32
χ4933−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32
χ5033−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ5133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i323i−3i3ζ223ζ14−3ζ22−3ζ14000000000000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32i−iζ22ζ14−ζ22−ζ14
χ5233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i323i−3i3ζ223ζ14−3ζ22−3ζ140000000000000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−ii−ζ22−ζ14ζ22ζ14
χ5333−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i32−3i3i−3ζ22−3ζ143ζ223ζ14000000000000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−ii−ζ22−ζ14ζ22ζ14
χ5433−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i32−3i3i−3ζ22−3ζ143ζ223ζ140000000000000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32i−iζ22ζ14−ζ22−ζ14
χ5533−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+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−i3211−1+i32−1−i32−1+i32−1−i32
χ5633−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+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+i32-1-11−i321+i321−i321+i32
χ5733−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32
χ5833−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ5933−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-333−3i323+3i32−3+3i32−3−3i323i−3i3ζ143ζ22−3ζ14−3ζ22000000000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32i−iζ14ζ22−ζ14−ζ22
χ6033−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-333−3i323+3i32−3+3i32−3−3i323i−3i3ζ143ζ22−3ζ14−3ζ220000000000000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−ii−ζ14−ζ22ζ14ζ22
χ6133−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-333−3i323+3i32−3+3i32−3−3i32−3i3i−3ζ14−3ζ223ζ143ζ22000000000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−ii−ζ14−ζ22ζ14ζ22
χ6233−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-333−3i323+3i32−3+3i32−3−3i32−3i3i−3ζ14−3ζ223ζ143ζ220000000000000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32i−iζ14ζ22−ζ14−ζ22
χ634-4444i−4i-4-44i4i−4i−4i0000000000004-2-2-2-42224i−4i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000
χ644-4444i−4i-4-44i4i−4i−4i000000000000-24-2-22-422−2i2i4i−4i−2i2i−2i2i000000000000000000000000000000000000000000
χ654-4444i−4i-4-44i4i−4i−4i000000000000-2-24-222-42−2i2i−2i2i4i−4i−2i2i000000000000000000000000000000000000000000
χ664-4444i−4i-4-44i4i−4i−4i000000000000-2-2-24222-4−2i2i−2i2i−2i2i4i−4i000000000000000000000000000000000000000000
χ674-444−4i4i-4-4−4i−4i4i4i0000000000004-2-2-2-4222−4i4i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000
χ684-444−4i4i-4-4−4i−4i4i4i000000000000-24-2-22-4222i−2i−4i4i2i−2i2i−2i000000000000000000000000000000000000000000
χ694-444−4i4i-4-4−4i−4i4i4i000000000000-2-24-222-422i−2i2i−2i−4i4i2i−2i000000000000000000000000000000000000000000
χ704-444−4i4i-4-4−4i−4i4i4i000000000000-2-2-24222-42i−2i2i−2i2i−2i−4i4i000000000000000000000000000000000000000000
χ7166−3−3i3−3+3i366−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3-6-63+3i33−3i33+3i33−3i30000000000000000000000000000000000000000000000000000000000000000
χ7266−3−3i3−3+3i3-6-6−3−3i3−3+3i33+3i33−3i33+3i33−3i36-6−3−3i3−3+3i33+3i33−3i30000000000000000000000000000000000000000000000000000000000000000
χ7366−3+3i3−3−3i366−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3-6-63−3i33+3i33−3i33+3i30000000000000000000000000000000000000000000000000000000000000000
χ7466−3+3i3−3−3i3-6-6−3+3i3−3−3i33−3i33+3i33−3i33+3i36-6−3+3i3−3−3i33−3i33+3i30000000000000000000000000000000000000000000000000000000000000000
χ756-6−3−3i3−3+3i36i−6i3+3i33−3i36ζ226ζ14−6ζ22−6ζ1400000000000000000000000000000000000000000000000000002−2−i2i2−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000000
χ766-6−3−3i3−3+3i36i−6i3+3i33−3i36ζ226ζ14−6ζ22−6ζ140000000000000000000000000000000000000000000000000000−22i2−i2ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000000
χ776-6−3−3i3−3+3i3−6i6i3+3i33−3i3−6ζ22−6ζ146ζ226ζ1400000000000000000000000000000000000000000000000000002−2i2−i2−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000000
χ786-6−3−3i3−3+3i3−6i6i3+3i33−3i3−6ζ22−6ζ146ζ226ζ140000000000000000000000000000000000000000000000000000−22−i2i2ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000000
χ796-6−3+3i3−3−3i36i−6i3−3i33+3i36ζ146ζ22−6ζ14−6ζ2200000000000000000000000000000000000000000000000000002−2−i2i2ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13000000
χ806-6−3+3i3−3−3i36i−6i3−3i33+3i36ζ146ζ22−6ζ14−6ζ220000000000000000000000000000000000000000000000000000−22i2−i2−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000000
χ816-6−3+3i3−3−3i3−6i6i3−3i33+3i3−6ζ14−6ζ226ζ146ζ2200000000000000000000000000000000000000000000000000002−2i2−i2ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000000
χ826-6−3+3i3−3−3i3−6i6i3−3i33+3i3−6ζ14−6ζ226ζ146ζ220000000000000000000000000000000000000000000000000000−22−i2i2−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13000000

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