Finite Group Databasebeta

← Group #11721843

Character table — Group #11721843

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size1111112224446666666612121212121212121212121218181818181836363611111122244466666666121212121212121212121212181818181818363636
order1233664121226633336666666666661212121288242424244121222666641212266666666666666666612121212882424242441212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ3111111111-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1111111111-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1
χ4111111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ52222222222222-1-1-12-1-1-122-1-1-1-1-1-12-1-1-10000000002222222222222-1-1-12-1-1-122-1-1-1-1-1-12-1-1-1000000000
χ6222222222222-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1000000000222222222222-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1000000000
χ7222222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1000000000222222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1000000000
χ8222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12000000000222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12000000000
χ9222222222-2-2-22-1-1-12-1-1-1-2-21111112-1-1-1000000000222222222-2-2-22-1-1-12-1-1-1-2-21111112-1-1-1000000000
χ10222222222-2-2-2-12-1-1-12-1-111-2-21111-12-1-1000000000222222222-2-2-2-12-1-1-12-1-111-2-21111-12-1-1000000000
χ11222222222-2-2-2-1-12-1-1-12-11111-2-211-1-12-1000000000222222222-2-2-2-1-12-1-1-12-11111-2-211-1-12-1000000000
χ12222222222-2-2-2-1-1-12-1-1-12111111-2-2-1-1-12000000000222222222-2-2-2-1-1-12-1-1-12111111-2-2-1-1-12000000000
χ13222222-2-2-20002222222200000000-2-2-2-2000000000222222-2-2-20002222222200000000-2-2-2-2000000000
χ14222222-2-2-20002-1-1-12-1-1-100−i3i3−i3i3−i3i3-2111000000000222222-2-2-20002-1-1-12-1-1-100−i3i3−i3i3−i3i3-2111000000000
χ15222222-2-2-20002-1-1-12-1-1-100i3−i3i3−i3i3−i3-2111000000000222222-2-2-20002-1-1-12-1-1-100i3−i3i3−i3i3−i3-2111000000000
χ16222222-2-2-2000-12-1-1-12-1-1−i3i300−i3i3i3−i31-211000000000222222-2-2-2000-12-1-1-12-1-1−i3i300−i3i3i3−i31-211000000000
χ17222222-2-2-2000-12-1-1-12-1-1i3−i300i3−i3−i3i31-211000000000222222-2-2-2000-12-1-1-12-1-1i3−i300i3−i3−i3i31-211000000000
χ18222222-2-2-2000-1-12-1-1-12-1−i3i3i3−i300−i3i311-21000000000222222-2-2-2000-1-12-1-1-12-1−i3i3i3−i300−i3i311-21000000000
χ19222222-2-2-2000-1-12-1-1-12-1i3−i3−i3i300i3−i311-21000000000222222-2-2-2000-1-12-1-1-12-1i3−i3−i3i300i3−i311-21000000000
χ20222222-2-2-2000-1-1-12-1-1-12−i3i3−i3i3i3−i300111-2000000000222222-2-2-2000-1-1-12-1-1-12−i3i3−i3i3i3−i300111-2000000000
χ21222222-2-2-2000-1-1-12-1-1-12i3−i3i3−i3−i3i300111-2000000000222222-2-2-2000-1-1-12-1-1-12i3−i3i3−i3−i3i300111-2000000000
χ222-222-2-20000002222-2-2-2-2000000000000−i2i2−i2−i2i2i20002-222-2-20000002222-2-2-2-2000000000000−i2i2−i2−i2i2i2000
χ232-222-2-20000002222-2-2-2-2000000000000i2−i2i2i2−i2−i20002-222-2-20000002222-2-2-2-2000000000000i2−i2i2i2−i2−i2000
χ2433−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320000000000000000000011−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320000000000000000000011−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ2533−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i3200000000000000000000-1-11+i321−i321+i321−i32-11+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i3200000000000000000000-1-11+i321−i321+i321−i32-11+i321−i32
χ2633−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000000000000000000011−1−i32−1+i32−1−i32−1+i32-11+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000000000000000000011−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ2733−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i3200000000000000000000-1-11+i321−i321+i321−i321−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i3200000000000000000000-1-11+i321−i321+i321−i321−1−i32−1+i32
χ2833−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000000011−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000000011−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ2933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i3200000000000000000000-1-11−i321+i321−i321+i32-11−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i3200000000000000000000-1-11−i321+i321−i321+i32-11−i321+i32
χ3033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000000000000000000011−1+i32−1−i32−1+i32−1−i32-11−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000000000000000000011−1+i32−1−i32−1+i32−1−i32-11−i321+i32
χ3133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i3200000000000000000000-1-11−i321+i321−i321+i321−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i3200000000000000000000-1-11−i321+i321−i321+i321−1+i32−1−i32
χ324-444-4-40000004-2-2-2-42220000000000000000000004-444-4-40000004-2-2-2-4222000000000000000000000
χ334-444-4-4000000-24-2-22-4220000000000000000000004-444-4-4000000-24-2-22-422000000000000000000000
χ344-444-4-4000000-2-24-222-420000000000000000000004-444-4-4000000-2-24-222-42000000000000000000000
χ354-444-4-4000000-2-2-24222-40000000000000000000004-444-4-4000000-2-2-24222-4000000000000000000000
χ3666−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i30000000000000000000000000000000066−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300000000000000000000000000000000
χ3766−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i30000000000000000000000000000000066−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i300000000000000000000000000000000
χ386-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000−i2i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ230006-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000−i2i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000
χ396-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000i2−i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ230006-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000i2−i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000
χ406-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000−i2i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ130006-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000−i2i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13000
χ416-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000i2−i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ130006-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000i2−i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000
χ4211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111
χ44111111111-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111
χ45111111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1
χ462222222222222-1-1-12-1-1-122-1-1-1-1-1-12-1-1-1000000000-2-2-2-2-2-2-2-2-2-2-2-2-2111-2111-2-2111111-2111000000000
χ47222222222222-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1000000000-2-2-2-2-2-2-2-2-2-2-2-21-2111-21111-2-211111-211000000000
χ48222222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1000000000-2-2-2-2-2-2-2-2-2-2-2-211-2111-211111-2-21111-21000000000
χ49222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12000000000-2-2-2-2-2-2-2-2-2-2-2-2111-2111-2111111-2-2111-2000000000
χ50222222222-2-2-22-1-1-12-1-1-1-2-21111112-1-1-1000000000-2-2-2-2-2-2-2-2-2222-2111-211122-1-1-1-1-1-1-2111000000000
χ51222222222-2-2-2-12-1-1-12-1-111-2-21111-12-1-1000000000-2-2-2-2-2-2-2-2-22221-2111-211-1-122-1-1-1-11-211000000000
χ52222222222-2-2-2-1-12-1-1-12-11111-2-211-1-12-1000000000-2-2-2-2-2-2-2-2-222211-2111-21-1-1-1-122-1-111-21000000000
χ53222222222-2-2-2-1-1-12-1-1-12111111-2-2-1-1-12000000000-2-2-2-2-2-2-2-2-2222111-2111-2-1-1-1-1-1-122111-2000000000
χ54222222-2-2-20002222222200000000-2-2-2-2000000000-2-2-2-2-2-2222000-2-2-2-2-2-2-2-2000000002222000000000
χ55222222-2-2-20002-1-1-12-1-1-100−i3i3−i3i3−i3i3-2111000000000-2-2-2-2-2-2222000-2111-211100i3−i3i3−i3i3−i32-1-1-1000000000
χ56222222-2-2-20002-1-1-12-1-1-100i3−i3i3−i3i3−i3-2111000000000-2-2-2-2-2-2222000-2111-211100−i3i3−i3i3−i3i32-1-1-1000000000
χ57222222-2-2-2000-12-1-1-12-1-1−i3i300−i3i3i3−i31-211000000000-2-2-2-2-2-22220001-2111-211i3−i300i3−i3−i3i3-12-1-1000000000
χ58222222-2-2-2000-12-1-1-12-1-1i3−i300i3−i3−i3i31-211000000000-2-2-2-2-2-22220001-2111-211−i3i300−i3i3i3−i3-12-1-1000000000
χ59222222-2-2-2000-1-12-1-1-12-1−i3i3i3−i300−i3i311-21000000000-2-2-2-2-2-222200011-2111-21i3−i3−i3i300i3−i3-1-12-1000000000
χ60222222-2-2-2000-1-12-1-1-12-1i3−i3−i3i300i3−i311-21000000000-2-2-2-2-2-222200011-2111-21−i3i3i3−i300−i3i3-1-12-1000000000
χ61222222-2-2-2000-1-1-12-1-1-12−i3i3−i3i3i3−i300111-2000000000-2-2-2-2-2-2222000111-2111-2i3−i3i3−i3−i3i300-1-1-12000000000
χ62222222-2-2-2000-1-1-12-1-1-12i3−i3i3−i3−i3i300111-2000000000-2-2-2-2-2-2222000111-2111-2−i3i3−i3i3i3−i300-1-1-12000000000
χ632-222-2-20000002222-2-2-2-2000000000000−i2i2−i2−i2i2i2000-22-2-222000000-2-2-2-22222000000000000i2−i2i2i2−i2−i2000
χ642-222-2-20000002222-2-2-2-2000000000000i2−i2i2i2−i2−i2000-22-2-222000000-2-2-2-22222000000000000−i2i2−i2−i2i2i2000
χ6533−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320000000000000000000011−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-3-33+3i323−3i323+3i323−3i32-33+3i323−3i32-33+3i323−3i3200000000000000000000-1-11+i321−i321+i321−i32-11+i321−i32
χ6633−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i3200000000000000000000-1-11+i321−i321+i321−i32-11+i321−i32-3-33+3i323−3i323+3i323−3i32-33+3i323−3i32-33+3i323−3i320000000000000000000011−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ6733−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000000000000000000011−1−i32−1+i32−1−i32−1+i32-11+i321−i32-3-33+3i323−3i323+3i323−3i32-33+3i323−3i323−3−3i32−3+3i3200000000000000000000-1-11+i321−i321+i321−i321−1−i32−1+i32
χ6833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i3200000000000000000000-1-11+i321−i321+i321−i321−1−i32−1+i32-3-33+3i323−3i323+3i323−3i32-33+3i323−3i323−3−3i32−3+3i320000000000000000000011−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ6933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000000011−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-3-33−3i323+3i323−3i323+3i32-33−3i323+3i32-33−3i323+3i3200000000000000000000-1-11−i321+i321−i321+i32-11−i321+i32
χ7033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i3200000000000000000000-1-11−i321+i321−i321+i32-11−i321+i32-3-33−3i323+3i323−3i323+3i32-33−3i323+3i32-33−3i323+3i320000000000000000000011−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ7133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000000000000000000011−1+i32−1−i32−1+i32−1−i32-11−i321+i32-3-33−3i323+3i323−3i323+3i32-33−3i323+3i323−3+3i32−3−3i3200000000000000000000-1-11−i321+i321−i321+i321−1+i32−1−i32
χ7233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i3200000000000000000000-1-11−i321+i321−i321+i321−1+i32−1−i32-3-33−3i323+3i323−3i323+3i32-33−3i323+3i323−3+3i32−3−3i320000000000000000000011−1+i32−1−i32−1+i32−1−i32-11−i321+i32
χ734-444-4-40000004-2-2-2-4222000000000000000000000-44-4-444000000-42224-2-2-2000000000000000000000
χ744-444-4-4000000-24-2-22-422000000000000000000000-44-4-4440000002-422-24-2-2000000000000000000000
χ754-444-4-4000000-2-24-222-42000000000000000000000-44-4-44400000022-42-2-24-2000000000000000000000
χ764-444-4-4000000-2-2-24222-4000000000000000000000-44-4-444000000222-4-2-2-24000000000000000000000
χ7766−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300000000000000000000000000000000-6-63+3i33−3i33+3i33−3i36−3−3i3−3+3i300000000000000000000000000000000
χ7866−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i300000000000000000000000000000000-6-63−3i33+3i33−3i33+3i36−3+3i3−3−3i300000000000000000000000000000000
χ796-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000−i2i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000-663+3i33−3i3−3−3i3−3+3i300000000000000000000000000i2−i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000
χ806-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000i2−i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000-663+3i33−3i3−3−3i3−3+3i300000000000000000000000000−i2i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000
χ816-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000−i2i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13000-663−3i33+3i3−3+3i3−3−3i300000000000000000000000000i2−i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000
χ826-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000i2−i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000-663−3i33+3i3−3+3i3−3−3i300000000000000000000000000−i2i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13000

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