Finite Group Databasebeta

← Group #11721794

Character table — Group #11721794

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size111111222222222444444666666669999991212121212121212121212121818181818181818182424242424242424363636363636
order1233664881212242424242266663333666644121212121212121224242424242424242668824242424666666664412121212
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111-1-1-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111-1-111-1-1-1-11-111-1-1111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ61111111-1-111-1-1-1-11-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-11-1-111
χ71111111-1-111-1-1-1-1-11-1-111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-11-1-111
χ81111111-1-111-1-1-1-1-11-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
χ92222222222222222222222-1-1-12-1-1-10000002-1-1-122-1-1-1-1-1-10000000002-1-1-12-1-1-1000000
χ10222222222222222222222-12-1-1-12-1-1000000-12-1-1-1-122-1-1-1-1000000000-12-1-1-12-1-1000000
χ11222222222222222222222-1-12-1-1-12-1000000-1-12-1-1-1-1-122-1-1000000000-1-12-1-1-12-1000000
χ12222222222222222222222-1-1-12-1-1-12000000-1-1-12-1-1-1-1-1-122000000000-1-1-12-1-1-12000000
χ13222222222222222-2-2-2-2-2-22-1-1-12-1-1-10000002-1-1-122-1-1-1-1-1-1000000000-2111-2111000000
χ14222222222222222-2-2-2-2-2-2-12-1-1-12-1-1000000-12-1-1-1-122-1-1-1-10000000001-2111-211000000
χ15222222222222222-2-2-2-2-2-2-1-12-1-1-12-1000000-1-12-1-1-1-1-122-1-100000000011-2111-21000000
χ16222222222222222-2-2-2-2-2-2-1-1-12-1-1-12000000-1-1-12-1-1-1-1-1-122000000000111-2111-2000000
χ172222222-2-222-2-2-2-22-222-2-22-1-1-12-1-1-10000002-1-1-1-2-21111110000000002-1-1-1-2111000000
χ182222222-2-222-2-2-2-22-222-2-2-12-1-1-12-1-1000000-12-1-111-2-21111000000000-12-1-11-211000000
χ192222222-2-222-2-2-2-22-222-2-2-1-12-1-1-12-1000000-1-12-11111-2-211000000000-1-12-111-21000000
χ202222222-2-222-2-2-2-22-222-2-2-1-1-12-1-1-12000000-1-1-12111111-2-2000000000-1-1-12111-2000000
χ212222222-2-222-2-2-2-2-22-2-2222-1-1-12-1-1-10000002-1-1-1-2-2111111000000000-21112-1-1-1000000
χ222222222-2-222-2-2-2-2-22-2-222-12-1-1-12-1-1000000-12-1-111-2-211110000000001-211-12-1-1000000
χ232222222-2-222-2-2-2-2-22-2-222-1-12-1-1-12-1000000-1-12-11111-2-21100000000011-21-1-12-1000000
χ242222222-2-222-2-2-2-2-22-2-222-1-1-12-1-1-12000000-1-1-12111111-2-2000000000111-2-1-1-12000000
χ25222222-200-2-2000000000022222222222222-2-2-2-200000000-2-2-200000000000000000000
χ26222222-200-2-2000000000022222222-2-2-2-2-2-2-2-2-2-20000000022200000000000000000000
χ272-222-2-202−20022−2−20000002222-2-2-2-22i−2i2i2i−2i−2i00002−22−22−22−2000−i2i2−i2−i2i2i200000000000000
χ282-222-2-202−20022−2−20000002222-2-2-2-2−2i2i−2i−2i2i2i00002−22−22−22−2000i2−i2i2i2−i2−i200000000000000
χ292-222-2-20−2200−2−2220000002222-2-2-2-22i−2i2i2i−2i−2i0000−22−22−22−22000i2−i2i2i2−i2−i200000000000000
χ302-222-2-20−2200−2−2220000002222-2-2-2-2−2i2i−2i−2i2i2i0000−22−22−22−22000−i2i2−i2−i2i2i200000000000000
χ3133−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i320000000000001−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i320000000011−1−i32−1+i32−1−i32−1+i32
χ3233−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i32000000000000-11+i321−i32-1-11+i321−i321+i321−i3200000000-1-11+i321−i321+i321−i32
χ3333−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320000000011−1−i32−1+i32−1−i32−1+i320000000000001−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3200000000-1-11+i321−i321+i321−i32
χ3433−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i3200000000-1-11+i321−i321+i321−i32000000000000-11+i321−i32-1-11+i321−i321+i321−i320000000011−1−i32−1+i32−1−i32−1+i32
χ3533−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i320000000011−1−i32−1+i32−1−i32−1+i320000000000001−1−i32−1+i32-1-11+i321−i321+i321−i32000000001-1−1−i32−1+i321+i321−i32
χ3633−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3200000000-1-11+i321−i321+i321−i32000000000000-11+i321−i3211−1−i32−1+i32−1−i32−1+i3200000000-111+i321−i32−1−i32−1+i32
χ3733−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i320000000011−1−i32−1+i32−1−i32−1+i320000000000001−1−i32−1+i32-1-11+i321−i321+i321−i3200000000-111+i321−i32−1−i32−1+i32
χ3833−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i3200000000-1-11+i321−i321+i321−i32000000000000-11+i321−i3211−1−i32−1+i32−1−i32−1+i32000000001-1−1−i32−1+i321+i321−i32
χ3933−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i320000000000001−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i320000000011−1+i32−1−i32−1+i32−1−i32
χ4033−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i32000000000000-11−i321+i32-1-11−i321+i321−i321+i3200000000-1-11−i321+i321−i321+i32
χ4133−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320000000011−1+i32−1−i32−1+i32−1−i320000000000001−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3200000000-1-11−i321+i321−i321+i32
χ4233−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i3200000000-1-11−i321+i321−i321+i32000000000000-11−i321+i32-1-11−i321+i321−i321+i320000000011−1+i32−1−i32−1+i32−1−i32
χ4333−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i320000000011−1+i32−1−i32−1+i32−1−i320000000000001−1+i32−1−i32-1-11−i321+i321−i321+i32000000001-1−1+i32−1−i321−i321+i32
χ4433−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i3200000000-1-11−i321+i321−i321+i32000000000000-11−i321+i3211−1+i32−1−i32−1+i32−1−i3200000000-111−i321+i32−1+i32−1−i32
χ4533−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-333−3i323+3i32−3+3i32−3−3i320000000011−1+i32−1−i32−1+i32−1−i320000000000001−1+i32−1−i32-1-11−i321+i321−i321+i3200000000-111−i321+i32−1+i32−1−i32
χ4633−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-333−3i323+3i32−3+3i32−3−3i3200000000-1-11−i321+i321−i321+i32000000000000-11−i321+i3211−1+i32−1−i32−1+i32−1−i32000000001-1−1+i32−1−i321−i321+i32
χ47444444-400-4-400000000004-2-2-24-2-2-2000000-42220000000000000000000000000000000
χ48444444-400-4-40000000000-24-2-2-24-2-20000002-4220000000000000000000000000000000
χ49444444-400-4-40000000000-2-24-2-2-24-200000022-420000000000000000000000000000000
χ50444444-400-4-40000000000-2-2-24-2-2-24000000222-40000000000000000000000000000000
χ514-444-4-4022−22002222−22−220000004-2-2-2-4222000000000022−22−22−22−2200000000000000000000000
χ524-444-4-4022−22002222−22−22000000-24-2-22-4220000000000−2222−22−22−2200000000000000000000000
χ534-444-4-4022−22002222−22−22000000-2-24-222-420000000000−22−2222−22−2200000000000000000000000
χ544-444-4-4022−22002222−22−22000000-2-2-24222-40000000000−22−22−2222−2200000000000000000000000
χ554-444-4-40−222200−22−2222220000004-2-2-2-42220000000000−22222−22−22−200000000000000000000000
χ564-444-4-40−222200−22−222222000000-24-2-22-42200000000002−2−22222−22−200000000000000000000000
χ574-444-4-40−222200−22−222222000000-2-24-222-4200000000002−22−2−22222−200000000000000000000000
χ584-444-4-40−222200−22−222222000000-2-2-24222-400000000002−22−22−2−222200000000000000000000000
χ5966−3−3i3−3+3i3−3−3i3−3+3i3-6003+3i33−3i300000000000000000022−1−i3−1+i3−1−i3−1+i3000000000000-21+i31−i300000000000000000000
χ6066−3−3i3−3+3i3−3−3i3−3+3i3-6003+3i33−3i3000000000000000000-2-21+i31−i31+i31−i30000000000002−1−i3−1+i300000000000000000000
χ6166−3+3i3−3−3i3−3+3i3−3−3i3-6003−3i33+3i300000000000000000022−1+i3−1−i3−1+i3−1−i3000000000000-21−i31+i300000000000000000000
χ6266−3+3i3−3−3i3−3+3i3−3−3i3-6003−3i33+3i3000000000000000000-2-21−i31+i31−i31+i30000000000002−1+i3−1−i300000000000000000000
χ636-6−3−3i3−3+3i33+3i33−3i3032−3200−3ζ7+3ζ133ζ5−3ζ233ζ7−3ζ13−3ζ5+3ζ23000000000000002i−2i2ζ222ζ14−2ζ22−2ζ14000000000000000−i2i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ2300000000000000
χ646-6−3−3i3−3+3i33+3i33−3i3032−3200−3ζ7+3ζ133ζ5−3ζ233ζ7−3ζ13−3ζ5+3ζ2300000000000000−2i2i−2ζ22−2ζ142ζ222ζ14000000000000000i2−i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ2300000000000000
χ656-6−3−3i3−3+3i33+3i33−3i30−3232003ζ7−3ζ13−3ζ5+3ζ23−3ζ7+3ζ133ζ5−3ζ23000000000000002i−2i2ζ222ζ14−2ζ22−2ζ14000000000000000i2−i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ2300000000000000
χ666-6−3−3i3−3+3i33+3i33−3i30−3232003ζ7−3ζ13−3ζ5+3ζ23−3ζ7+3ζ133ζ5−3ζ2300000000000000−2i2i−2ζ22−2ζ142ζ222ζ14000000000000000−i2i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ2300000000000000
χ676-6−3+3i3−3−3i33−3i33+3i3032−32003ζ5−3ζ23−3ζ7+3ζ13−3ζ5+3ζ233ζ7−3ζ13000000000000002i−2i2ζ142ζ22−2ζ14−2ζ22000000000000000−i2i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ1300000000000000
χ686-6−3+3i3−3−3i33−3i33+3i3032−32003ζ5−3ζ23−3ζ7+3ζ13−3ζ5+3ζ233ζ7−3ζ1300000000000000−2i2i−2ζ14−2ζ222ζ142ζ22000000000000000i2−i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ1300000000000000
χ696-6−3+3i3−3−3i33−3i33+3i30−323200−3ζ5+3ζ233ζ7−3ζ133ζ5−3ζ23−3ζ7+3ζ13000000000000002i−2i2ζ142ζ22−2ζ14−2ζ22000000000000000i2−i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ1300000000000000
χ706-6−3+3i3−3−3i33−3i33+3i30−323200−3ζ5+3ζ233ζ7−3ζ133ζ5−3ζ23−3ζ7+3ζ1300000000000000−2i2i−2ζ14−2ζ222ζ142ζ22000000000000000−i2i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ1300000000000000

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