Finite Group Databasebeta

← Group #10828739

Character table — Group #10828739

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888816161616161624242424242424242424242424242424
order12222234444446661212121222444446666121212124444446121212121212121212121212121212121288242424242444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ511111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11111
χ611111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1
χ711111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-111-1-1-1-1
χ811111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-111-1-11111
χ911111111-1-11111111111-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-1-111-111-1-111-1-1
χ1011111111-1-11111111111-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-1111-1-11-1-111-1-111
χ1111111111-1-11111111111-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-11111-1-1-1-1-1-11111-1-111
χ1211111111-1-11111111111-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-1111111-1-1-1-111-1-1
χ1311111111-1-11111111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-111-1-1-1-1-11111-1-1
χ1411111111-1-11111111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-11-1-111111-1-1-1-111
χ1511111111-1-11111111111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-111-11111-1-1-1-1-1-1-111
χ1611111111-1-11111111111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-11-1-1-1-11111111-1-1
χ172222222-222-2-2-2222-2-2-2-2-2-220000-2-222-2-222000000-2200000000000000000000000002-20002-2000000
χ182222222-222-2-2-2222-2-2-2-2-2-220000-2-222-2-222000000-220000000000000000000000000-22000-22000000
χ192222222-2-2-2-2-2-2222-2-2-2-222-200002222-2-2-2-20000002-200000000000000000000000002-2000-22000000
χ202222222-2-2-2-2-2-2222-2-2-2-222-200002222-2-2-2-20000002-20000000000000000000000000-220002-2000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-211110000000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111122-1-1-1-10000000000000000
χ25222222-12-2-2222-1-1-1-1-1-1-1-2-2-2222211-1-1-1-111-2-222-2-211-1-1-1-11111-1-1-1-111112-2-1-1110000000000000000
χ26222222-12-2-2222-1-1-1-1-1-1-1-2-2-2222211-1-1-1-111-2-2-2-22211-1-1-1-111111111-1-1-1-1-2211-1-10000000000000000
χ27222222-12-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-211-1-1-1-1112222-2-2111111-1-1-1-1-1-1-1-11111-2211-1-10000000000000000
χ28222222-12-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-211-1-1-1-11122-2-222111111-1-1-1-11111-1-1-1-12-2-1-1110000000000000000
χ292222-2-22222-2-22222-2-2-2-22-2-222-2-2-2-2-2-22222-2200002-222-2-222-2-2000000000000000000000000000000
χ302222-2-22222-2-22222-2-2-2-22-2-2-2-222-2-2-2-222222-200002-2-2-222-2-222000000000000000000000000000000
χ312222-2-222-2-2-2-22222-2-2-2-2-22222-2-222-2-222-2-22-20000-2222-2-2-2-222000000000000000000000000000000
χ322222-2-222-2-2-2-22222-2-2-2-2-222-2-22222-2-222-2-2-220000-22-2-22222-2-2000000000000000000000000000000
χ332222-2-22-22222-22222222-22-2000022-2-2-2-222000000-2-200000000000000000000002-220000-200000000
χ342222-2-22-22222-22222222-22-2000022-2-2-2-222000000-2-20000000000000000000000-22-20000200000000
χ352222-2-22-2-2-222-222222222-220000-2-2-2-2-2-2-2-20000002200000000000000000000002-2-20000200000000
χ362222-2-22-2-2-222-222222222-220000-2-2-2-2-2-2-2-2000000220000000000000000000000-2220000-200000000
χ372222-2-2-1222-2-22-1-1-111112-2-222-2-21111-1-1-1-1-220000-11-1-111-1-11133−3−333−3−3003−33−30000000000000000
χ382222-2-2-1222-2-22-1-1-111112-2-222-2-21111-1-1-1-1-220000-11-1-111-1-111−3−333−3−33300−33−330000000000000000
χ392222-2-2-1222-2-22-1-1-111112-2-2-2-2221111-1-1-1-12-20000-1111-1-111-1-133−3−333−3−300−33−330000000000000000
χ402222-2-2-1222-2-22-1-1-111112-2-2-2-2221111-1-1-1-12-20000-1111-1-111-1-1−3−333−3−333003−33−30000000000000000
χ412222-2-2-12-2-2-2-22-1-1-11111-22222-2-2-1-111-1-1112-200001-1-1-11111-1-133−3−3−3−333003−3−330000000000000000
χ422222-2-2-12-2-2-2-22-1-1-11111-22222-2-2-1-111-1-1112-200001-1-1-11111-1-1−3−33333−3−300−333−30000000000000000
χ432222-2-2-12-2-2-2-22-1-1-11111-222-2-222-1-111-1-111-2200001-111-1-1-1-11133−3−3−3−33300−333−30000000000000000
χ442222-2-2-12-2-2-2-22-1-1-11111-222-2-222-1-111-1-111-2200001-111-1-1-1-111−3−33333−3−3003−3−330000000000000000
χ4522-2-22-22-2002-222-2-222-2-20002i−2i2i−2i002-22-200000000002i−2i2i−2i000000000000000000000002i−2i000002-200
χ4622-2-22-22-2002-222-2-222-2-20002i−2i2i−2i002-22-200000000002i−2i2i−2i00000000000000000000000−2i2i00000-2200
χ4722-2-22-22-2002-222-2-222-2-2000−2i2i−2i2i002-22-20000000000−2i2i−2i2i000000000000000000000002i−2i00000-2200
χ4822-2-22-22-2002-222-2-222-2-2000−2i2i−2i2i002-22-20000000000−2i2i−2i2i00000000000000000000000−2i2i000002-200
χ4922-2-2-222-200-2222-2-2-2-2220002i−2i−2i2i00-222-200000000002i−2i−2i2i00000000000000000000000000002i−2i002-2
χ5022-2-2-222-200-2222-2-2-2-2220002i−2i−2i2i00-222-200000000002i−2i−2i2i0000000000000000000000000000−2i2i00-22
χ5122-2-2-222-200-2222-2-2-2-222000−2i2i2i−2i00-222-20000000000−2i2i2i−2i00000000000000000000000000002i−2i00-22
χ5222-2-2-222-200-2222-2-2-2-222000−2i2i2i−2i00-222-20000000000−2i2i2i−2i0000000000000000000000000000−2i2i002-2
χ53444444-2-444-4-4-4-2-2-22222-4-44000022-2-222-2-20000002-200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2222244-40000-2-2-2-22222000000-2200000000000000000000000000000000000000
χ554444-4-4-2-44444-4-2-2-2-2-2-2-2-44-40000-2-22222-2-20000002200000000000000000000000000000000000000
χ564444-4-4-2-4-4-444-4-2-2-2-2-2-2-24-44000022222222000000-2-200000000000000000000000000000000000000
χ5744-4-44-44400-44-44-4-4-4-4440000000004-4-44000000000000000000000000000000000000000000000000
χ5844-4-44-4-2400-44-4-22222-2-2000000000-222-20000000000000023−2323−23000000000000000000000000000000
χ5944-4-44-4-2400-44-4-22222-2-2000000000-222-200000000000000−2323−2323000000000000000000000000000000
χ6044-4-44-4-2-4004-44-222-2-2220004i−4i4i−4i00-22-220000000000−2i2i−2i2i0000000000000000000000000000000000
χ6144-4-44-4-2-4004-44-222-2-222000−4i4i−4i4i00-22-2200000000002i−2i2i−2i0000000000000000000000000000000000
χ6244-4-4-4444004-4-44-4-444-4-4000000000-44-44000000000000000000000000000000000000000000000000
χ6344-4-4-44-24004-4-4-222-2-2220000000002-22-20000000000000023−23−2323000000000000000000000000000000
χ6444-4-4-44-24004-4-4-222-2-2220000000002-22-200000000000000−232323−23000000000000000000000000000000
χ6544-4-4-44-2-400-444-22222-2-20004i−4i−4i4i002-2-220000000000−2i2i2i−2i0000000000000000000000000000000000
χ6644-4-4-44-2-400-444-22222-2-2000−4i4i4i−4i002-2-2200000000002i−2i−2i2i0000000000000000000000000000000000
χ674-4-4400404i−4i000-44-4000000000000000004i−4i002i−2i2-200000000002i−2i2i−2i2-22-20000000000000000000000
χ684-4-4400404i−4i000-44-4000000000000000004i−4i00−2i2i-220000000000−2i2i−2i2i-22-220000000000000000000000
χ694-4-440040−4i4i000-44-400000000000000000−4i4i002i−2i-2200000000002i−2i2i−2i-22-220000000000000000000000
χ704-4-440040−4i4i000-44-400000000000000000−4i4i00−2i2i2-20000000000−2i2i−2i2i2-22-20000000000000000000000
χ714-4-4400-204i−4i0002-2223−2323−230000000−2i32i30000−2i2i002i−2i2-20000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−1−31+3−1+31−30000000000000000000000
χ724-4-4400-204i−4i0002-2223−2323−230000000−2i32i30000−2i2i00−2i2i-220000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ111+3−1−31−3−1+30000000000000000000000
χ734-4-4400-204i−4i0002-22−2323−232300000002i3−2i30000−2i2i002i−2i2-20000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−1+31−3−1−31+30000000000000000000000
χ744-4-4400-204i−4i0002-22−2323−232300000002i3−2i30000−2i2i00−2i2i-220000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ111−3−1+31+3−1−30000000000000000000000
χ754-4-4400-20−4i4i0002-2223−2323−2300000002i3−2i300002i−2i002i−2i-220000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ111+3−1−31−3−1+30000000000000000000000
χ764-4-4400-20−4i4i0002-2223−2323−2300000002i3−2i300002i−2i00−2i2i2-20000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−1−31+3−1+31−30000000000000000000000
χ774-4-4400-20−4i4i0002-22−2323−23230000000−2i32i300002i−2i002i−2i-220000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ111−3−1+31+3−1−30000000000000000000000
χ784-4-4400-20−4i4i0002-22−2323−23230000000−2i32i300002i−2i00−2i2i2-20000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−1+31−3−1−31+30000000000000000000000
χ798-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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