Finite Group Databasebeta

← Group #10828715

Character table — Group #10828715

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888816161616161624242424242424242424242424242424
order12222222344446661212121224444446666121212124444446121212121212121212121212121212121288242424242444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ711111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-1-1-1
χ811111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-11111
χ91111-1-111111111111111-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-111-1-1-111-1-111-1-1
χ101111-1-111111111111111-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-11-1-1111-1-111-1-111
χ111111-1-111111111111111-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-11111-111-1-1-1-1-111-1-111
χ121111-1-111111111111111-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-11-1-111111-1-111-1-1
χ131111-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-111-1-1-11111-1-1
χ141111-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-1111-1-1111-1-1-1-111
χ151111-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-111-1-1-111-111-1-1-1-111
χ161111-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-1111-1-11-1-11111-1-1
χ17222222222-2-2-2-2222-2-2-2-22-2-200002222-2-2-2-20000002-200000000000000000000000002-22-2000000000
χ18222222222-2-2-2-2222-2-2-2-22-2-200002222-2-2-2-20000002-20000000000000000000000000-22-22000000000
χ1922222222-12222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000000000
χ2022222222-12222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-211110000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000000000
χ2222222222-12222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111122-1-1-1-10000000000000000
χ23222222-2-222-2-22222-2-2-2-2-22-222-2-222-2-222-2-22-20000-2222-2-222-2-2000000000000000000000000000000
χ24222222-2-222-2-22222-2-2-2-2-22-2-2-22222-2-222-2-2-220000-22-2-222-2-222000000000000000000000000000000
χ25222222-2-22-222-22222222-2-22000022-2-2-2-222000000-2-200000000000000000000002-2-20000200000000
χ26222222-2-22-222-22222222-2-22000022-2-2-2-222000000-2-20000000000000000000000-2220000-200000000
χ27222222-2-2-12-2-22-1-1-11111-22-222-2-2-1-111-1-1112-200001-1-1-111-1-11133−3−333−3−3003−33−30000000000000000
χ28222222-2-2-12-2-22-1-1-11111-22-222-2-2-1-111-1-1112-200001-1-1-111-1-111−3−333−3−33300−33−330000000000000000
χ29222222-2-2-12-2-22-1-1-11111-22-2-2-222-1-111-1-111-2200001-111-1-111-1-133−3−333−3−300−33−330000000000000000
χ30222222-2-2-12-2-22-1-1-11111-22-2-2-222-1-111-1-111-2200001-111-1-111-1-1−3−333−3−333003−33−30000000000000000
χ312222-2-2222-2-2-2-2222-2-2-2-2-2220000-2-222-2-222000000-2200000000000000000000000002-2-22000000000
χ322222-2-2222-2-2-2-2222-2-2-2-2-2220000-2-222-2-222000000-220000000000000000000000000-222-2000000000
χ332222-2-222-12222-1-1-1-1-1-1-1-2-2-2222211-1-1-1-111-2-222-2-211-1-1-1-11111-1-1-1-111112-2-1-1110000000000000000
χ342222-2-222-12222-1-1-1-1-1-1-1-2-2-2222211-1-1-1-111-2-2-2-22211-1-1-1-111111111-1-1-1-1-2211-1-10000000000000000
χ352222-2-222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-211-1-1-1-1112222-2-2111111-1-1-1-1-1-1-1-11111-2211-1-10000000000000000
χ362222-2-222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-211-1-1-1-11122-2-222111111-1-1-1-11111-1-1-1-12-2-1-1110000000000000000
χ372222-2-2-2-222-2-22222-2-2-2-22-2222-2-2-2-2-2-22222-2200002-222-2-2-2-222000000000000000000000000000000
χ382222-2-2-2-222-2-22222-2-2-2-22-22-2-222-2-2-2-222222-200002-2-2-22222-2-2000000000000000000000000000000
χ392222-2-2-2-22-222-2222222222-20000-2-2-2-2-2-2-2-20000002200000000000000000000002-220000-200000000
χ402222-2-2-2-22-222-2222222222-20000-2-2-2-2-2-2-2-2000000220000000000000000000000-22-20000200000000
χ412222-2-2-2-2-12-2-22-1-1-111112-2222-2-21111-1-1-1-1-220000-11-1-11111-1-133−3−3−3−333003−3−330000000000000000
χ422222-2-2-2-2-12-2-22-1-1-111112-2222-2-21111-1-1-1-1-220000-11-1-11111-1-1−3−33333−3−300−333−30000000000000000
χ432222-2-2-2-2-12-2-22-1-1-111112-22-2-2221111-1-1-1-12-20000-1111-1-1-1-11133−3−3−3−33300−333−30000000000000000
χ442222-2-2-2-2-12-2-22-1-1-111112-22-2-2221111-1-1-1-12-20000-1111-1-1-1-111−3−33333−3−3003−3−330000000000000000
χ4522-2-2002-22-22-222-2-222-2-20002i−2i2i−2i002-22-200000000002i−2i2i−2i000000000000000000000000002i−2i002-200
χ4622-2-2002-22-22-222-2-222-2-20002i−2i2i−2i002-22-200000000002i−2i2i−2i00000000000000000000000000−2i2i00-2200
χ4722-2-2002-22-22-222-2-222-2-2000−2i2i−2i2i002-22-20000000000−2i2i−2i2i000000000000000000000000002i−2i00-2200
χ4822-2-2002-22-22-222-2-222-2-2000−2i2i−2i2i002-22-20000000000−2i2i−2i2i00000000000000000000000000−2i2i002-200
χ4922-2-200-222-2-2222-2-2-2-2220002i−2i−2i2i00-222-200000000002i−2i−2i2i00000000000000000000000000002i−2i002-2
χ5022-2-200-222-2-2222-2-2-2-2220002i−2i−2i2i00-222-200000000002i−2i−2i2i0000000000000000000000000000−2i2i00-22
χ5122-2-200-222-2-2222-2-2-2-222000−2i2i2i−2i00-222-20000000000−2i2i2i−2i00000000000000000000000000002i−2i00-22
χ5222-2-200-222-2-2222-2-2-2-222000−2i2i2i−2i00-222-20000000000−2i2i2i−2i0000000000000000000000000000−2i2i002-2
χ5344444444-2-4-4-4-4-2-2-222224-4-40000-2-2-2-22222000000-2200000000000000000000000000000000000000
χ54444444-4-4-2-444-4-2-2-2-2-2-2-2-4-440000-2-22222-2-20000002200000000000000000000000000000000000000
χ554444-4-444-2-4-4-4-4-2-2-22222-444000022-2-222-2-20000002-200000000000000000000000000000000000000
χ564444-4-4-4-4-2-444-4-2-2-2-2-2-2-244-4000022222222000000-2-200000000000000000000000000000000000000
χ5744-4-4004-444-44-44-4-4-4-4440000000004-4-44000000000000000000000000000000000000000000000000
χ5844-4-4004-4-24-44-4-22222-2-2000000000-222-20000000000000023−2323−23000000000000000000000000000000
χ5944-4-4004-4-24-44-4-22222-2-2000000000-222-200000000000000−2323−2323000000000000000000000000000000
χ6044-4-4004-4-2-44-44-222-2-2220004i−4i4i−4i00-22-220000000000−2i2i−2i2i0000000000000000000000000000000000
χ6144-4-4004-4-2-44-44-222-2-222000−4i4i−4i4i00-22-2200000000002i−2i2i−2i0000000000000000000000000000000000
χ6244-4-400-44444-4-44-4-444-4-4000000000-44-44000000000000000000000000000000000000000000000000
χ6344-4-400-44-244-4-4-222-2-2220000000002-22-20000000000000023−23−2323000000000000000000000000000000
χ6444-4-400-44-244-4-4-222-2-2220000000002-22-200000000000000−232323−23000000000000000000000000000000
χ6544-4-400-44-2-4-444-22222-2-20004i−4i−4i4i002-2-220000000000−2i2i2i−2i0000000000000000000000000000000000
χ6644-4-400-44-2-4-444-22222-2-2000−4i4i4i−4i002-2-2200000000002i−2i−2i2i0000000000000000000000000000000000
χ674-4-444-40040000-44-4000000000004-4000000002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ684-4-444-40040000-44-4000000000004-400000000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ694-4-444-400-200002-2223−2323−230000000-22000023−23002i−2i2i−2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ704-4-444-400-200002-2223−2323−230000000-22000023−2300−2i2i−2i2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ714-4-444-400-200002-22−2323−23230000000-220000−2323002i−2i2i−2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ724-4-444-400-200002-22−2323−23230000000-220000−232300−2i2i−2i2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ734-4-44-440040000-44-400000000000-44000000002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ744-4-44-440040000-44-400000000000-4400000000−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ754-4-44-4400-200002-2223−2323−2300000002-20000−2323002i−2i−2i2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ764-4-44-4400-200002-2223−2323−2300000002-20000−232300−2i2i2i−2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ774-4-44-4400-200002-22−2323−232300000002-2000023−23002i−2i−2i2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ784-4-44-4400-200002-22−2323−232300000002-2000023−2300−2i2i2i−2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ798-88-8000080000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-88-80000-4000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-88-80000-4000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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