Finite Group Databasebeta

← Group #10828065

Character table — Group #10828065

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888816161616161624242424242424242424242424242424
order1222222234444666121212122224444666612121212244444666661212121212121212121212121288242424242224444444448888
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
χ5111111111111111111111-1-111-1-111111111-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ6111111111111111111111-1-111-1-111111111-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ7111111111111111111111-1-111-1-111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111
χ8111111111111111111111-1-111-1-111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1
χ91111-1-111111111111111-111-1-111-1-11111-1-1-1-111-1-1-111-1-1-111-1-11111-1-1-1-11-111-1-11111-1-1-1-111-1-111-1-1
χ101111-1-111111111111111-111-1-111-1-11111-1-1-1-111-1-1-111-1-1-111-1-11111-1-1-1-11-111-1-1-1-1-1-11111-1-111-1-111
χ111111-1-111111111111111-111-1-111-1-11111-1-1-1-1-1-111-111-1-1-111-1-1-1-1-1-11111-11-1-1111111-1-1-1-1-1-111-1-111
χ121111-1-111111111111111-111-1-111-1-11111-1-1-1-1-1-111-111-1-1-111-1-1-1-1-1-11111-11-1-111-1-1-1-1111111-1-111-1-1
χ131111-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-111
χ141111-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-1-1-1111111-1-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1
χ151111-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-111-1-1-111-1-1-1-111111-111-1-111-1-1-1-111-1-11111-1-1
χ161111-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-111-1-1-111-1-1-1-111111-111-1-1-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-2222-2-2-2-2200-2-2002222-2-2-2-200000020000-20000000000000000002-2002-20000000000
χ18222222222-2-2-2-2222-2-2-2-2200-2-2002222-2-2-2-200000020000-2000000000000000000-2200-220000000000
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
χ2122222222-12222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-2-22222-11111-11111-1-1-1-1-1-1-1-1-2-211110000000000000000
χ2222222222-12222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-11111-111111111111122-1-1-1-10000000000000000
χ23222222-2-222-2-22222-2-2-2-2-2222-2-2-222-2-222-2-22-20000-222222-2-2-2-2000000000000000000000000000000
χ24222222-2-222-2-22222-2-2-2-2-2-2-22-22222-2-222-2-2-220000-2-2-2-2-222222000000000000000000000000000000
χ25222222-2-22-222-22222222-200-220022-2-2-2-222000000-20000-2000000000000000000002-2002-200000000
χ26222222-2-22-222-22222222-200-220022-2-2-2-222000000-20000-200000000000000000000-2200-2200000000
χ27222222-2-2-12-2-22-1-1-11111-2222-2-2-2-1-111-1-1112-200001-1-1-1-1-1111133−3−333−3−3003−33−30000000000000000
χ28222222-2-2-12-2-22-1-1-11111-2222-2-2-2-1-111-1-1112-200001-1-1-1-1-11111−3−333−3−33300−33−330000000000000000
χ29222222-2-2-12-2-22-1-1-11111-2-2-22-222-1-111-1-111-22000011111-1-1-1-1-133−3−333−3−300−33−330000000000000000
χ30222222-2-2-12-2-22-1-1-11111-2-2-22-222-1-111-1-111-22000011111-1-1-1-1-1−3−333−3−333003−33−30000000000000000
χ312222-2-2222-2-2-2-2222-2-2-2-2-2002200-2-222-2-222000000-2000020000000000000000002-200-220000000000
χ322222-2-2222-2-2-2-2222-2-2-2-2-2002200-2-222-2-222000000-200002000000000000000000-22002-20000000000
χ332222-2-222-12222-1-1-1-1-1-1-1-222-2-22211-1-1-1-111-2-222-2-21-1-1111-1-111-1-1-1-111112-2-1-1110000000000000000
χ342222-2-222-12222-1-1-1-1-1-1-1-222-2-22211-1-1-1-111-2-2-2-2221-1-1111-1-1111111-1-1-1-1-2211-1-10000000000000000
χ352222-2-222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-211-1-1-1-1112222-2-2111-1-1111-1-1-1-1-1-11111-2211-1-10000000000000000
χ362222-2-222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-211-1-1-1-11122-2-222111-1-1111-1-11111-1-1-1-12-2-1-1110000000000000000
χ372222-2-2-2-222-2-22222-2-2-2-2222-22-2-2-2-2-2-22222-220000222-2-2-2-2-222000000000000000000000000000000
χ382222-2-2-2-222-2-22222-2-2-2-22-2-2-2222-2-2-2-222222-200002-2-222-222-2-2000000000000000000000000000000
χ392222-2-2-2-22-222-222222222002-200-2-2-2-2-2-2-2-2000000200002000000000000000000002-200-2200000000
χ402222-2-2-2-22-222-222222222002-200-2-2-2-2-2-2-2-200000020000200000000000000000000-22002-200000000
χ412222-2-2-2-2-12-2-22-1-1-11111222-22-2-21111-1-1-1-1-220000-1-1-111111-1-133−3−3−3−333003−3−330000000000000000
χ422222-2-2-2-2-12-2-22-1-1-11111222-22-2-21111-1-1-1-1-220000-1-1-111111-1-1−3−33333−3−300−333−30000000000000000
χ432222-2-2-2-2-12-2-22-1-1-111112-2-2-22221111-1-1-1-12-20000-111-1-11-1-11133−3−3−3−33300−333−30000000000000000
χ442222-2-2-2-2-12-2-22-1-1-111112-2-2-22221111-1-1-1-12-20000-111-1-11-1-111−3−33333−3−3003−3−330000000000000000
χ4522-2-2002-2222-2-2-2-2222-2-202-2002-2002-22-20000000002-20002-2000000000000000000000000002i−2i002i−2i
χ4622-2-2002-2222-2-2-2-2222-2-202-2002-2002-22-20000000002-20002-200000000000000000000000000−2i2i00−2i2i
χ4722-2-2002-2222-2-2-2-2222-2-20-2200-22002-22-2000000000-22000-22000000000000000000000000002i−2i00−2i2i
χ4822-2-2002-2222-2-2-2-2222-2-20-2200-22002-22-2000000000-22000-2200000000000000000000000000−2i2i002i−2i
χ4922-2-200-2222-22-2-2-22-2-22202-200-2200-222-20000000002-2000-220000000000000000000000002i−2i002i−2i00
χ5022-2-200-2222-22-2-2-22-2-22202-200-2200-222-20000000002-2000-22000000000000000000000000−2i2i00−2i2i00
χ5122-2-200-2222-22-2-2-22-2-2220-22002-200-222-2000000000-220002-20000000000000000000000002i−2i00−2i2i00
χ5222-2-200-2222-22-2-2-22-2-2220-22002-200-222-2000000000-220002-2000000000000000000000000−2i2i002i−2i00
χ5344444444-2-4-4-4-4-2-2-22222400-4-400-2-2-2-22222000000-2000020000000000000000000000000000000000
χ54444444-4-4-2-444-4-2-2-2-2-2-2-2-400-4400-2-22222-2-20000002000020000000000000000000000000000000000
χ554444-4-444-2-4-4-4-4-2-2-22222-400440022-2-222-2-200000020000-20000000000000000000000000000000000
χ564444-4-4-4-4-2-444-4-2-2-2-2-2-2-24004-40022222222000000-20000-20000000000000000000000000000000000
χ5744-4-4004-44-4-444-4-44-4-4440000000004-4-44000000000000000000000000000000000000000000000000
χ5844-4-4004-4-244-4-422-2-2-22204-4004-400-22-22000000000-22000-2200000000000000000000000000000000
χ5944-4-4004-4-244-4-422-2-2-2220-4400-4400-22-220000000002-20002-200000000000000000000000000000000
χ6044-4-4004-4-2-4-44422-222-2-2000000000-222-200000000000−2i32i3000−2i32i3000000000000000000000000000000
χ6144-4-4004-4-2-4-44422-222-2-2000000000-222-2000000000002i3−2i30002i3−2i3000000000000000000000000000000
χ6244-4-400-444-44-44-4-4444-4-4000000000-44-44000000000000000000000000000000000000000000000000
χ6344-4-400-44-24-44-422-222-2-204-400-44002-2-22000000000-220002-200000000000000000000000000000000
χ6444-4-400-44-24-44-422-222-2-20-44004-4002-2-220000000002-2000-2200000000000000000000000000000000
χ6544-4-400-44-2-44-4422-2-2-2220000000002-22-200000000000−2i32i30002i3−2i3000000000000000000000000000000
χ6644-4-400-44-2-44-4422-2-2-2220000000002-22-2000000000002i3−2i3000−2i32i3000000000000000000000000000000
χ674-44-44-400400004-4-4000000000004-4000000002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ684-44-44-400400004-4-4000000000004-400000000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ694-44-44-400-20000-22223−2323−230000000-22000023−23002i−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
χ704-44-44-400-20000-22223−2323−230000000-22000023−2300−2i2i−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
χ714-44-44-400-20000-222−2323−23230000000-220000−2323002i−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
χ724-44-44-400-20000-222−2323−23230000000-220000−232300−2i2i−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
χ734-44-4-4400400004-4-400000000000-44000000002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ744-44-4-4400400004-4-400000000000-4400000000−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ754-44-4-4400-20000-22223−2323−2300000002-20000−2323002i−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
χ764-44-4-4400-20000-22223−2323−2300000002-20000−232300−2i2i2i−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
χ774-44-4-4400-20000-222−2323−232300000002-2000023−23002i−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
χ784-44-4-4400-20000-222−2323−232300000002-2000023−2300−2i2i2i−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
χ798-8-88000080000-88-800000000000000000000000000000000000000000000000000000000000000000
χ808-8-880000-400004-4443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-8-880000-400004-44−434343−430000000000000000000000000000000000000000000000000000000000000

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