Finite Group Databasebeta

← Group #10829796

Character table — Group #10829796

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888816161616161624242424242424242424242424242424
order122222344444466612121212444444466121212121212244444661212121212121212121212121212121288242424242244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111-1-111-1-111111111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ6111111111111111111111-1-111-1-111111111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1
χ8111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111
χ91111111-1-111111111111-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11-111-1-11-11-11111-1-1-1-111-1-1
χ101111111-1-111111111111-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11-111-1-1-11-11-1-1-1-11111-1-111
χ111111111-1-111111111111-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-11-1-1111-11-1-1-111-1-111-1-111
χ121111111-1-111111111111-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-11-1-111-11-1111-1-111-1-111-1-1
χ131111111-1-111111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-11-1-1111-11-1-1-1-1-1111111-1-1
χ141111111-1-111111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-11-111111-1-1-1-1-1-111
χ151111111-1-111111111111-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-11-11-111-1-111-1-1-1-111
χ161111111-1-111111111111-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-1-11-11-1-111-1-11111-1-1
χ17222222222-2-2-2-2222-2-2-2-2200-2-20022-2-222-2-2000000002-2000000000000000000000000002-22-2000000
χ18222222222-2-2-2-2222-2-2-2-2200-2-20022-2-222-2-2000000002-200000000000000000000000000-22-22000000
χ192222222-2-2-2-2-2-2222-2-2-2-2-200220022-2-2-2-22200000000-22000000000000000000000000002-2-22000000
χ202222222-2-2-2-2-2-2222-2-2-2-2-200220022-2-2-2-22200000000-2200000000000000000000000000-222-2000000
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
χ23222222-1222222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-2-2222211-1-1111111-1-1-1-1-1-1-1-1-2-211110000000000000000
χ24222222-1222222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-211-1-11111111111111122-1-1-1-10000000000000000
χ25222222-1-2-22222-1-1-1-1-1-1-1-222-2-222-1-1-1-11111-2-222-2-21111-1-1-1-111-1-1-1-111112-2-1-1110000000000000000
χ26222222-1-2-22222-1-1-1-1-1-1-1-222-2-222-1-1-1-11111-2-2-2-2221111-1-1-1-1111111-1-1-1-1-2211-1-10000000000000000
χ27222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-1-1-111112222-2-2-1-1111111-1-1-1-1-1-11111-2211-1-10000000000000000
χ28222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-1-1-1111122-2-222-1-1111111-1-11111-1-1-1-12-2-1-1110000000000000000
χ292222-2-222222-2-22222222-2002-200-2-2-2-2222200000000-2-20000000000000000000022-2-2000000000000
χ302222-2-222222-2-22222222-2002-200-2-2-2-2222200000000-2-200000000000000000000-2-222000000000000
χ312222-2-2222-2-222222-2-2-2-2-222-22-2-2-2-22222-2-22-2000022-2222-2-2-2-2000000000000000000000000000000
χ322222-2-2222-2-222222-2-2-2-2-2-2-2-2222-2-22222-2-2-220000-2-2-22-2-22222000000000000000000000000000000
χ332222-2-22-2-222-2-22222222200-2200-2-2-2-2-2-2-2-20000000022000000000000000000002-2-22000000000000
χ342222-2-22-2-222-2-22222222200-2200-2-2-2-2-2-2-2-2000000002200000000000000000000-222-2000000000000
χ352222-2-22-2-2-2-222222-2-2-2-22222-2-2-2-2-222-2-222-220000-2-22-222-2-222000000000000000000000000000000
χ362222-2-22-2-2-2-222222-2-2-2-22-2-22-222-2-222-2-2222-20000222-2-2-222-2-2000000000000000000000000000000
χ372222-2-2-122-2-222-1-1-11111-222-22-2-211-1-1-1-1112-20000-1-11-1-1-1111133−3−333−3−3003−33−30000000000000000
χ382222-2-2-122-2-222-1-1-11111-222-22-2-211-1-1-1-1112-20000-1-11-1-1-11111−3−333−3−33300−33−330000000000000000
χ392222-2-2-122-2-222-1-1-11111-2-2-2-222211-1-1-1-111-220000111-111-1-1-1-133−3−333−3−300−33−330000000000000000
χ402222-2-2-122-2-222-1-1-11111-2-2-2-222211-1-1-1-111-220000111-111-1-1-1-1−3−333−3−333003−33−30000000000000000
χ412222-2-2-1-2-2-2-222-1-1-111112222-2-2-211-1-111-1-1-22000011-11-1-111-1-133−3−3−3−333003−3−330000000000000000
χ422222-2-2-1-2-2-2-222-1-1-111112222-2-2-211-1-111-1-1-22000011-11-1-111-1-1−3−33333−3−300−333−30000000000000000
χ432222-2-2-1-2-2-2-222-1-1-111112-2-22-22211-1-111-1-12-20000-1-1-1111-1-11133−3−3−3−33300−333−30000000000000000
χ442222-2-2-1-2-2-2-222-1-1-111112-2-22-22211-1-111-1-12-20000-1-1-1111-1-111−3−33333−3−3003−3−330000000000000000
χ452-22-22-2200-222-22-2-2-2-22202i−2i002i−2i2-22-2000000000000002i−2i2i−2i000000000000000000002-20000002i−2i00
χ462-22-22-2200-222-22-2-2-2-22202i−2i002i−2i2-22-2000000000000002i−2i2i−2i00000000000000000000-22000000−2i2i00
χ472-22-22-2200-222-22-2-2-2-2220−2i2i00−2i2i2-22-200000000000000−2i2i−2i2i000000000000000000002-2000000−2i2i00
χ482-22-22-2200-222-22-2-2-2-2220−2i2i00−2i2i2-22-200000000000000−2i2i−2i2i00000000000000000000-220000002i−2i00
χ492-22-2-222002-22-22-2-222-2-202i−2i00−2i2i-222-2000000000000002i−2i−2i2i000000000000000000000000002i−2i002-2
χ502-22-2-222002-22-22-2-222-2-202i−2i00−2i2i-222-2000000000000002i−2i−2i2i00000000000000000000000000−2i2i00-22
χ512-22-2-222002-22-22-2-222-2-20−2i2i002i−2i-222-200000000000000−2i2i2i−2i000000000000000000000000002i−2i00-22
χ522-22-2-222002-22-22-2-222-2-20−2i2i002i−2i-222-200000000000000−2i2i2i−2i00000000000000000000000000−2i2i002-2
χ53444444-244-4-4-4-4-2-2-22222400-4-400-2-222-2-22200000000-22000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-22222-4004400-2-22222-2-2000000002-2000000000000000000000000000000000000
χ554444-4-4-24444-4-4-2-2-2-2-2-2-2-4004-4002222-2-2-2-20000000022000000000000000000000000000000000000
χ564444-4-4-2-4-444-4-4-2-2-2-2-2-2-2400-44002222222200000000-2-2000000000000000000000000000000000000
χ5744-4-40044-40000-44-40000000000000004-400002-22-200000000002-22-22-22-20000000000000000000000
χ5844-4-40044-40000-44-40000000000000004-40000-22-220000000000-22-22-22-220000000000000000000000
χ5944-4-4004-440000-44-4000000000000000-4400002-2-2200000000002-22-2-22-220000000000000000000000
χ6044-4-4004-440000-44-4000000000000000-440000-222-20000000000-22-222-22-20000000000000000000000
χ6144-4-400-24-400002-2223−2323−2300000000000-2223−23002-22-20000000000−1+31−3−1−31+3−1+31−3−1−31+30000000000000000000000
χ6244-4-400-24-400002-2223−2323−2300000000000-2223−2300-22-2200000000001−3−1+31+3−1−31−3−1+31+3−1−30000000000000000000000
χ6344-4-400-24-400002-22−2323−232300000000000-22−2323002-22-20000000000−1−31+3−1+31−3−1−31+3−1+31−30000000000000000000000
χ6444-4-400-24-400002-22−2323−232300000000000-22−232300-22-2200000000001+3−1−31−3−1+31+3−1−31−3−1+30000000000000000000000
χ6544-4-400-2-4400002-2223−2323−23000000000002-2−2323002-2-220000000000−1+31−3−1−31+31−3−1+31+3−1−30000000000000000000000
χ6644-4-400-2-4400002-2223−2323−23000000000002-2−232300-222-200000000001−3−1+31+3−1−3−1+31−3−1−31+30000000000000000000000
χ6744-4-400-2-4400002-22−2323−2323000000000002-223−23002-2-220000000000−1−31+3−1+31−31+3−1−31−3−1+30000000000000000000000
χ6844-4-400-2-4400002-22−2323−2323000000000002-223−2300-222-200000000001+3−1−31−3−1+3−1−31+3−1+31−30000000000000000000000
χ694-44-44-44004-4-444-4-444-4-400000004-4-4400000000000000000000000000000000000000000000000000
χ704-44-44-4-2004-4-44-222-2-2220000000-222-20000000000−2i32i3000000−2i32i3000000000000000000000000000000
χ714-44-44-4-2004-4-44-222-2-2220000000-222-200000000002i3−2i30000002i3−2i3000000000000000000000000000000
χ724-44-44-4-200-444-4-22222-2-204i−4i004i−4i-22-2200000000000000−2i2i−2i2i00000000000000000000000000000000
χ734-44-44-4-200-444-4-22222-2-20−4i4i00−4i4i-22-22000000000000002i−2i2i−2i00000000000000000000000000000000
χ744-44-4-44400-44-444-4-4-4-4440000000-44-4400000000000000000000000000000000000000000000000000
χ754-44-4-44-2004-44-4-222-2-22204i−4i00−4i4i2-2-2200000000000000−2i2i2i−2i00000000000000000000000000000000
χ764-44-4-44-2004-44-4-222-2-2220−4i4i004i−4i2-2-22000000000000002i−2i−2i2i00000000000000000000000000000000
χ774-44-4-44-200-44-44-22222-2-200000002-22-20000000000−2i32i30000002i3−2i3000000000000000000000000000000
χ784-44-4-44-200-44-44-22222-2-200000002-22-200000000002i3−2i3000000−2i32i3000000000000000000000000000000
χ798-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).