Finite Group Databasebeta

← Group #10828723

Character table — Group #10828723

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11112222222222222222444444444448888888888888888888888888888881212121216161616242424242424242424244848
order1222222234444666121212122446666121212122444444468888121212121212121212242424242424242444446121212444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111
χ61111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-11-1-11111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ91111-1-111111111111111-1-1-1-1-11111-1-11-11-111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-11111-1-11-1
χ101111-1-111111111111111-1-1-1-1-11111-1-11-11-111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-11
χ111111-1-111111111111111-1-1-1-1-11111-1-11-11-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-1111111111-1-11-1-1-1-111-1-111-11
χ121111-1-111111111111111-1-1-1-1-11111-1-11-11-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111111-1-111-1-11-1
χ131111-1-111111111111111-1-1-1-1-11111-1-1-11-1111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111111111-111-1-111-1-1-1-1-1111-1
χ141111-1-111111111111111-1-1-1-1-11111-1-1-11-1111-1-1-1-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-11-1-111111-1-1-11
χ151111-1-111111111111111-1-1-1-1-11111-1-1-11-11-1-111-111-1-1-1-1-1-1-111111111-1-1-1-11111-111-1-111-1-1-111-1-1-11
χ161111-1-111111111111111-1-1-1-1-11111-1-1-11-11-1-111-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11-1-1111-1-1111-1
χ17222222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-20000000020000-200000000000000000000000002-202-2000000
χ18222222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-20000000020000-20000000000000000000000000-220-22000000
χ1922222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-2-2-2-2-111111111111111110000-1-1-1-1000000000000
χ2122222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1-1-11111111100001111000000000000
χ2222222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-12222-111111111-1-1-1-1-1-1-1-100001111000000000000
χ23222222-2-2222-2-22222222-22-222-2-2-2-22200000000-20000-2000000000000000022-2-20000200-200000000
χ24222222-2-2222-2-22222222-22-222-2-2-2-22200000000-20000-20000000000000000-2-2220000-200200000000
χ25222222-2-22-2-222222-2-2-2-2-2-2222-2-222-2-222-2-20000-2000020000000000000000000022-2-2000000000000
χ26222222-2-22-2-222222-2-2-2-2-2-2222-2-222-2-2-2-2220000-20000200000000000000000000-2-222000000000000
χ27222222-2-2-1-2-222-1-1-11111-2-22-1-111-1-11122-2-2000010000-133−3−333−3−333−3−333−3−30000-1-111000000000000
χ28222222-2-2-1-2-222-1-1-11111-2-22-1-111-1-11122-2-2000010000-1−3−333−3−333−3−333−3−3330000-1-111000000000000
χ29222222-2-2-1-2-222-1-1-11111-2-22-1-111-1-111-2-222000010000-133−3−333−3−3−3−333−3−333000011-1-1000000000000
χ30222222-2-2-1-2-222-1-1-11111-2-22-1-111-1-111-2-222000010000-1−3−333−3−33333−3−333−3−3000011-1-1000000000000
χ312222-2-2222-2-2-2-2222-2-2-2-2-222-2-222-2-22200000000-20000200000000000000000000000002-20-22000000
χ322222-2-2222-2-2-2-2222-2-2-2-2-222-2-222-2-22200000000-2000020000000000000000000000000-2202-2000000
χ332222-2-222-12222-1-1-1-1-1-1-1-2-2-211-1-1-1-1112-22-222-2-2122-2-21-1-1-1-11111-1-1-1-111110000-111-1000000000000
χ342222-2-222-12222-1-1-1-1-1-1-1-2-2-211-1-1-1-1112-22-2-2-2221-2-22211111-1-1-1-11111-1-1-1-10000-111-1000000000000
χ352222-2-222-12222-1-1-1-1-1-1-1-2-2-211-1-1-1-111-22-2222-2-21-2-2221-1-1-1-111111111-1-1-1-100001-1-11000000000000
χ362222-2-222-12222-1-1-1-1-1-1-1-2-2-211-1-1-1-111-22-22-2-222122-2-211111-1-1-1-1-1-1-1-1111100001-1-11000000000000
χ372222-2-2-2-2222-2-222222222-22-2-2-2-2-2-2-2-200000000200002000000000000000022-2-20000-200200000000
χ382222-2-2-2-2222-2-222222222-22-2-2-2-2-2-2-2-2000000002000020000000000000000-2-2220000200-200000000
χ392222-2-2-2-22-2-222222-2-2-2-222-2-2-2-2-222222-2-22000020000-2000000000000000000002-22-2000000000000
χ402222-2-2-2-22-2-222222-2-2-2-222-2-2-2-2-22222-222-2000020000-200000000000000000000-22-22000000000000
χ412222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-12-2-220000-10000133−3−3−3−33333−3−3−3−3330000-11-11000000000000
χ422222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-12-2-220000-100001−3−33333−3−3−3−33333−3−30000-11-11000000000000
χ432222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-1-222-20000-10000133−3−3−3−333−3−33333−3−300001-11-1000000000000
χ442222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-1-222-20000-100001−3−33333−3−333−3−3−3−33300001-11-1000000000000
χ452-22-2002-22-222-2-2-22-2-222000002-22-2000000000002-2000000000002-22-200002i−2i2i−2i00000000002i−2i0000
χ462-22-2002-22-222-2-2-22-2-222000002-22-2000000000002-2000000000002-22-20000−2i2i−2i2i0000000000−2i2i0000
χ472-22-2002-22-222-2-2-22-2-222000002-22-200000000000-2200000000000-22-2200002i−2i2i−2i0000000000−2i2i0000
χ482-22-2002-22-222-2-2-22-2-222000002-22-200000000000-2200000000000-22-220000−2i2i−2i2i00000000002i−2i0000
χ492-22-200-222-22-22-2-22-2-22200000-22-2200000000000002-200000000000002-22-22i−2i−2i2i0000000000002i−2i00
χ502-22-200-222-22-22-2-22-2-22200000-22-2200000000000002-200000000000002-22-2−2i2i2i−2i000000000000−2i2i00
χ512-22-200-222-22-22-2-22-2-22200000-22-220000000000000-220000000000000-22-222i−2i−2i2i000000000000−2i2i00
χ522-22-200-222-22-22-2-22-2-22200000-22-220000000000000-220000000000000-22-22−2i2i2i−2i0000000000002i−2i00
χ5344444444-2-4-4-4-4-2-2-222224-4-4-2-2-2-2222200000000-200002000000000000000000000000000000000000
χ54444444-4-4-244-4-4-2-2-2-2-2-2-2-44-4-2-22222-2-200000000200002000000000000000000000000000000000000
χ554444-4-444-2-4-4-4-4-2-2-22222-44422-2-222-2-20000000020000-2000000000000000000000000000000000000
χ564444-4-4-4-4-244-4-4-2-2-2-2-2-2-24-442222222200000000-20000-2000000000000000000000000000000000000
χ5744-4-44-400400004-4-400000004-400000000002-22-20000002-22-22-22-20000000000000000000000000000
χ5844-4-44-400400004-4-400000004-40000000000-22-22000000-22-22-22-220000000000000000000000000000
χ5944-4-44-400-20000-22223−2323−23000-22000023−2300002-22-2000000−1+31−3−1−31+3−1+31−3−1−31+30000000000000000000000000000
χ6044-4-44-400-20000-22223−2323−23000-22000023−230000-22-220000001−3−1+31+3−1−31−3−1+31+3−1−30000000000000000000000000000
χ6144-4-44-400-20000-222−2323−2323000-220000−232300002-22-2000000−1−31+3−1+31−3−1−31+3−1+31−30000000000000000000000000000
χ6244-4-44-400-20000-222−2323−2323000-220000−23230000-22-220000001+3−1−31−3−1+31+3−1−31−3−1+30000000000000000000000000000
χ6344-4-4-4400400004-4-40000000-4400000000002-2-220000002-22-2-22-220000000000000000000000000000
χ6444-4-4-4400400004-4-40000000-440000000000-222-2000000-22-222-22-20000000000000000000000000000
χ6544-4-4-4400-20000-22223−2323−230002-20000−232300002-2-22000000−1+31−3−1−31+31−3−1+31+3−1−30000000000000000000000000000
χ6644-4-4-4400-20000-22223−2323−230002-20000−23230000-222-20000001−3−1+31+3−1−3−1+31−3−1−31+30000000000000000000000000000
χ6744-4-4-4400-20000-222−2323−23230002-2000023−2300002-2-22000000−1−31+3−1+31−31+3−1−31−3−1+30000000000000000000000000000
χ6844-4-4-4400-20000-222−2323−23230002-2000023−230000-222-20000001+3−1−31−3−1+3−1−31+3−1+31−30000000000000000000000000000
χ694-44-4004-444-4-44-4-4444-4-4000004-4-440000000000000000000000000000000000000000000000000000
χ704-44-4004-4-24-4-4422-2-2-22200000-222-2000000000000000000000000000023−23−232300000000000000000000
χ714-44-4004-4-24-4-4422-2-2-22200000-222-20000000000000000000000000000−232323−2300000000000000000000
χ724-44-4004-4-2-444-422-222-2-200000-22-22000000000004-400000000000-22-22000000000000000000000000
χ734-44-4004-4-2-444-422-222-2-200000-22-2200000000000-44000000000002-22-2000000000000000000000000
χ744-44-400-4444-44-4-4-4444-4-400000-444-40000000000000000000000000000000000000000000000000000
χ754-44-400-44-24-44-422-2-2-222000002-2-2200000000000000000000000023−23−2323000000000000000000000000
χ764-44-400-44-24-44-422-2-2-222000002-2-22000000000000000000000000−232323−23000000000000000000000000
χ774-44-400-44-2-44-4422-222-2-2000002-22-200000000000004-40000000000000-22-2200000000000000000000
χ784-44-400-44-2-44-4422-222-2-2000002-22-20000000000000-4400000000000002-22-200000000000000000000
χ798-8-88000080000-88-800000000000000000000000000000000000000000000000000000000000000000
χ808-8-880000-400004-4443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-8-880000-400004-44−434343−430000000000000000000000000000000000000000000000000000000000000

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