Finite Group Databasebeta

← Group #10828729

Character table — Group #10828729

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212161616161616161616162424242424242424242424242424
order12222222344446662446666121212121212444468888122424242424242424444488121212122424242424444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-1-1-1-11111
χ711111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11-11-1-1-1-1-11111
χ811111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11-111111-1-1-1-1
χ91111-1-11111111111-1-1-111-1-11-1-111111-1-1-111-1-1-11111-1-1-1-111111-1-1-11111-1-1-1-1-11-1111-1-111-1-1
χ101111-1-11111111111-1-1-111-1-11-1-111111-1-1-111-1-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-1111-11-1-1-111-1-111
χ111111-1-11111111111-1-1-111-1-11-1-111111-1-1-1-1-111-1-1-1-1-111111111-11-1-111-1-111-1-1-11-11-1-111-1-111
χ121111-1-11111111111-1-1-111-1-11-1-111111-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-11-1-111-1-111111-11-111-1-111-1-1
χ131111-1-11111111111-1-1-111-1-11-1-1111-1-111-111-1-1-11111-1-1-1-11111-1111-1-1-1-11111-1-1-1-111-1-1-1-111
χ141111-1-11111111111-1-1-111-1-11-1-1111-1-111-111-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-11111-1-1
χ151111-1-11111111111-1-1-111-1-11-1-1111-1-111-1-1-111-1-1-1-1-1111111111-111-1-111-1-111-1-1-1-1-1-11111-1-1
χ161111-1-11111111111-1-1-111-1-11-1-1111-1-111-1-1-111-1-1-1-1-11111-1-1-1-11-111-1-111-1-1-1-1111111-1-1-1-111
χ17222222222-2-2-2-22222-2-22222-2-2-2-2-2-22-22-220000-2000000000000002-22-2000000000000000000
χ18222222222-2-2-2-22222-2-22222-2-2-2-2-2-2-22-2220000-200000000000000-22-22000000000000000000
χ1922222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-100000000000000
χ2022222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-1111111110000-2-2-1-1-1-1111100000000000000
χ2122222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-10000-2-21111111100000000000000
χ2222222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-1111111110000221111-1-1-1-100000000000000
χ2322222222-1-2-2-2-2-1-1-12-2-2-1-1-1-11111112-22-2-10000133−3−333−3−3000000-11-113−33−300000000000000
χ2422222222-1-2-2-2-2-1-1-12-2-2-1-1-1-11111112-22-2-100001−3−333−3−333000000-11-11−33−3300000000000000
χ2522222222-1-2-2-2-2-1-1-12-2-2-1-1-1-1111111-22-22-10000133−3−333−3−30000001-11-1−33−3300000000000000
χ2622222222-1-2-2-2-2-1-1-12-2-2-1-1-1-1111111-22-22-100001−3−333−3−3330000001-11-13−33−300000000000000
χ27222222-2-222-2-22222-22-2-2-222222-2-220000-20000-20000000022-2-200000000000020-2000000000
χ28222222-2-222-2-22222-22-2-2-222222-2-220000-20000-200000000-2-222000000000000-202000000000
χ29222222-2-22-222-2222-2-22-2-222-2-2-222-20000-20000200000000000000000000002-2020-200000000
χ30222222-2-22-222-2222-2-22-2-222-2-2-222-20000-2000020000000000000000000000-220-20200000000
χ312222-2-2222-2-2-2-2222-22222-2-2-222-2-2-22-2-22-20000200000000000000-222-2000000000000000000
χ322222-2-2222-2-2-2-2222-22222-2-2-222-2-2-2-222-2-200002000000000000002-2-22000000000000000000
χ332222-2-222-12222-1-1-1-2-2-2-1-111-111-1-1-122-2-2122-2-21-1-1-1-1111100002-211-1-1-1-11100000000000000
χ342222-2-222-12222-1-1-1-2-2-2-1-111-111-1-1-122-2-21-2-22211111-1-1-1-10000-2211-1-111-1-100000000000000
χ352222-2-222-12222-1-1-1-2-2-2-1-111-111-1-1-1-2-222122-2-21-1-1-1-111110000-22-1-11111-1-100000000000000
χ362222-2-222-12222-1-1-1-2-2-2-1-111-111-1-1-1-2-2221-2-22211111-1-1-1-100002-2-1-111-1-11100000000000000
χ372222-2-222-1-2-2-2-2-1-1-1-222-1-1111-1-11112-2-2210000-133−3−3−3−3330000001-1-113−3−3300000000000000
χ382222-2-222-1-2-2-2-2-1-1-1-222-1-1111-1-11112-2-2210000-1−3−33333−3−30000001-1-11−333−300000000000000
χ392222-2-222-1-2-2-2-2-1-1-1-222-1-1111-1-1111-222-210000-133−3−3−3−333000000-111-1−333−300000000000000
χ402222-2-222-1-2-2-2-2-1-1-1-222-1-1111-1-1111-222-210000-1−3−33333−3−3000000-111-13−3−3300000000000000
χ412222-2-2-2-222-2-222222-22-2-2-2-22-2-2-2-2200002000020000000022-2-2000000000000-202000000000
χ422222-2-2-2-222-2-222222-22-2-2-2-22-2-2-2-22000020000200000000-2-22200000000000020-2000000000
χ432222-2-2-2-22-222-222222-2-2-2-2-2-22222-2000020000-200000000000000000000002-20-20200000000
χ442222-2-2-2-22-222-222222-2-2-2-2-2-22222-2000020000-20000000000000000000000-22020-200000000
χ4522-2-2002-22-22-22-2-220002-200-2002-2200000002-2000002-22-22i−2i2i−2i0000000000000000002i−2i0000
χ4622-2-2002-22-22-22-2-220002-200-2002-2200000002-2000002-22-2−2i2i−2i2i000000000000000000−2i2i0000
χ4722-2-2002-22-22-22-2-220002-200-2002-220000000-2200000-22-222i−2i2i−2i000000000000000000−2i2i0000
χ4822-2-2002-22-22-22-2-220002-200-2002-220000000-2200000-22-22−2i2i−2i2i0000000000000000002i−2i0000
χ4922-2-200-222-2-222-2-22000-2200-200-222000002-20002-22-200002i−2i−2i2i00000000000000002i−2i000000
χ5022-2-200-222-2-222-2-22000-2200-200-222000002-20002-22-20000−2i2i2i−2i0000000000000000−2i2i000000
χ5122-2-200-222-2-222-2-22000-2200-200-22200000-22000-22-2200002i−2i−2i2i0000000000000000−2i2i000000
χ5222-2-200-222-2-222-2-22000-2200-200-22200000-22000-22-220000−2i2i2i−2i00000000000000002i−2i000000
χ53444444-4-4-24-4-44-2-2-2-44-422-2-2-2-2-222-20000200002000000000000000000000000000000000000
χ54444444-4-4-2-444-4-2-2-2-4-4422-2-2222-2-22000020000-2000000000000000000000000000000000000
χ554444-4-4-4-4-24-4-44-2-2-24-442222-22222-20000-20000-2000000000000000000000000000000000000
χ564444-4-4-4-4-2-444-4-2-2-244-422222-2-2-2-220000-200002000000000000000000000000000000000000
χ5744-4-4004-444-44-4-4-440004-400400-44-40000000000000000000000000000000000000000000000
χ5844-4-4004-4-24-44-422-2000-2200-2002-220000000000000023−23−23230000000000000000000000000000
χ5944-4-4004-4-24-44-422-2000-2200-2002-2200000000000000−232323−230000000000000000000000000000
χ6044-4-4004-4-2-44-4422-2000-2200200-22-200000004-400000-22-220000000000000000000000000000
χ6144-4-4004-4-2-44-4422-2000-2200200-22-20000000-44000002-22-20000000000000000000000000000
χ6244-4-400-44444-4-4-4-44000-44004004-4-40000000000000000000000000000000000000000000000
χ6344-4-400-44-244-4-422-20002-200-200-222000000000023−23−232300000000000000000000000000000000
χ6444-4-400-44-244-4-422-20002-200-200-2220000000000−232323−2300000000000000000000000000000000
χ6544-4-400-44-2-4-44422-20002-2002002-2-2000004-4000-22-2200000000000000000000000000000000
χ6644-4-400-44-2-4-44422-20002-2002002-2-200000-440002-22-200000000000000000000000000000000
χ674-44-44-400400004-4-4000004-40000000000000000000000000000000000000000000000002-22-2
χ684-44-44-400400004-4-4000004-4000000000000000000000000000000000000000000000000-22-22
χ694-44-4-4400400004-4-400000-440000000000000000000000000000000000000000000000002-2-22
χ704-44-4-4400400004-4-400000-44000000000000000000000000000000000000000000000000-222-2
χ718-88-88-800-40000-44400000-440000000000000000000000000000000000000000000000000000
χ728-88-8-8800-40000-444000004-40000000000000000000000000000000000000000000000000000
χ738-8-88000080000-88-800000000000000000000000000000000000000000000000000000000000
χ748-8-880000-400004-440000000043−430000000000000000000000000000000000000000000000000
χ758-8-880000-400004-4400000000−43430000000000000000000000000000000000000000000000000

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