Finite Group Databasebeta

← Group #10829940

Character table — Group #10829940

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order1222222234444444466666664444444444121212121212121212121212121212121212121212121212222244446666666612121212121212121212888888882244888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-11111111111-1-1111111-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-11111111111-1-1111111-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-11111111111-1-11111-1-1111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-11
χ121111111111-1-1-1-11111111111-1-11111-1-1111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-11-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-111-1-1-11
χ17222222222-22222-2-2-22222222-2-200002222-2-2-2-222220000000022222222000000-2-2000000000000-2-2-2-2-2-2000000000000000000
χ18222222222-22222-2-2-22222222-2-20000-2-2-2-2-2-2-2-2222200000000-2-2-2-2-2-2-2-2000000220000000000002222-2-2000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222000022-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000-22000000000000-2-22222000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-222-2-2-2-2-2-2-2-200000000-2-2-2-222220000002-200000000000022-2-222000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-222-2-211111111-1-1-1-11111-1-1000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-1-1-1000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1000000000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2222222-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111122-2-2-2-22-2-1-1-1-111111111-1-11111000000000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-2-222-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-2-222-2-2-221111-1-1-1-1111111-1-111000000000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-1-1-1-1111111111111-1-1-1-11111-2-222222-21111-1-1-1-1-1-1-1-1-1-11111000000000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-11111111111111111-1-1-1-122-2-222-22-1-1-1-11111-1-1-1-111-1-111000000000000000000
χ2922222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-2000022221111-1-1-1-1−i3−i3−i3−i3i3i3i3i3-1-1-1-1-1-1-1-1000000-2-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3111111000000000000000000
χ3022222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-2000022221111-1-1-1-1i3i3i3i3−i3−i3−i3−i3-1-1-1-1-1-1-1-1000000-2-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3111111000000000000000000
χ3122222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-21111-1-1-1-1−i3−i3−i3−i3i3i3i3i31111111100000022i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-1-1-1-111000000000000000000
χ3222222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-21111-1-1-1-1i3i3i3i3−i3−i3−i3−i31111111100000022−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-1-1-1-111000000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000022-2-211111111−i3−i3−i3−i3i3i3i3i3-1-1-1-11111000000-22−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-1-1-1000000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000022-2-211111111i3i3i3i3−i3−i3−i3−i3-1-1-1-11111000000-22i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-1-1-1000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000-2-22211111111−i3−i3−i3−i3i3i3i3i31111-1-1-1-10000002-2i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-111-1-1000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000-2-22211111111i3i3i3i3−i3−i3−i3−i31111-1-1-1-10000002-2−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-111-1-1000000000000000000
χ37222-22-2-2-22-200002-2222-2-22-2-2002i2i−2i−2i000022-2-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000002i2i−2i−2i00002-200000000
χ38222-22-2-2-22-200002-2222-2-22-2-2002i2i−2i−2i000022-2-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000−2i−2i2i2i0000-2200000000
χ39222-22-2-2-22-200002-2222-2-22-2-200−2i−2i2i2i000022-2-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000002i2i−2i−2i0000-2200000000
χ40222-22-2-2-22-200002-2222-2-22-2-200−2i−2i2i2i000022-2-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000−2i−2i2i2i00002-200000000
χ4122-22-2-22-22022-2-20002-22-2-22-20000002i−2i2i−2i000022-2-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000−i2i2−i2i2−i2−i2i2i200002−22−200
χ4222-22-2-22-22022-2-20002-22-2-22-20000002i−2i2i−2i000022-2-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000i2−i2i2−i2i2i2−i2−i20000−22−2200
χ4322-22-2-22-22022-2-20002-22-2-22-2000000−2i2i−2i2i000022-2-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000−i2i2−i2i2−i2−i2i2i20000−22−2200
χ4422-22-2-22-22022-2-20002-22-2-22-2000000−2i2i−2i2i000022-2-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000i2−i2i2−i2i2i2−i2−i200002−22−200
χ4522-22-2-22-220-2-2220002-22-2-22-20000002i−2i−2i2i0000-2-222000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000−i2i2−i2i2i2i2−i2−i200002−2−2200
χ4622-22-2-22-220-2-2220002-22-2-22-20000002i−2i−2i2i0000-2-222000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000i2−i2i2−i2−i2−i2i2i20000−222−200
χ4722-22-2-22-220-2-2220002-22-2-22-2000000−2i2i2i−2i0000-2-22200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000−i2i2−i2i2i2i2−i2−i20000−222−200
χ4822-22-2-22-220-2-2220002-22-2-22-2000000−2i2i2i−2i0000-2-22200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000i2−i2i2−i2−i2−i2i2i200002−2−2200
χ492-2-222-2-222200002-2-2-2-2222-2-2002i−2i2i−2i00002-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000002-22-2002i−2i000000
χ502-2-222-2-222200002-2-2-2-2222-2-2002i−2i2i−2i00002-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000-22-2200−2i2i000000
χ512-2-222-2-222200002-2-2-2-2222-2-200−2i2i−2i2i00002-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000002-22-200−2i2i000000
χ522-2-222-2-222200002-2-2-2-2222-2-200−2i2i−2i2i00002-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000-22-22002i−2i000000
χ532-2-2-2222-2222-22-2-2-22-2-2-2-22222-200000000-222-22-22-200000000000000002-22-200002-22-22-22-2000000002-2000000000000000000
χ542-2-2-2222-2222-22-2-2-22-2-2-2-22222-200000000-222-22-22-20000000000000000-22-220000-22-22-22-22000000002-2000000000000000000
χ552-2-2-2222-222-22-22-2-22-2-2-2-2222-2200000000-222-2-22-2200000000000000002-2-2200002-22-2-22-2200000000-22000000000000000000
χ562-2-2-2222-222-22-22-2-22-2-2-2-2222-2200000000-222-2-22-220000000000000000-222-20000-22-222-22-200000000-22000000000000000000
χ572-2-2-2222-22-22-22-222-2-2-2-2-2222-222-2-2200002-2-222-22-22-2-222-2-220000000000002-200000000002-22-20000-22000000000000000000
χ582-2-2-2222-22-22-22-222-2-2-2-2-2222-22-222-200002-2-222-22-2-222-2-222-2000000000000-220000000000-22-220000-22000000000000000000
χ592-2-2-2222-22-2-22-2222-2-2-2-2-22222-22-2-2200002-2-22-22-222-2-222-2-22000000000000-220000000000-22-2200002-2000000000000000000
χ602-2-2-2222-22-2-22-2222-2-2-2-2-22222-2-222-200002-2-22-22-22-222-2-222-20000000000002-200000000002-22-200002-2000000000000000000
χ612-2-2-2222-2-122-22-2-2-221111-1-1-12-2000000001-1-11-11-11−i3i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3−i3i32-22-20000-11-11-11-11−i3i3i3−i3−i3i3−i3i3-11000000000000000000
χ622-2-2-2222-2-122-22-2-2-221111-1-1-12-2000000001-1-11-11-11−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3i3−i3i3−i3-22-2200001-11-11-11-1−i3i3i3−i3i3−i3i3−i3-11000000000000000000
χ632-2-2-2222-2-122-22-2-2-221111-1-1-12-2000000001-1-11-11-11i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3−i3i3−i3i3-22-2200001-11-11-11-1i3−i3−i3i3−i3i3−i3i3-11000000000000000000
χ642-2-2-2222-2-122-22-2-2-221111-1-1-12-2000000001-1-11-11-11i3−i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3i3−i32-22-20000-11-11-11-11i3−i3−i3i3i3−i3i3−i3-11000000000000000000
χ652-2-2-2222-2-12-22-22-2-221111-1-1-1-22000000001-1-111-11-1−i3i3i3−i3i3−i3−i3i3−i3i3−i3i3i3−i3i3−i32-2-220000-11-111-11-1i3−i3−i3i3−i3i3i3−i31-1000000000000000000
χ662-2-2-2222-2-12-22-22-2-221111-1-1-1-22000000001-1-111-11-1−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3−i3i3-222-200001-11-1-11-11i3−i3−i3i3i3−i3−i3i31-1000000000000000000
χ672-2-2-2222-2-12-22-22-2-221111-1-1-1-22000000001-1-111-11-1i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3i3−i3-222-200001-11-1-11-11−i3i3i3−i3−i3i3i3−i31-1000000000000000000
χ682-2-2-2222-2-12-22-22-2-221111-1-1-1-22000000001-1-111-11-1i3−i3−i3i3−i3i3i3−i3i3−i3i3−i3−i3i3−i3i32-2-220000-11-111-11-1−i3i3i3−i3i3−i3−i3i31-1000000000000000000
χ692-2-2-2222-2-1-22-22-222-21111-1-1-1-222-2-220000-111-1-11-11-111-1-111-1−i3i3−i3i3−i3i3−i3i300002-200−i3i3i3−i3−i3i3i3−i3-11-11i3−i3i3−i31-1000000000000000000
χ702-2-2-2222-2-1-22-22-222-21111-1-1-1-222-2-220000-111-1-11-11-111-1-111-1i3−i3i3−i3i3−i3i3−i300002-200i3−i3−i3i3i3−i3−i3i3-11-11−i3i3−i3i31-1000000000000000000
χ712-2-2-2222-2-1-22-22-222-21111-1-1-1-22-222-20000-111-1-11-111-1-111-1-11−i3i3−i3i3−i3i3−i3i30000-2200i3−i3−i3i3i3−i3−i3i31-11-1i3−i3i3−i31-1000000000000000000
χ722-2-2-2222-2-1-22-22-222-21111-1-1-1-22-222-20000-111-1-11-111-1-111-1-11i3−i3i3−i3i3−i3i3−i30000-2200−i3i3i3−i3−i3i3i3−i31-11-1−i3i3−i3i31-1000000000000000000
χ732-2-2-2222-2-1-2-22-2222-21111-1-1-12-22-2-220000-111-11-11-1-111-1-111-1−i3i3−i3i3i3−i3i3−i30000-2200−i3i3i3−i3i3−i3−i3i31-11-1i3−i3−i3i3-11000000000000000000
χ742-2-2-2222-2-1-2-22-2222-21111-1-1-12-22-2-220000-111-11-11-1-111-1-111-1i3−i3i3−i3−i3i3−i3i30000-2200i3−i3−i3i3−i3i3i3−i31-11-1−i3i3i3−i3-11000000000000000000
χ752-2-2-2222-2-1-2-22-2222-21111-1-1-12-2-222-20000-111-11-11-11-1-111-1-11−i3i3−i3i3i3−i3i3−i300002-200i3−i3−i3i3−i3i3i3−i3-11-11i3−i3−i3i3-11000000000000000000
χ762-2-2-2222-2-1-2-22-2222-21111-1-1-12-2-222-20000-111-11-11-11-1-111-1-11i3−i3i3−i3−i3i3−i3i300002-200−i3i3i3−i3i3−i3−i3i3-11-11−i3i3i3−i3-11000000000000000000
χ77444-44-4-4-4440000-44-444-4-44-4-40000000000-4-4440000000000000000000000000000000000000000000000000000000000000000
χ78444-44-4-4-4-240000-44-4-2-222-222000000000022-2-200002323−23−23−23−2323230000000000000000000000000000000000000000000000000000
χ79444-44-4-4-4-240000-44-4-2-222-222000000000022-2-20000−23−2323232323−23−230000000000000000000000000000000000000000000000000000
χ80444-44-4-4-4-2-400004-44-2-222-222004i4i−4i−4i0000-2-2220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ81444-44-4-4-4-2-400004-44-2-222-22200−4i−4i4i4i0000-2-22200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ8244-44-4-44-4-2044-4-4000-22-222-220000004i−4i4i−4i0000-2-22200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000
χ8344-44-4-44-4-2044-4-4000-22-222-22000000−4i4i−4i4i0000-2-222000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000
χ8444-44-4-44-4-20-4-444000-22-222-220000004i−4i−4i4i000022-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000
χ8544-44-4-44-4-20-4-444000-22-222-22000000−4i4i4i−4i000022-2-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000
χ8644-4-4-44-444000000004-4-44-4-4400000000000000000000000000000000000000000000000000000000000022−22−222200000000000000
χ8744-4-4-44-444000000004-4-44-4-44000000000000000000000000000000000000000000000000000000000000−222222−2200000000000000
χ884-444-44-4-4400000000-444-4-4-440000000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ894-444-44-4-4400000000-444-4-4-4400000000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ904-44-4-4-444404-4-44000-44-44-44-4000000000000004-4-44000000000000000000000000000000000000000000000000000000000000
χ914-44-4-4-44440-444-4000-44-44-44-400000000000000-444-4000000000000000000000000000000000000000000000000000000000000
χ924-44-4-4-444-204-4-440002-22-22-2200000000000000-222-20000000023−23−232323−23−232300000000000000000000000000000000000000000000
χ934-44-4-4-444-204-4-440002-22-22-2200000000000000-222-200000000−232323−23−232323−2300000000000000000000000000000000000000000000
χ944-44-4-4-444-20-444-40002-22-22-22000000000000002-2-220000000023−23−2323−232323−2300000000000000000000000000000000000000000000
χ954-44-4-4-444-20-444-40002-22-22-22000000000000002-2-2200000000−232323−2323−23−232300000000000000000000000000000000000000000000
χ964-4-444-4-444-40000-444-4-4444-4-40000000000-44-440000000000000000000000000000000000000000000000000000000000000000
χ974-4-444-4-44-2400004-4-422-2-2-222004i−4i4i−4i0000-22-220000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ984-4-444-4-44-2400004-4-422-2-2-22200−4i4i−4i4i0000-22-2200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ994-4-444-4-44-2-40000-44422-2-2-22200000000002-22-2000023−2323−23−2323−23230000000000000000000000000000000000000000000000000000
χ1004-4-444-4-44-2-40000-44422-2-2-22200000000002-22-20000−2323−232323−2323−230000000000000000000000000000000000000000000000000000
χ10188-8-8-88-88-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-888-88-8-8-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000000000

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