Finite Group Databasebeta

← Group #72253712

Character table — Group #72253712

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222244444444888888888888888888161616161616161616161616242424243232323232323232323232324848484848484848484848484848
order122222366622444466222222446666661212121244666612121212121222224444121212121212121244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-111-1-11111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11-11-11-11111-1-1-1-1
χ611111111111111111111-1-111-1-11111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-11-11-1-1-1-1-11111
χ711111111111111111111-1-111-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-11-11-1-1-1-11111
χ811111111111111111111-1-111-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-11-11-111111-1-1-1-1
χ91111111111-1-111-1-1111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111i−ii−iii−i−iii−i−i-1-1-1-111ii−i−iii−i−i
χ101111111111-1-111-1-1111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111−ii−ii−i−iii−i−iii-1-1-1-111−i−iii−i−iii
χ111111111111-1-111-1-1111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1i−ii−iii−i−iii−i−i1111-1-1−i−iii−i−iii
χ121111111111-1-111-1-1111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1−ii−ii−i−iii−i−iii1111-1-1ii−i−iii−i−i
χ131111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1i−i−iiii−i−i−i−iii-11-111-1ii−i−i−i−iii
χ141111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1−iii−i−i−iiiii−i−i-11-111-1−i−iiiii−i−i
χ151111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-111i−i−iiii−i−i−i−iii1-11-1-11−i−iiiii−i−i
χ161111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-111−iii−i−i−iiiii−i−i1-11-1-11ii−i−i−i−iii
χ17222222222222222222-2-222-2-2-2-222-2-2-2-222222-2-2-22222-2-2-2-2000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-22222-2-2-2-22222-22-2-2-2-2-2-22222000000000000000000000000000000
χ19222222222222-2-2-2-2222-2002-2002222-2-2-2-2-2-2002-2000000000022000000000000020-20-200000000
χ20222222222222-2-2-2-2222-2002-2002222-2-2-2-2-2-2002-20000000000-2-20000000000000-2020200000000
χ21222222222222-2-2-2-222-2200-220022-2-222-2-2-2-200-2200000000220000000000000020-20-2000000000
χ22222222222222-2-2-2-222-2200-220022-2-222-2-2-2-200-2200000000-2-200000000000000-20202000000000
χ232222222222-2-222-2-222-2-22222-2-2-2-2222222-2-2-22-2-222-2-2-2-222000000000000000000000000000000
χ242222222222-2-222-2-222-2-2-2-22222-2-2222222-2-22-2-2-2-2-22222-2-2000000000000000000000000000000
χ252222222222-2-2-2-222222-200-2200-2-2-2-222-2-222002-20000000000220000000000000-2020-200000000
χ262222222222-2-2-2-222222-200-2200-2-2-2-222-2-222002-20000000000-2-2000000000000020-20200000000
χ272222222222-2-2-2-22222-22002-200-2-222-2-2-2-22200-22000000002200000000000000-2020-2000000000
χ282222222222-2-2-2-22222-22002-200-2-222-2-2-2-22200-2200000000-2-20000000000000020-202000000000
χ29222222-1-1-1-1222222-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-100000000000000
χ30222222-1-1-1-1222222-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-21111111100000000000000
χ31222222-1-1-1-1222222-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-2-2-1-111111111000022-2-2-1-1-1-1111100000000000000
χ32222222-1-1-1-1222222-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2221111-1-1-1-100000000000000
χ33222222-1-1-1-1222222-1-1-2-222-2-2-2-2-1-11111-1-1-1-12-211-1-1-1-11111000000003−33−33−33−300000000000000
χ34222222-1-1-1-1222222-1-1-2-222-2-2-2-2-1-11111-1-1-1-12-211-1-1-1-1111100000000−33−33−33−3300000000000000
χ35222222-1-1-1-1222222-1-1-2-2-2-2-2-222-1-11111-1-1-1-1-22111111-1-1-1-1000000003−33−3−33−3300000000000000
χ36222222-1-1-1-1222222-1-1-2-2-2-2-2-222-1-11111-1-1-1-1-22111111-1-1-1-100000000−33−333−33−300000000000000
χ37222222-1-1-1-1-2-222-2-2-1-12222-2-222111111-1-111-2-2-1-1-1-111-1-11100002i−2i2i−2i−i−iii−i−iii00000000000000
χ38222222-1-1-1-1-2-222-2-2-1-12222-2-222111111-1-111-2-2-1-1-1-111-1-1110000−2i2i−2i2iii−i−iii−i−i00000000000000
χ39222222-1-1-1-1-2-222-2-2-1-122-2-2-2-2-2-2111111-1-11122-1-111-1-111-1-100002i−2i−2i2i−i−iiiii−i−i00000000000000
χ40222222-1-1-1-1-2-222-2-2-1-122-2-2-2-2-2-2111111-1-11122-1-111-1-111-1-10000−2i2i2i−2iii−i−i−i−iii00000000000000
χ41222222-1-1-1-1-2-222-2-2-1-1-2-22222-2-211-1-1-1-1-1-111-2211-1-11111-1-100000000−i3i3i3−i3−i3i3i3−i300000000000000
χ42222222-1-1-1-1-2-222-2-2-1-1-2-22222-2-211-1-1-1-1-1-111-2211-1-11111-1-100000000i3−i3−i3i3i3−i3−i3i300000000000000
χ43222222-1-1-1-1-2-222-2-2-1-1-2-2-2-2222211-1-1-1-1-1-1112-21111-1-1-1-11100000000−i3i3i3−i3i3−i3−i3i300000000000000
χ44222222-1-1-1-1-2-222-2-2-1-1-2-2-2-2222211-1-1-1-1-1-1112-21111-1-1-1-11100000000i3−i3−i3i3−i3i3i3−i300000000000000
χ45444444-2-2-2-244-4-4-4-4-2-24-4004-400-2-2-2-222222200-2200000000000000000000000000000000000000
χ46444444-2-2-2-244-4-4-4-4-2-2-4400-4400-2-222-2-22222002-200000000000000000000000000000000000000
χ47444444-2-2-2-2-4-4-4-444-2-24-400-44002222-2-222-2-200-2200000000000000000000000000000000000000
χ48444444-2-2-2-2-4-4-4-444-2-2-44004-40022-2-22222-2-2002-200000000000000000000000000000000000000
χ494444-4-444444-40000-4-4000000004-40000000000000000000000000000000000000000002i−2i2i−2i0000
χ504444-4-444444-40000-4-4000000004-4000000000000000000000000000000000000000000−2i2i−2i2i0000
χ514444-4-44444-440000-4-400000000-440000000000000000000000000000000000000000002-2-220000
χ524444-4-44444-440000-4-400000000-44000000000000000000000000000000000000000000-222-20000
χ5344-4-44-44-4-4400004-44-400000000000000004-4000000000000000000000000000000000000002i−2i2i−2i
χ5444-4-44-44-4-4400004-44-400000000000000004-400000000000000000000000000000000000000−2i2i−2i2i
χ5544-4-44-44-4-440000-444-40000000000000000-44000000000000000000000000000000000000002-2-22
χ5644-4-44-44-4-440000-444-40000000000000000-4400000000000000000000000000000000000000-222-2
χ5744-4-4-444-4-44004-400-440000004-40000004-400000000004-400000000000000000000000000000000
χ5844-4-4-444-4-44004-400-44000000-440000004-40000000000-4400000000000000000000000000000000
χ5944-4-4-444-4-4400-4400-44004-40000000000-440000004-4000000000000000000000000000000000000
χ6044-4-4-444-4-4400-4400-4400-440000000000-44000000-44000000000000000000000000000000000000
χ6144-4-4-44-222-2004-4002-20000004-400−2i32i3−2i32i3-2200000000−2i32i3-2200000000000000000000000000000000
χ6244-4-4-44-222-2004-4002-20000004-4002i3−2i32i3−2i3-22000000002i3−2i3-2200000000000000000000000000000000
χ6344-4-4-44-222-2004-4002-2000000-4400−2i32i3−2i32i3-22000000002i3−2i32-200000000000000000000000000000000
χ6444-4-4-44-222-2004-4002-2000000-44002i3−2i32i3−2i3-2200000000−2i32i32-200000000000000000000000000000000
χ6544-4-4-44-222-200-44002-2004-4000000−2i32i32i3−2i32-2000000-220000−2i32i3000000000000000000000000000000
χ6644-4-4-44-222-200-44002-2004-40000002i3−2i3−2i32i32-2000000-2200002i3−2i3000000000000000000000000000000
χ6744-4-4-44-222-200-44002-200-44000000−2i32i32i3−2i32-20000002-200002i3−2i3000000000000000000000000000000
χ6844-4-4-44-222-200-44002-200-440000002i3−2i3−2i32i32-20000002-20000−2i32i3000000000000000000000000000000
χ698888-8-8-4-4-4-48-800004400000000-4400000000000000000000000000000000000000000000000000
χ708888-8-8-4-4-4-4-88000044000000004-400000000000000000000000000000000000000000000000000
χ7188-8-88-8-444-400008-8-440000000000000000-44000000000000000000000000000000000000000000
χ7288-8-88-8-444-40000-88-4400000000000000004-4000000000000000000000000000000000000000000
χ738-88-80088-8-800000000000000000000000000000000000000004-400000000000000000000000000
χ748-88-80088-8-80000000000000000000000000000000000000000-4400000000000000000000000000
χ758-8-88008-88-8000000000000000000000000000000000000004-40000000000000000000000000000
χ768-8-88008-88-800000000000000000000000000000000000000-440000000000000000000000000000
χ7716-1616-1600-8-88800000000000000000000000000000000000000000000000000000000000000000000
χ7816-16-161600-88-8800000000000000000000000000000000000000000000000000000000000000000000

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