Finite Group Databasebeta

← Group #10833505

Character table — Group #10833505

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222222224444444444444444888888888888888881212121216161616161616161616242424242424242424244848
order122223444466622444466121212121212121244444668812121212121212122244481212121224242424224488888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-111111-1-1111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1
χ411111111111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111
χ511111111111111111-1-111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-1111111-1-1-1-1-1-1
χ611111111111111111-1-111-1-1-1-1111111-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111
χ711111111111111111-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1-1-1-1-1-1-111
χ811111111111111111-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-11-11111111-1-1
χ91111111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111-11111-1-1-1-1-11-11-1-111-1-1-11
χ101111111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11-11-111-1-1111-1
χ111111111111111-1-1-1-1111111111111-1-11-1-1-1-11111-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-11111-1-11-1
χ121111111111111-1-1-1-1111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111-11
χ131111111111111-1-1-1-1-1-111-1-1-1-1111111-111-1-1-1-1-1-11111-1-11111-1111-1-1-1-111-11-11-1-1-1-1111-1
χ141111111111111-1-1-1-1-1-111-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-1111-11-11111-1-1-11
χ151111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-111-1-11111-1-111111-1-1-11111-1-1-1-1-1-111-1-111-11
χ161111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-111-1-11111-1-1-1-1-1-11-1-1-11111-1-11111-1-111-1-11-1
χ1722222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ1822222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2222-1-1-2-2-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ1922222-12222-1-1-12222-2-2-1-11111-1-1-1-122-2-2-2-1-122111111-1-10000-2-2-1-111-1-111000000000000
χ2022222-12222-1-1-12222-2-2-1-11111-1-1-1-1-2-2-2-2-2-1-1-2-2111111-1-100002211-1-111-1-1000000000000
χ2122222-12222-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-1222-2-211-2-2-1-111111100002-2-1-1-1-11111000000000000
χ2222222-12222-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-1-2-22-2-21122-1-11111110000-221111-1-1-1-1000000000000
χ2322222-12222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-122-22211-2-211-1-1-1-1110000-22-1-11111-1-1000000000000
χ2422222-12222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-1-2-2-222112211-1-1-1-11100002-211-1-1-1-111000000000000
χ25222-2-2222-2-2-2-220000002-2000022-2-20002i−2i0000002i2i−2i−2i0022-2-20000000000000000002i−2i00
χ26222-2-2222-2-2-2-220000002-2000022-2-20002i−2i0000002i2i−2i−2i00-2-222000000000000000000−2i2i00
χ27222-2-2222-2-2-2-220000002-2000022-2-2000−2i2i000000−2i−2i2i2i0022-2-2000000000000000000−2i2i00
χ28222-2-2222-2-2-2-220000002-2000022-2-2000−2i2i000000−2i−2i2i2i00-2-2220000000000000000002i−2i00
χ29222-2-22-2-222-2-222-22-2002-20000-2-222000002-2000000002-200000000000000020-22-2000000
χ30222-2-22-2-222-2-222-22-2002-20000-2-222000002-2000000002-2000000000000000-202-22000000
χ31222-2-22-2-222-2-22-22-22002-20000-2-22200000-2200000000-2200000000000000020-2-22000000
χ32222-2-22-2-222-2-22-22-22002-20000-2-22200000-2200000000-22000000000000000-2022-2000000
χ3322-22-222-22-222222-2-200-2-200002-2-222-2000222-2000000-2-20000002-2002-200000000000000
χ3422-22-222-22-222222-2-200-2-200002-2-22-2200022-22000000-2-2000000-2200-2200000000000000
χ3522-22-222-22-2222-2-22200-2-200002-2-222-2000-2-2-22000000220000002-200-2200000000000000
χ3622-22-222-22-2222-2-22200-2-200002-2-22-22000-2-22-200000022000000-22002-200000000000000
χ3722-22-22-22-22222000022-2-22222-222-200-2000000-2-20000002-22-200000000000000002-20000
χ3822-22-22-22-22222000022-2-22222-222-200-2000000-2-2000000-22-220000000000000000-220000
χ3922-22-22-22-222220000-2-2-2-2-2-2-2-2-222-2002000000220000002-22-20000000000000000-220000
χ4022-22-22-22-222220000-2-2-2-2-2-2-2-2-222-200200000022000000-22-2200000000000000002-20000
χ4122-22-2-12-22-2-1-1-122-2-20011−i3−i3i3i3-111-12-2000-1-12-2−i3i3−i3i3−i3i311000000-11−i3i3-11−i3i3000000000000
χ4222-22-2-12-22-2-1-1-122-2-20011−i3−i3i3i3-111-1-22000-1-1-22−i3i3−i3i3−i3i3110000001-1i3−i31-1i3−i3000000000000
χ4322-22-2-12-22-2-1-1-122-2-20011i3i3−i3−i3-111-12-2000-1-12-2i3−i3i3−i3i3−i311000000-11i3−i3-11i3−i3000000000000
χ4422-22-2-12-22-2-1-1-122-2-20011i3i3−i3−i3-111-1-22000-1-1-22i3−i3i3−i3i3−i3110000001-1−i3i31-1−i3i3000000000000
χ4522-22-2-12-22-2-1-1-1-2-2220011−i3−i3i3i3-111-12-200011-22−i3i3i3−i3i3−i3-1-1000000-11−i3i31-1i3−i3000000000000
χ4622-22-2-12-22-2-1-1-1-2-2220011−i3−i3i3i3-111-1-22000112-2−i3i3i3−i3i3−i3-1-10000001-1i3−i3-11−i3i3000000000000
χ4722-22-2-12-22-2-1-1-1-2-2220011i3i3−i3−i3-111-12-200011-22i3−i3−i3i3−i3i3-1-1000000-11i3−i31-1−i3i3000000000000
χ4822-22-2-12-22-2-1-1-1-2-2220011i3i3−i3−i3-111-1-22000112-2i3−i3−i3i3−i3i3-1-10000001-1−i3i3-11i3−i3000000000000
χ4922-2-222-222-2-2-222-2-2200-220000-22-22000002-200000000-222-2-22000000000020-2000000000
χ5022-2-222-222-2-2-222-2-2200-220000-22-22000002-200000000-22-222-20000000000-202000000000
χ5122-2-222-222-2-2-22-222-200-220000-22-2200000-22000000002-22-2-220000000000-202000000000
χ5222-2-222-222-2-2-22-222-200-220000-22-2200000-22000000002-2-222-2000000000020-2000000000
χ53444444-4-4-4-4444000000440000-4-4-4-40000000000000000000000000000000000000000000
χ5444444-2-4-4-4-4-2-2-2000000-2-2−2i3−2i32i32i322220000000002i3−2i300000000000000000000000000000000
χ5544444-2-4-4-4-4-2-2-2000000-2-22i32i3−2i3−2i32222000000000−2i32i300000000000000000000000000000000
χ56444-4-4-244-4-422-2000000-220000-2-2220004i−4i000000−2i−2i2i2i0000000000000000000000000000
χ57444-4-4-244-4-422-2000000-220000-2-222000−4i4i0000002i2i−2i−2i0000000000000000000000000000
χ58444-4-4-2-4-44422-24-44-400-22000022-2-200000-2200000000-2200000000000000000000000000
χ59444-4-4-2-4-44422-2-44-4400-22000022-2-2000002-2000000002-200000000000000000000000000
χ6044-44-4-2-44-44-2-2-200004422-2-2-2-22-2-2200-40000002200000000000000000000000000000000
χ6144-44-4-2-44-44-2-2-20000-4-42222222-2-22004000000-2-200000000000000000000000000000000
χ6244-4-4444-4-44-4-44000000-4400004-44-40000000000000000000000000000000000000000000
χ6344-4-44-24-4-4422-20000002-20000-22-220000000000023−23−23230000000000000000000000000000
χ6444-4-44-24-4-4422-20000002-20000-22-2200000000000−232323−230000000000000000000000000000
χ6544-4-44-2-444-422-24-4-44002-200002-22-200000-22000000002-200000000000000000000000000
χ6644-4-44-2-444-422-2-444-4002-200002-22-2000002-200000000-2200000000000000000000000000
χ678-80008000000-800004-4004-44-400000000000000000000000000000000000000000000000
χ688-80008000000-80000-4400-44-4400000000000000000000000000000000000000000000000
χ698-8000-40000−4i34i3400004-400−2−2i32+2i3−2+2i32−2i300000000000000000000000000000000000000000000000
χ708-8000-40000−4i34i340000-44002+2i3−2−2i32−2i3−2+2i300000000000000000000000000000000000000000000000
χ718-8000-400004i3−4i3400004-400−2+2i32−2i3−2−2i32+2i300000000000000000000000000000000000000000000000
χ728-8000-400004i3−4i340000-44002−2i3−2+2i32+2i3−2−2i300000000000000000000000000000000000000000000000

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