Finite Group Databasebeta

← Group #13151360

Character table — Group #13151360

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order12223666224121233666666663666666644444466666612121212222444444121212121212121212121212666121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111-1-111-1-11111111111-1-1-111-1-11-1-1-1-1-1-1-1-1-11111-1-1-111-1
χ41111111111111111111111111111111-1-1-1-1111111111111-1-11-1-11-1-11-1-1-1-11111-1-1-1-1-1-11-1-11
χ5111111111-1-1-1-1111111111-1111-1-1111111111-1111-1-1-1-1-1-11-1-1-111-1-1-111-1-111-1-111111-1-1-1-11
χ6111111111-1-1-1-1111111111-1111-1-111111-1-1-1-1-1111-1-1-1-1-1-11-111-1-1-11111-1-1-1-111-1-1-1-11-1111-1
χ7111111111-1-1-1-1111111111-1111-1-1111-1-111-1-1-1111-1-1-1-1-1-1-111-11-11-11-1-111-1-1111111-111-1-1-1
χ8111111111-1-1-1-1111111111-1111-1-1111-1-1-1-111-1111-1-1-1-1-1-1-11-11-1111-1-1-11111-1-1-1-1-1-1-11-1111
χ911111111-11-1-1-111111111-111-1-1111111111111-1-1-111-1-1-1-1-11-1-1-1-1-11111-1-1111111-1-1-11-11-1-1
χ1011111111-11-1-1-111111111-111-1-11111111-1-1-1-11-1-1-111-1-1-1-1-111111-1-1-111-1-1-1-1-1-1-1-111-111-111
χ1111111111-11-1-1-111111111-111-1-111111-1-111-1-11-1-1-111-1-1-1-11-11-1-1111-1-1-111-1-1-1-111-1-11-111-11
χ1211111111-11-1-1-111111111-111-1-111111-1-1-1-1111-1-1-111-1-1-1-11-1-111-11-11-1-1111111-1-1111-1-1-11-1
χ1311111111-1-111111111111-1-11-1-1-1-1111111111-1-1-1-1-1-11111-1-111-1-11-1-1111111-1-111-1-1-1-11-11-1
χ1411111111-1-111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-111-1-111-1-1-11-11
χ1511111111-1-111111111111-1-11-1-1-1-1111-1-111-1-1-1-1-1-1-1-1111111-11-11-1-11-1-1-1-1-1-11111-1-111-1-111
χ1611111111-1-111111111111-1-11-1-1-1-1111-1-1-1-111-1-1-1-1-1-11111111-11-1-11-1-1-1-1-111-1-1-1-1111111-1-1
χ1722222222222222-1-122-1-1222-122-1-1-1-1-10000222-1-1-1-1-1-12-1-10020020020000-1-1-1-1000000-100-1
χ1822222222222222-1-122-1-1222-122-1-1-1-1-10000-2-22-1-1-1-1-1-12-1-100-200-200-2000011110000001001
χ192222222222222-122-1-122-122-1-1-122-1-1-1002200-12-1-1-1-12-1-1-100022002000000000-1-1-1-1000-1-10
χ202222222222222-122-1-122-122-1-1-122-1-1-100-2-200-12-1-1-1-12-1-1-1000-2-200-20000000001111000110
χ21222222222-2-2-2-22-1-122-1-122-2-12211-1-1-1000022-2-1-1-1111-21100-200200-20000-1-111000000100-1
χ22222222222-2-2-2-22-1-122-1-122-2-12211-1-1-10000-2-2-2-1-1-1111-21100200-2002000011-1-1000000-1001
χ23222222222-2-2-2-2-122-1-122-12-2-1-1-1-2-2-1-1-100220012-1-111-2111000-2200-2000000000-1-1-1-1000110
χ24222222222-2-2-2-2-122-1-122-12-2-1-1-1-2-2-1-1-100-2-20012-1-111-21110002-20020000000001111000-1-10
χ2522222222-22-2-2-22-1-122-1-12-22-1-2-2-1-1-1-1-10000222111-1-11-21100-200-20020000-1-1-1-10000001001
χ2622222222-22-2-2-22-1-122-1-12-22-1-2-2-1-1-1-1-10000-2-22111-1-11-21100200200-200001111000000-100-1
χ2722222222-22-2-2-2-122-1-122-1-22-11122-1-1-1002200-1-211-1-1-2111000-2-2002000000000-1-111000-110
χ2822222222-22-2-2-2-122-1-122-1-22-11122-1-1-100-2-200-1-211-1-1-21110002200-200000000011-1-10001-10
χ2922222222-2-22222-1-122-1-12-2-2-1-2-211-1-1-1000022-211111-12-1-100200-200-20000-1-111000000-1001
χ3022222222-2-22222-1-122-1-12-2-2-1-2-211-1-1-10000-2-2-211111-12-1-100-2002002000011-1-1000000100-1
χ3122222222-2-2222-122-1-122-1-2-2-111-2-2-1-1-10022001-211112-1-1-10002-200-2000000000-1-1110001-10
χ3222222222-2-2222-122-1-122-1-2-2-111-2-2-1-1-100-2-2001-211112-1-1-1000-2200200000000011-1-1000-110
χ3322-2-22-22-2000002222-2-2-2-200200002-2-22-22i−2i2i−2i00000000000000000002-2002i−2i002i−2i00000000
χ3422-2-22-22-2000002222-2-2-2-200200002-2-22-2−2i2i−2i2i00000000000000000002-200−2i2i00−2i2i00000000
χ3522-2-22-22-2000002222-2-2-2-200200002-2-2-222i−2i−2i2i0000000000000000000-2200−2i2i002i−2i00000000
χ3622-2-22-22-2000002222-2-2-2-200200002-2-2-22−2i2i2i−2i0000000000000000000-22002i−2i00−2i2i00000000
χ374444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111000000-2-21111-2-211000000000000000000000000000
χ38444444444-4-4-4-4-2-2-2-2-2-2-2-24-41-2-2221110000002-211-1-122-1-1000000000000000000000000000
χ3944444444-44-4-4-4-2-2-2-2-2-2-2-2-44122-2-2111000000-22-1-11122-1-1000000000000000000000000000
χ4044444444-4-4444-2-2-2-2-2-2-2-2-4-41222211100000022-1-1-1-1-2-211000000000000000000000000000
χ4144-4-44-44-4000004-2-24-422-400-20000-22200004i−4i00000000000000000000000−2i2i000000000000
χ4244-4-44-44-4000004-2-24-422-400-20000-2220000−4i4i000000000000000000000002i−2i000000000000
χ4344-4-44-44-400000-244-22-4-4200-20000-222004i−4i00000000000000000000000000000−2i2i00000000
χ4444-4-44-44-400000-244-22-4-4200-20000-22200−4i4i000000000000000000000000000002i−2i00000000
χ454-44-444-4-40000044-4-4-44-440040000-4-440000000000000000000000000000000000000000000
χ464-44-444-4-4000004-22-4-4-22400-200−2i32i322-20000000000−2i32i30000000000000000000000000000000
χ474-44-444-4-4000004-22-4-4-22400-2002i3−2i322-200000000002i3−2i30000000000000000000000000000000
χ484-44-444-4-400000-24-4224-4-200-2−2i32i30022-200000000−2i32i3000000000000000000000000000000000
χ494-44-444-4-400000-24-4224-4-200-22i3−2i30022-2000000002i3−2i3000000000000000000000000000000000
χ504-44-444-4-400000-2-2222-22-2001−2i32i3−2i32i3-1-1100000000i3−i3i3−i3003-3000000000000000000000000000
χ514-44-444-4-400000-2-2222-22-2001−2i32i32i3−2i3-1-1100000000i3−i3−i3i300-33000000000000000000000000000
χ524-44-444-4-400000-2-2222-22-20012i3−2i3−2i32i3-1-1100000000−i3i3i3−i300-33000000000000000000000000000
χ534-44-444-4-400000-2-2222-22-20012i3−2i32i3−2i3-1-1100000000−i3i3−i3i3003-3000000000000000000000000000
χ544-4-444-4-440000044-4-44-44-40040000-44-40000000000000000000000000000000000000000000
χ554-4-444-4-44000004-22-442-2-400-200002-220000000000000000000000000000000−2i32i30000000000
χ564-4-444-4-44000004-22-442-2-400-200002-2200000000000000000000000000000002i3−2i30000000000
χ574-4-444-4-4400000-24-42-2-44200-200002-220000000000000000000000000000000000023−23000000
χ584-4-444-4-4400000-24-42-2-44200-200002-2200000000000000000000000000000000000−2323000000
χ596666-3-3-3-3666-3-300000000-3-3000000002200000000000000220000200-1-1-1-100000000-1-10000
χ606666-3-3-3-3666-3-300000000-3-300000000-2-200000000000000-2-20000-200111100000000110000
χ616666-3-3-3-36-6-63300000000-330000000022000000000000002-20000-200-1-11100000000-110000
χ626666-3-3-3-36-6-63300000000-3300000000-2-200000000000000-22000020011-1-1000000001-10000
χ636666-3-3-3-3-66-633000000003-3000000002200000000000000-220000-200-1-111000000001-10000
χ646666-3-3-3-3-66-633000000003-300000000-2-2000000000000002-2000020011-1-100000000-110000
χ656666-3-3-3-3-6-66-3-30000000033000000002200000000000000-2-20000200-1-1-1-100000000110000
χ666666-3-3-3-3-6-66-3-3000000003300000000-2-200000000000000220000-200111100000000-1-10000
χ6788-8-88-88-800000-4-4-4-4444400200002-2-20000000000000000000000000000000000000000000
χ688-8-888-8-8800000-4-444-44-440020000-22-20000000000000000000000000000000000000000000
χ691212-12-12-66-66000000000000000000000004-400000000000000000000000-220000000000000000
χ701212-12-12-66-6600000000000000000000000-44000000000000000000000002-20000000000000000
χ7112-1212-12-6-666000−6i36i30000000000000000000000000000000000000000000000000000000000000
χ7212-1212-12-6-6660006i3−6i30000000000000000000000000000000000000000000000000000000000000
χ7312-12-1212-666-600000000000000000000000000000000000000000000000000−2i32i300000000000000
χ7412-12-1212-666-6000000000000000000000000000000000000000000000000002i3−2i300000000000000

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