Finite Group Databasebeta

← Group #13151488

Character table — Group #13151488

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order1222366622412123366666666366666664444446666661212121222244444466121212121212121212126612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-11-1
χ31111111111111111111111111111111-1-111-1-11111111111-11-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111-1-1-1-1111111111111-1-11-1-11-1-11-1-1-1-1-1-1-1-11111-11-1-1-11
χ5111111111-1-1-1-1111111111-1111-1-11111111111-111-1-1-1-1-1-11-1-1-1-1-11-11-1-11111-1-111111-11-1-1-1
χ6111111111-1-1-1-1111111111-1111-1-111111-1-1-1-11-111-1-1-1-1-1-1111-1-11-11-111-1-111-1-1-1-1-1-111-11-11
χ7111111111-1-1-1-1111111111-1111-1-1111-1-111-1-11-111-1-1-1-1-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-111-111
χ8111111111-1-1-1-1111111111-1111-1-1111-1-1-1-1111-111-1-1-1-1-1-1-11-111-1-11111-1-1-1-1111111-1-1-111-1
χ911111111-11-1-1-111111111-111-1-111111111111-11-1-111-1-1-1-1-1-1-11-11-11-1-1-111111111-1-1-1-1-11-11
χ1011111111-11-1-1-111111111-111-1-11111111-1-1-1-1-11-1-111-1-1-1-1-1111-1-11-1111-1-11111-1-111-111-1-1-1
χ1111111111-11-1-1-111111111-111-1-111111-1-111-1-1-11-1-111-1-1-1-11-11-11-1-111-1-111-1-1-1-1-1-11111-111-1
χ1211111111-11-1-1-111111111-111-1-111111-1-1-1-111-11-1-111-1-1-1-111-1-1111-1-111-1-1-1-1-1-111-1-11-11-111
χ1311111111-1-111111111111-1-11-1-1-1-1111111111-1-1-1-1-1-11111-111-11-1-1-1-1111111-1-111-1-1-11-1-11-1
χ1411111111-1-111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-111-1-11111
χ1511111111-1-111111111111-1-11-1-1-1-1111-1-111-1-1-1-1-1-1-1-1111111-11-11-1-111111-1-111-1-1111-1-1-1-11
χ1611111111-1-111111111111-1-11-1-1-1-1111-1-1-1-111-1-1-1-1-1-111111-111-1-111-1-1-1-1-1-1-11111-1-11111-1-1
χ1722222222222222-12-12-12-122-122-1-1-1-1-1220000-12-1-1-1-12-1-1-12002200000000-1-1-1-10000-1000-10
χ1822222222222222-12-12-12-122-122-1-1-1-1-1-2-20000-12-1-1-1-12-1-1-1-200-2-20000000011110000100010
χ192222222222222-12-12-12-1222-1-1-122-1-1-10000222-1-1-1-1-1-12-1-100200200200000000-1-1-1-10-1000-1
χ202222222222222-12-12-12-1222-1-1-122-1-1-10000-2-22-1-1-1-1-1-12-1-100-200-200-2000000001111010001
χ21222222222-2-2-2-22-12-12-12-12-2-12211-1-1-1220000-1-2-1-111-2111200-2-200000000-1-1110000-100010
χ22222222222-2-2-2-22-12-12-12-12-2-12211-1-1-1-2-20000-1-2-1-111-2111-200220000000011-1-100001000-10
χ23222222222-2-2-2-2-12-12-12-122-2-1-1-1-2-2-1-1-100002221-1-1111-21100-200-200200000000-1-1-1-1010001
χ24222222222-2-2-2-2-12-12-12-122-2-1-1-1-2-2-1-1-10000-2-221-1-1111-21100200200-20000000011110-1000-1
χ2522222222-22-2-2-22-12-12-12-1-22-1-2-2-1-1-1-1-12200001211-1-1-2111-2002-200000000-1-1-1-10000100010
χ2622222222-22-2-2-22-12-12-12-1-22-1-2-2-1-1-1-1-1-2-200001211-1-1-2111200-220000000011110000-1000-10
χ2722222222-22-2-2-2-12-12-12-12-22-11122-1-1-1000022-2-111-1-11-21100-200200-200000000-1-11101000-1
χ2822222222-22-2-2-2-12-12-12-12-22-11122-1-1-10000-2-2-2-111-1-11-21100200-20020000000011-1-10-10001
χ2922222222-2-22222-12-12-12-1-2-2-1-2-211-1-1-12200001-211112-1-1-1-200-2200000000-1-11100001000-10
χ3022222222-2-22222-12-12-12-1-2-2-1-2-211-1-1-1-2-200001-211112-1-1-12002-20000000011-1-10000-100010
χ3122222222-2-2222-12-12-12-12-2-2-111-2-2-1-1-1000022-211111-12-1-100200-200-200000000-1-1110-10001
χ3222222222-2-2222-12-12-12-12-2-2-111-2-2-1-1-10000-2-2-211111-12-1-100-20020020000000011-1-101000-1
χ3322-2-222-2-200000222-2-2-2-2200200002-2-22-22i−2i2i−2i0000000000000000000002i−2i2-2002i−2i00000000
χ3422-2-222-2-200000222-2-2-2-2200200002-2-22-2−2i2i−2i2i000000000000000000000−2i2i2-200−2i2i00000000
χ3522-2-222-2-200000222-2-2-2-2200200002-2-2-222i−2i−2i2i0000000000000000000002i−2i-2200−2i2i00000000
χ3622-2-222-2-200000222-2-2-2-2200200002-2-2-22−2i2i2i−2i000000000000000000000−2i2i-22002i−2i00000000
χ374444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111000000-2-21111-2-211000000000000000000000000000
χ38444444444-4-4-4-4-2-2-2-2-2-2-2-24-41-2-222111000000-2211-1-122-1-1000000000000000000000000000
χ3944444444-44-4-4-4-2-2-2-2-2-2-2-2-44122-2-21110000002-2-1-11122-1-1000000000000000000000000000
χ4044444444-4-4444-2-2-2-2-2-2-2-2-4-41222211100000022-1-1-1-1-2-211000000000000000000000000000
χ4144-4-444-4-4000004-242-42-4-200-20000-2224-4000000000000000000000000000-22000000000000
χ4244-4-444-4-4000004-242-42-4-200-20000-222-440000000000000000000000000002-2000000000000
χ4344-4-444-4-400000-24-2-42-42400-20000-22200004i−4i000000000000000000000000000−2i2i00000000
χ4444-4-444-4-400000-24-2-42-42400-20000-2220000−4i4i0000000000000000000000000002i−2i00000000
χ454-44-44-44-40000044-4-444-4-40040000-4-440000000000000000000000000000000000000000000
χ464-44-44-44-4000004-2-424-2-4200-200−2i32i322-20000000000−2i32i30000000000000000000000000000000
χ474-44-44-44-4000004-2-424-2-4200-2002i3−2i322-200000000002i3−2i30000000000000000000000000000000
χ484-44-44-44-400000-242-4-242-400-2−2i32i30022-200000000−2i32i3000000000000000000000000000000000
χ494-44-44-44-400000-242-4-242-400-22i3−2i30022-2000000002i3−2i3000000000000000000000000000000000
χ504-44-44-44-400000-2-222-2-222001−2i32i3−2i32i3-1-1100000000i3−i3i3−i3003-3000000000000000000000000000
χ514-44-44-44-400000-2-222-2-222001−2i32i32i3−2i3-1-1100000000i3−i3−i3i300-33000000000000000000000000000
χ524-44-44-44-400000-2-222-2-2220012i3−2i3−2i32i3-1-1100000000−i3i3i3−i300-33000000000000000000000000000
χ534-44-44-44-400000-2-222-2-2220012i3−2i32i3−2i3-1-1100000000−i3i3−i3i3003-3000000000000000000000000000
χ544-4-444-4-440000044-44-4-44-40040000-44-40000000000000000000000000000000000000000000
χ554-4-444-4-44000004-2-4-2-424200-200002-22000000000000000000000000000000023−230000000000
χ564-4-444-4-44000004-2-4-2-424200-200002-220000000000000000000000000000000−23230000000000
χ574-4-444-4-4400000-24242-4-2-400-200002-2200000000000000000000000000000000000−2i32i3000000
χ584-4-444-4-4400000-24242-4-2-400-200002-22000000000000000000000000000000000002i3−2i3000000
χ596666-3-3-3-3666-3-300000000-3-3000000000022000000000000020000220-1-1-1-10000000000-1-100
χ606666-3-3-3-3666-3-300000000-3-30000000000-2-20000000000000-20000-2-20111100000000001100
χ616666-3-3-3-36-6-63300000000-330000000000220000000000000-200002-2011-1-10000000000-1100
χ626666-3-3-3-36-6-63300000000-330000000000-2-2000000000000020000-220-1-11100000000001-100
χ636666-3-3-3-3-66-633000000003-30000000000220000000000000-20000-22011-1-100000000001-100
χ646666-3-3-3-3-66-633000000003-30000000000-2-20000000000000200002-20-1-1110000000000-1100
χ656666-3-3-3-3-6-66-3-30000000033000000000022000000000000020000-2-20-1-1-1-100000000001100
χ666666-3-3-3-3-6-66-3-300000000330000000000-2-20000000000000-2000022011110000000000-1-100
χ6788-8-888-8-800000-4-4-44444-400200002-2-20000000000000000000000000000000000000000000
χ688-8-888-8-8800000-4-44-444-440020000-22-20000000000000000000000000000000000000000000
χ691212-12-12-6-66600000000000000000000000004i−4i00000000000000000000000−2i2i00000000000000
χ701212-12-12-6-6660000000000000000000000000−4i4i000000000000000000000002i−2i00000000000000
χ7112-1212-12-66-66000−6i36i30000000000000000000000000000000000000000000000000000000000000
χ7212-1212-12-66-660006i3−6i30000000000000000000000000000000000000000000000000000000000000
χ7312-12-1212-666-6000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ7412-12-1212-666-60000000000000000000000000000000000000000000000002i3−2i30000000000000000

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