Finite Group Databasebeta

← Group #13151484

Character table — Group #13151484

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order12223666224121233666666663666666622444466666612121212224444444666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-111111111111-11-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111-1-111-1-11111111111-11-1-1-1-111-111-1-1-1-111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111111111111-1-1-111-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111-1-1-1-1111111111-1111-1-1111111111-1111-1-1-1-1-1-1-1-11-11-11-1-1-1-111-1-11111111-11-1-1-1
χ6111111111-1-1-1-1111111111-1111-1-111111-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-111-111
χ7111111111-1-1-1-1111111111-1111-1-1111-1-111-1-1-1111-1-1-1-1-1-11-1-11-111-11-1-1-1-11111-1-1-1-11-1-1111
χ8111111111-1-1-1-1111111111-1111-1-1111-1-1-1-111-1111-1-1-1-1-1-111-1-111-11-111-1-111-1-11111-11-11-1-1
χ911111111-11-1-1-111111111-111-1-1111111111111-1-1-111-1-1-1-11-1-1-1-1-1-111-1-111111111-1-1-11-1-11-1
χ1011111111-11-1-1-111111111-111-1-11111111-1-1-1-11-1-1-111-1-1-1-111-111-11-1-1111111-1-1-1-1111-1-1-1-11
χ1111111111-11-1-1-111111111-111-1-111111-1-111-1-11-1-1-111-1-1-1-1-1-11111-11-1-1-1-1-1-1-111-1-111-1111-11
χ1211111111-11-1-1-111111111-111-1-111111-1-1-1-1111-1-1-111-1-1-1-1-111-1-111-1111-1-1-1-1-1-111-1-11-1111-1
χ1311111111-1-111111111111-1-11-1-1-1-1111111111-1-1-1-1-1-11111-11-11-11-1-1-11111-1-11111-1-1-1-1-11-11
χ1411111111-1-111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1-1-11111-111-1
χ1511111111-1-111111111111-1-11-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111111-11-1-1-1111-1-11111-1-111-1-11-11-1
χ1611111111-1-111111111111-1-11-1-1-1-1111-1-1-1-111-1-1-1-1-1-111111-111-1-111-1-1-1-1-111-1-111-1-1111-1-11
χ1722222222222222-1-122-1-1222-122-1-1-1-1-12200002-1-1-1-1-1-12-1-120200200000-1-1-1-100000000-1-100
χ1822222222222222-1-122-1-1222-122-1-1-1-1-1-2-200002-1-1-1-1-1-12-1-1-20-200-2000001111000000001100
χ192222222222222-122-1-122-122-1-1-122-1-1-1000022-12-1-1-1-12-1-1-100022000200000000-1-1-1-10000-1-1
χ202222222222222-122-1-122-122-1-1-122-1-1-10000-2-2-12-1-1-1-12-1-1-1000-2-2000-2000000001111000011
χ21222222222-2-2-2-22-1-122-1-122-2-12211-1-1-1220000-2-1-1-1111-211-20200-200000-1-11100000000-1100
χ22222222222-2-2-2-22-1-122-1-122-2-12211-1-1-1-2-20000-2-1-1-1111-21120-20020000011-1-1000000001-100
χ23222222222-2-2-2-2-122-1-122-12-2-1-1-1-2-2-1-1-100002212-1-111-2111000-22000-200000000-1-1-1-1000011
χ24222222222-2-2-2-2-122-1-122-12-2-1-1-1-2-2-1-1-10000-2-212-1-111-21110002-200020000000011110000-1-1
χ2522222222-22-2-2-22-1-122-1-12-22-1-2-2-1-1-1-1-12200002111-1-11-21120-200-200000-1-1-1-1000000001100
χ2622222222-22-2-2-22-1-122-1-12-22-1-2-2-1-1-1-1-1-2-200002111-1-11-211-20200200000111100000000-1-100
χ2722222222-22-2-2-2-122-1-122-1-22-11122-1-1-1000022-1-211-1-1-2111000-2-2000200000000-1-1110000-11
χ2822222222-22-2-2-2-122-1-122-1-22-11122-1-1-10000-2-2-1-211-1-1-211100022000-20000000011-1-100001-1
χ2922222222-2-22222-1-122-1-12-2-2-1-2-211-1-1-1220000-211111-12-1-1-20-200200000-1-111000000001-100
χ3022222222-2-22222-1-122-1-12-2-2-1-2-211-1-1-1-2-20000-211111-12-1-120200-20000011-1-100000000-1100
χ3122222222-2-2222-122-1-122-1-2-2-111-2-2-1-1-10000221-211112-1-1-10002-2000-200000000-1-11100001-1
χ3222222222-2-2222-122-1-122-1-2-2-111-2-2-1-1-10000-2-21-211112-1-1-1000-2200020000000011-1-10000-11
χ3322-2-222-2-20000022-22-22-2-200200002-2-22-22i−2i2i−2i0000000000000000000002-2002i−2i2i−2i00000000
χ3422-2-222-2-20000022-22-22-2-200200002-2-22-2−2i2i−2i2i0000000000000000000002-200−2i2i−2i2i00000000
χ3522-2-222-2-20000022-22-22-2-200200002-2-2-222i−2i−2i2i000000000000000000000-22002i−2i−2i2i00000000
χ3622-2-222-2-20000022-22-22-2-200200002-2-2-22−2i2i2i−2i000000000000000000000-2200−2i2i2i−2i00000000
χ374444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111000000-2-21111-2-211000000000000000000000000000
χ38444444444-4-4-4-4-2-2-2-2-2-2-2-24-41-2-2221110000002-211-1-122-1-1000000000000000000000000000
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
χ4144-4-444-4-4000004-224-4-22-400-20000-2224-40000000000000000000000000-2200000000000000
χ4244-4-444-4-4000004-224-4-22-400-20000-222-4400000000000000000000000002-200000000000000
χ4344-4-444-4-400000-24-4-224-4200-20000-22200004i−4i000000000000000000000000000−2i2i00000000
χ4444-4-444-4-400000-24-4-224-4200-20000-2220000−4i4i0000000000000000000000000002i−2i00000000
χ454-44-44-44-400000444-4-4-4-440040000-4-440000000000000000000000000000000000000000000
χ464-44-44-44-4000004-2-2-4-422400-200−2i32i322-20000000000−2i32i30000000000000000000000000000000
χ474-44-44-44-4000004-2-2-4-422400-2002i3−2i322-200000000002i3−2i30000000000000000000000000000000
χ484-44-44-44-400000-24422-4-4-200-2−2i32i30022-200000000−2i32i3000000000000000000000000000000000
χ494-44-44-44-400000-24422-4-4-200-22i3−2i30022-2000000002i3−2i3000000000000000000000000000000000
χ504-44-44-44-400000-2-2-22222-2001−2i32i3−2i32i3-1-1100000000i3−i3i3−i3003-3000000000000000000000000000
χ514-44-44-44-400000-2-2-22222-2001−2i32i32i3−2i3-1-1100000000i3−i3−i3i300-33000000000000000000000000000
χ524-44-44-44-400000-2-2-22222-20012i3−2i3−2i32i3-1-1100000000−i3i3i3−i300-33000000000000000000000000000
χ534-44-44-44-400000-2-2-22222-20012i3−2i32i3−2i3-1-1100000000−i3i3−i3i3003-3000000000000000000000000000
χ544-4-444-4-440000044-4-44-44-40040000-44-40000000000000000000000000000000000000000000
χ554-4-444-4-44000004-22-442-2-400-200002-2200000000000000000000000000000−2i32i3000000000000
χ564-4-444-4-44000004-22-442-2-400-200002-22000000000000000000000000000002i3−2i3000000000000
χ574-4-444-4-4400000-24-42-2-44200-200002-220000000000000000000000000000000000023−23000000
χ584-4-444-4-4400000-24-42-2-44200-200002-2200000000000000000000000000000000000−2323000000
χ596666-3-3-3-3666-3-300000000-3-3000000000022000000000000020000220-1-10000-1-10000-1-10000
χ606666-3-3-3-3666-3-300000000-3-30000000000-2-20000000000000-20000-2-20110000110000110000
χ616666-3-3-3-36-6-63300000000-330000000000220000000000000-200002-20110000-1-10000-110000
χ626666-3-3-3-36-6-63300000000-330000000000-2-2000000000000020000-220-1-100001100001-10000
χ636666-3-3-3-3-66-633000000003-30000000000220000000000000-20000-220110000-1-100001-10000
χ646666-3-3-3-3-66-633000000003-30000000000-2-20000000000000200002-20-1-10000110000-110000
χ656666-3-3-3-3-6-66-3-30000000033000000000022000000000000020000-2-20-1-10000-1-10000110000
χ666666-3-3-3-3-6-66-3-300000000330000000000-2-20000000000000-20000220110000110000-1-10000
χ6788-8-888-8-800000-4-44-44-44400200002-2-20000000000000000000000000000000000000000000
χ688-8-888-8-8800000-4-444-44-440020000-22-20000000000000000000000000000000000000000000
χ691212-12-12-6-66600000000000000000000000004i−4i000000000000000000000000000−2i2i0000000000
χ701212-12-12-6-6660000000000000000000000000−4i4i0000000000000000000000000002i−2i0000000000
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).