Finite Group Databasebeta

← Group #13151499

Character table — Group #13151499

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order122236662246633666666612366666121222444466666661212122244444446666121212121212121261212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-111111111111-11-1-1-1-11-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111-1-111-1-11111111111-11-1-11-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111111111111-1-1-11-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111-1-11111111111-1-11-1-1111-1-11111111-1111-1-1-1-1-1-1-11-1-11-1-1111-1-1111111-1-1-1-11-11-1
χ6111111111-1-11111111111-1-11-1-1111-1-111-1-1-1-11-1111-1-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1-111111-1-11
χ7111111111-1-11111111111-1-11-1-1111-1-1-1-111-1-11-1111-1-1-1-1-11-1-11-1-1111-1-1111111-1-111-1-1-11-11
χ8111111111-1-11111111111-1-11-1-1111-1-1-1-1-1-1111-1111-1-1-1-1-111-1-111-11-1-1-111-1-1-1-111-1-111-111-1
χ911111111-11-1-1-1111111111-1111111-1-1111111-11-1-1-111-1-1-11-1-1-11-11-1-1111111-1-111-1-1-11-1-1-11
χ1011111111-11-1-1-1111111111-1111111-1-111-1-1-1-1-11-1-1-111-1-1-111-11-11-1-111111-1-111-1-1111-1-1-11-1
χ1111111111-11-1-1-1111111111-1111111-1-1-1-111-1-1-11-1-1-111-1-1-1-1-11111-11-1-1-1-1-111-1-1-1-111-11111-1
χ1211111111-11-1-1-1111111111-1111111-1-1-1-1-1-111-11-1-1-111-1-1-1-111-1-1-1111-1-1-1-1-1-11111-1-11-111-11
χ1311111111-1-11-1-111111111-111-1-111111111111-1-1-1-1-1-1-1111-11-11-1-1-11-111-1-111-1-111111-1-11-1-1
χ1411111111-1-11-1-111111111-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-111-1-1-1-1-11-1111
χ1511111111-1-11-1-111111111-111-1-111111-1-111-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-11-11-111
χ1611111111-1-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-1-1-1-11111-1111-1-1-11-1-111-1-1111111-111-1-1-1
χ1722222222222222-1-122-1-1222-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1202000020-1-1-1-10000000000-1-100
χ1822222222222222-1-122-1-1222-1-1-1-1-1-122-2-2000022-1-1-1-1-1-1-1-1-20-20000-20111100000000001100
χ192222222222222-122-1-122-122-122-1-1-1-1-1000022-1-12-1-1-1-12-1-100020220000000000-1-1-1-10000-1-1
χ202222222222222-122-1-122-122-122-1-1-1-1-10000-2-2-1-12-1-1-1-12-1-1000-20-2-200000000001111000011
χ21222222222-2-2222-1-122-1-12-2-2-111-1-1-1-2-22200002-2-1-1-111111-2020000-20-1-1110000000000-1100
χ22222222222-2-2222-1-122-1-12-2-2-111-1-1-1-2-2-2-200002-2-1-1-11111120-200002011-1-100000000001-100
χ23222222222-2-222-122-1-122-1-2-2-1-2-2-1-1-111000022-112-1-111-211000-202-20000000000-1-1110000-11
χ24222222222-2-222-122-1-122-1-2-2-1-2-2-1-1-1110000-2-2-112-1-111-21100020-22000000000011-1-100001-1
χ2522222222-22-2-2-22-1-122-1-122-2-1-1-1-1-1-1-2-2220000-22111-1-111120-20000-20-1-1-1-100000000001100
χ2622222222-22-2-2-22-1-122-1-122-2-1-1-1-1-1-1-2-2-2-20000-22111-1-1111-20200002011110000000000-1-100
χ2722222222-22-2-2-2-122-1-122-12-2-122-1-1-1110000221-1-211-1-1-211000-20-220000000000-1-11100001-1
χ2822222222-22-2-2-2-122-1-122-12-2-122-1-1-1110000-2-21-1-211-1-1-211000202-2000000000011-1-10000-11
χ2922222222-2-22-2-22-1-122-1-12-22-111-1-1-122220000-2-211111-1-1-1-20-2000020-1-11100000000001-100
χ3022222222-2-22-2-22-1-122-1-12-22-111-1-1-122-2-20000-2-211111-1-1-12020000-2011-1-10000000000-1100
χ3122222222-2-22-2-2-122-1-122-1-22-1-2-2-1-1-1-1-100002211-211112-1-100020-2-20000000000-1-1-1-1000011
χ3222222222-2-22-2-2-122-1-122-1-22-1-2-2-1-1-1-1-10000-2-211-211112-1-1000-2022000000000011110000-1-1
χ3322-2-222-2-20000022-22-22-2-2002002-2-2002-22i−2i2i−2i00000000000000000002-2002i−2i002i−2i00000000
χ3422-2-222-2-20000022-22-22-2-2002002-2-2002-2−2i2i−2i2i00000000000000000002-200−2i2i00−2i2i00000000
χ3522-2-222-2-20000022-22-22-2-2002002-2-200-222i−2i−2i2i0000000000000000000-22002i−2i00−2i2i00000000
χ3622-2-222-2-20000022-22-22-2-2002002-2-200-22−2i2i2i−2i0000000000000000000-2200−2i2i002i−2i00000000
χ374444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2000000-2-2-21111-211000000000000000000000000000
χ38444444444-4-444-2-2-2-2-2-2-2-2-4-412211122000000-22-211-1-12-1-1000000000000000000000000000
χ3944444444-44-4-4-4-2-2-2-2-2-2-2-24-41-2-2111220000002-22-1-1112-1-1000000000000000000000000000
χ4044444444-4-44-4-4-2-2-2-2-2-2-2-2-44122111-2-2000000222-1-1-1-1-211000000000000000000000000000
χ4144-4-444-4-4000004-224-4-22-400-200-222004-400000000000000000000000-220000000000000000
χ4244-4-444-4-4000004-224-4-22-400-200-22200-44000000000000000000000002-20000000000000000
χ4344-4-444-4-400000-24-4-224-4200-200-2220000004i−4i000000000000000000000000000−2i2i00000000
χ4444-4-444-4-400000-24-4-224-4200-200-222000000−4i4i0000000000000000000000000002i−2i00000000
χ454-44-44-44-400000444-4-4-4-4400400-4-44000000000000000000000000000000000000000000000
χ464-44-44-44-4000004-2-2-4-422400-2−2i32i322-20000000000000−2i32i3000000000000000000000000000000
χ474-44-44-44-4000004-2-2-4-422400-22i3−2i322-200000000000002i3−2i3000000000000000000000000000000
χ484-44-44-44-400000-24422-4-4-200-20022-2−2i32i300000000000000−2i32i3000000000000000000000000000
χ494-44-44-44-400000-24422-4-4-200-20022-22i3−2i3000000000000002i3−2i3000000000000000000000000000
χ504-44-44-44-400000-2-2-22222-2001−2i32i3-1-11−2i32i30000000003-3i3−i30i3−i3000000000000000000000000000
χ514-44-44-44-400000-2-2-22222-2001−2i32i3-1-112i3−2i3000000000-33i3−i30−i3i3000000000000000000000000000
χ524-44-44-44-400000-2-2-22222-20012i3−2i3-1-11−2i32i3000000000-33−i3i30i3−i3000000000000000000000000000
χ534-44-44-44-400000-2-2-22222-20012i3−2i3-1-112i3−2i30000000003-3−i3i30−i3i3000000000000000000000000000
χ544-4-444-4-440000044-4-44-44-400400-44-4000000000000000000000000000000000000000000000
χ554-4-444-4-44000004-22-442-2-400-2002-2200000000000000000000000000000−2i32i300000000000000
χ564-4-444-4-44000004-22-442-2-400-2002-22000000000000000000000000000002i3−2i300000000000000
χ574-4-444-4-4400000-24-42-2-44200-2002-22000000000000000000000000000000000000023−23000000
χ584-4-444-4-4400000-24-42-2-44200-2002-220000000000000000000000000000000000000−2323000000
χ596666-3-3-3-3666-3-300000000-3-30000000000220000000000000200200020000-1-1-1-10000-1-10000
χ606666-3-3-3-3666-3-300000000-3-30000000000-2-20000000000000-200-2000-2000011110000110000
χ616666-3-3-3-36-6-6-3-300000000330000000000220000000000000-200-200020000-1-1-1-10000110000
χ626666-3-3-3-36-6-6-3-300000000330000000000-2-200000000000002002000-2000011110000-1-10000
χ636666-3-3-3-3-66-63300000000-330000000000220000000000000-2002000-20000-1-11100001-10000
χ646666-3-3-3-3-66-63300000000-330000000000-2-20000000000000200-20002000011-1-10000-110000
χ656666-3-3-3-3-6-6633000000003-30000000000220000000000000200-2000-20000-1-1110000-110000
χ666666-3-3-3-3-6-6633000000003-30000000000-2-20000000000000-20020002000011-1-100001-10000
χ6788-8-888-8-800000-4-44-44-444002002-2-2000000000000000000000000000000000000000000000
χ688-8-888-8-8800000-4-444-44-4400200-22-2000000000000000000000000000000000000000000000
χ691212-12-12-6-66600000000000000000000000004i−4i0000000000000000000000000−2i2i000000000000
χ701212-12-12-6-6660000000000000000000000000−4i4i00000000000000000000000002i−2i000000000000
χ7112-1212-12-66-66000−6i36i30000000000000000000000000000000000000000000000000000000000000
χ7212-1212-12-66-660006i3−6i30000000000000000000000000000000000000000000000000000000000000
χ7312-12-1212-666-6000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ7412-12-1212-666-60000000000000000000000000000000000000000000000000000002i3−2i30000000000

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