Finite Group Databasebeta

← Group #13151380

Character table — Group #13151380

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order12223666224663366666661236666612124444446666666121212222444444121212121212121212121212666121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-111-1-1-1
χ31111111111111111111111111111111-1-111-1-11111111111-1-1-111-1-11-11111-1-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111-1-1-1-1111111111111-1-11-1-11-1-11-1-1-1-1-1-1-1-111111-1-1-1-11
χ5111111111-1-11111111111-1-11-1-1111-1-111111111-111-1-1-1-1-11-1-1-111-1-1-1111111-1-111-1-1-11-1-1-11
χ6111111111-1-11111111111-1-11-1-1111-1-111-1-1-1-111-111-1-1-1-1-11-111-1-1-111-1-1-1-111-1-1-1-11111-111-1
χ7111111111-1-11111111111-1-11-1-1111-1-1-1-111-1-111-111-1-1-1-1-1-111-11-11-111111-1-111-1-1111-11-1-1-1
χ8111111111-1-11111111111-1-11-1-1111-1-1-1-1-1-11111-111-1-1-1-1-1-11-11-1111-1-1-1-1-1-1-11111-1-1-1-11111
χ911111111-11-1-1-1111111111-1111111-1-1111111-1-11-1-111-1-1-1-11-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1011111111-11-1-1-1111111111-1111111-1-111-1-1-1-1-1-11-1-111-1-1-1-111111-1-1-1-1-11111-1-1-1-1-1-11-11-111
χ1111111111-11-1-1-1111111111-1111111-1-1-1-111-1-1-1-11-1-111-1-1-11-11-1-1111-111-1-1-1-111-1-1-1-111-11-11
χ1211111111-11-1-1-1111111111-1111111-1-1-1-1-1-111-1-11-1-111-1-1-11-1-111-11-11-1-111-1-1111111-11-1-11-1
χ1311111111-1-11-1-111111111-111-1-111111111111-1-1-1-1-1-1-1111-1-111-1-11-1-111-1-1111111-1-11-1-1-11-1
χ1411111111-1-11-1-111111111-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1111111-1-111-1-1-11-11
χ1511111111-1-11-1-111111111-111-1-111111-1-111-1-1-1-1-1-1-1-1-111111-11-11-1-1111-1-1-1-1-1-1-1-111-111-111
χ1611111111-1-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-1-1-1-1111111-11-1-11-1-1-111-1-1-1-111-1-11111-1-1
χ1722222222222222-12-1-1-12222-122-1-1-1-1-12200002-1-1-1-1-1-12-1-12200002000000-1-1-1-100000-1-1000
χ1822222222222222-12-1-1-12222-122-1-1-1-1-1-2-200002-1-1-1-1-1-12-1-1-2-20000-200000011110000011000
χ192222222222222-12-1222-1-122-1-1-1-1-1-122000022-122-1-1-1-1-1-1-100200200200000000-1-1-1-1-10000-1
χ202222222222222-12-1222-1-122-1-1-1-1-1-1220000-2-2-122-1-1-1-1-1-1-100-200-200-2000000001111100001
χ21222222222-2-2222-12-1-1-122-2-2-1-2-2-1-1-1112200002-11-1-111-2112-20000-2000000-1-11100000-11000
χ22222222222-2-2222-12-1-1-122-2-2-1-2-2-1-1-111-2-200002-11-1-111-211-220000200000011-1-1000001-1000
χ23222222222-2-222-12-1222-1-1-2-2-111-1-1-1-2-2000022-12-2-1-11111100-200200-200000000-1-11110000-1
χ24222222222-2-222-12-1222-1-1-2-2-111-1-1-1-2-20000-2-2-12-2-1-11111100200-20020000000011-1-1-100001
χ2522222222-22-2-2-22-12-1-1-1222-2-122-1-1-111220000-21-111-1-1-211-220000-2000000-1-111000001-1000
χ2622222222-22-2-2-22-12-1-1-1222-2-122-1-1-111-2-20000-21-111-1-1-2112-20000200000011-1-100000-11000
χ2722222222-22-2-2-2-12-1222-1-12-2-1-1-1-1-1-1-2-20000221-2211-1-111100-200-200200000000-1-1-1-1100001
χ2822222222-22-2-2-2-12-1222-1-12-2-1-1-1-1-1-1-2-20000-2-21-2211-1-111100200200-2000000001111-10000-1
χ2922222222-2-22-2-22-12-1-1-122-22-1-2-2-1-1-1-1-1220000-21111112-1-1-2-200002000000-1-1-1-10000011000
χ3022222222-2-22-2-22-12-1-1-122-22-1-2-2-1-1-1-1-1-2-20000-21111112-1-1220000-2000000111100000-1-1000
χ3122222222-2-22-2-2-12-1222-1-1-22-111-1-1-1220000221-2-21111-1-1-100200-200-200000000-1-111-100001
χ3222222222-2-22-2-2-12-1222-1-1-22-111-1-1-1220000-2-21-2-21111-1-1-100-20020020000000011-1-110000-1
χ3322-2-222-2-200000222-22-2-2-2002002-2-2002-22i−2i2i−2i00000000000000000002i−2i002-2002i−2i00000000
χ3422-2-222-2-200000222-22-2-2-2002002-2-2002-2−2i2i−2i2i0000000000000000000−2i2i002-200−2i2i00000000
χ3522-2-222-2-200000222-22-2-2-2002002-2-200-222i−2i−2i2i00000000000000000002i−2i00-2200−2i2i00000000
χ3622-2-222-2-200000222-22-2-2-2002002-2-200-22−2i2i2i−2i0000000000000000000−2i2i00-22002i−2i00000000
χ374444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2000000-2-2-21111-211000000000000000000000000000
χ38444444444-4-444-2-2-2-2-2-2-2-2-4-412211122000000-2-2211-1-12-1-1000000000000000000000000000
χ3944444444-44-4-4-4-2-2-2-2-2-2-2-24-41-2-21112200000022-2-1-1112-1-1000000000000000000000000000
χ4044444444-4-44-4-4-2-2-2-2-2-2-2-2-44122111-2-2000000222-1-1-1-1-211000000000000000000000000000
χ4144-4-444-4-4000004-242-22-4-400-200-222004-4000000000000000000000000000-22000000000000
χ4244-4-444-4-4000004-242-22-4-400-200-22200-440000000000000000000000000002-2000000000000
χ4344-4-444-4-400000-24-2-44-42200-200-2220000004i−4i000000000000000000000000000−2i2i00000000
χ4444-4-444-4-400000-24-2-44-42200-200-222000000−4i4i0000000000000000000000000002i−2i00000000
χ454-44-44-4-440000044-44-4-44-400400-4-44000000000000000000000000000000000000000000000
χ464-44-44-4-44000004-2-4-2224-400-20022-2−2i32i300000000000000−2i32i3000000000000000000000000000
χ474-44-44-4-44000004-2-4-2224-400-20022-22i3−2i3000000000000002i3−2i3000000000000000000000000000
χ484-44-44-4-4400000-2424-4-4-2200-2−2i32i322-20000000000000−2i32i3000000000000000000000000000000
χ494-44-44-4-4400000-2424-4-4-2200-22i3−2i322-200000000000002i3−2i3000000000000000000000000000000
χ504-44-44-4-4400000-2-22-222-22001−2i32i3-1-11−2i32i30000000003-3i3−i30i3−i3000000000000000000000000000
χ514-44-44-4-4400000-2-22-222-22001−2i32i3-1-112i3−2i3000000000-33i3−i30−i3i3000000000000000000000000000
χ524-44-44-4-4400000-2-22-222-220012i3−2i3-1-11−2i32i3000000000-33−i3i30i3−i3000000000000000000000000000
χ534-44-44-4-4400000-2-22-222-220012i3−2i3-1-112i3−2i30000000003-3−i3i30−i3i3000000000000000000000000000
χ544-4-444-44-40000044-4-4-44-4400400-44-4000000000000000000000000000000000000000000000
χ554-4-444-44-4000004-2-422-2-4400-2002-22000000000000000000000000000000000−2i32i30000000000
χ564-4-444-44-4000004-2-422-2-4400-2002-220000000000000000000000000000000002i3−2i30000000000
χ574-4-444-44-400000-242-4-442-200-2002-220000000000000000000000000000000000000−2i32i3000000
χ584-4-444-44-400000-242-4-442-200-2002-2200000000000000000000000000000000000002i3−2i3000000
χ596666-3-3-3-3666-3-300000000-3-3000000000022000000000000000220020-1-1-1-100000000000-1-10
χ606666-3-3-3-3666-3-300000000-3-30000000000-2-2000000000000000-2-200-20111100000000000110
χ616666-3-3-3-36-6-6-3-30000000033000000000022000000000000000-2200-20-1-1-1-100000000000110
χ626666-3-3-3-36-6-6-3-300000000330000000000-2-20000000000000002-20020111100000000000-1-10
χ636666-3-3-3-3-66-63300000000-33000000000022000000000000000-2-20020-1-11100000000000-110
χ646666-3-3-3-3-66-63300000000-330000000000-2-20000000000000002200-2011-1-1000000000001-10
χ656666-3-3-3-3-6-6633000000003-30000000000220000000000000002-200-20-1-111000000000001-10
χ666666-3-3-3-3-6-6633000000003-30000000000-2-2000000000000000-22002011-1-100000000000-110
χ6788-8-888-8-800000-4-4-44-4444002002-2-2000000000000000000000000000000000000000000000
χ688-8-888-88-800000-4-4444-44-400200-22-2000000000000000000000000000000000000000000000
χ691212-12-12-6-66600000000000000000000000004i−4i000000000000000000000−2i2i0000000000000000
χ701212-12-12-6-6660000000000000000000000000−4i4i0000000000000000000002i−2i0000000000000000
χ7112-1212-12-666-6000−6i36i30000000000000000000000000000000000000000000000000000000000000
χ7212-1212-12-666-60006i3−6i30000000000000000000000000000000000000000000000000000000000000
χ7312-12-1212-66-660000000000000000000000000000000000000000000000000023−2300000000000000
χ7412-12-1212-66-6600000000000000000000000000000000000000000000000000−232300000000000000

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