Finite Group Databasebeta

← Group #13151328

Character table — Group #13151328

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order1222366622466336666666123666661212444444666666612121224444444412121212121212121212121261212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-11111111111-1-11-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111-1-111-1-111111111111-1-11-1-1-11-1-1-1-1-1-1-1-1-111111-1-11-1-1
χ41111111111111111111111111111111-1-1-1-1111111111111-11-1-11-1-1-111111-1-1-1-1-1-1-1-1-111-1-1-1
χ5111111111-1-11111111111-1-11-1-1111-1-11111111-1111-1-1-1-1-11-1-1-1-11-1-11111111-1-111-1-11-1-1-11-1
χ6111111111-1-11111111111-1-11-1-1111-1-111-1-1-1-11-1111-1-1-1-1-1-11-1111-11-1-1-1-1-111-1-1-1-111-11111-1
χ7111111111-1-11111111111-1-11-1-1111-1-1-1-111-1-11-1111-1-1-1-1-1111-11-11-1-1-1-1-1-1-1-11111-1-1111-1-11
χ8111111111-1-11111111111-1-11-1-1111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-111-1-11111111-1-111-1-111-1-1-11-11
χ911111111-11-1-1-1111111111-1111111-1-1111111-11-1-1-111-1-1-1-11-11-1-11-1-111-1-111-1-11111-11-1-1-11
χ1011111111-11-1-1-1111111111-1111111-1-111-1-1-1-1-11-1-1-111-1-1-11-1-1-11-1111-1-11111-1-1-1-1-1-11-111-11
χ1111111111-11-1-1-1111111111-1111111-1-1-1-111-1-1-11-1-1-111-1-1-1-1-11111-1-11-1-111-1-1111111-1-11-11-1
χ1211111111-11-1-1-1111111111-1111111-1-1-1-1-1-111-11-1-1-111-1-1-1111-1-11-11-111-1-1-1-111-1-1-1-111-111-1
χ1311111111-1-11-1-111111111-111-1-111111111111-1-1-1-1-1-1-1111-1-11-11-1-11-111-1-1111111-1-1-1-111-1-1
χ1411111111-1-11-1-111111111-111-1-11111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1111111-1-11111-1-1-1-1
χ1511111111-1-11-1-111111111-111-1-111111-1-111-1-1-1-1-1-1-1-1-1111-11-1-1-11111-1-111-1-1-1-111-1-1-11-1111
χ1611111111-1-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1111-11-111
χ1722222222222222-1-122-1-1222-1-1-1-1-1-12200220022-1-1-1-1-1-1-1-120020002000000000-1-1-1-1-100-100
χ1822222222222222-1-122-1-1222-1-1-1-1-1-12200-2-20022-1-1-1-1-1-1-1-1-200-2000-20000000001111100100
χ192222222222222-122-1-122-122-122-1-1-1-1-1220000-1-12-1-1-1-12-1-10020022000000-1-1-1-100000000-1-1
χ202222222222222-122-1-122-122-122-1-1-1-1-1-2-20000-1-12-1-1-1-12-1-100-200-2-200000011110000000011
χ21222222222-2-2222-1-122-1-12-2-2-111-1-1-1-2-20022002-2-1-1-111111200-2000-2000000000-1-111-100100
χ22222222222-2-2222-1-122-1-12-2-2-111-1-1-1-2-200-2-2002-2-1-1-111111-2002000200000000011-1-1100-100
χ23222222222-2-222-122-1-122-1-2-2-1-2-2-1-1-111220000-112-1-111-21100-2002-2000000-1-11100000000-11
χ24222222222-2-222-122-1-122-1-2-2-1-2-2-1-1-111-2-20000-112-1-111-21100200-2200000011-1-1000000001-1
χ2522222222-22-2-2-22-1-122-1-122-2-1-1-1-1-1-1-2-2002200-22111-1-1111-2002000-2000000000-1-1-1-1100100
χ2622222222-22-2-2-22-1-122-1-122-2-1-1-1-1-1-1-2-200-2-200-22111-1-1111200-200020000000001111-100-100
χ2722222222-22-2-2-2-122-1-122-12-2-122-1-1-1112200001-1-211-1-1-21100-200-22000000-1-111000000001-1
χ2822222222-22-2-2-2-122-1-122-12-2-122-1-1-111-2-200001-1-211-1-1-211002002-200000011-1-100000000-11
χ2922222222-2-22-2-22-1-122-1-12-22-111-1-1-122002200-2-211111-1-1-1-200-20002000000000-1-111100-100
χ3022222222-2-22-2-22-1-122-1-12-22-111-1-1-12200-2-200-2-211111-1-1-12002000-200000000011-1-1-100100
χ3122222222-2-22-2-2-122-1-122-1-22-1-2-2-1-1-1-1-122000011-211112-1-100200-2-2000000-1-1-1-10000000011
χ3222222222-2-22-2-2-122-1-122-1-22-1-2-2-1-1-1-1-1-2-2000011-211112-1-100-20022000000111100000000-1-1
χ332-22-222-2-20000022-22-2-22-2002002-2-2002i−2i2-22i−2i00000000000000000002i−2i002i−2i002-200000000
χ342-22-222-2-20000022-22-2-22-2002002-2-2002i−2i-22−2i2i0000000000000000000−2i2i002i−2i00-2200000000
χ352-22-222-2-20000022-22-2-22-2002002-2-200−2i2i2-2−2i2i0000000000000000000−2i2i00−2i2i002-200000000
χ362-22-222-2-20000022-22-2-22-2002002-2-200−2i2i-222i−2i00000000000000000002i−2i00−2i2i00-2200000000
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
χ4144-4-44-44-400000444-44-4-4-400400-44-4000000000000000000000000000000000000000000000
χ4244-4-44-44-4000004-2-2-4422-400-2002-22000000000000000000000000000000000000023−23000000
χ4344-4-44-44-4000004-2-2-4422-400-2002-220000000000000000000000000000000000000−2323000000
χ4444-4-44-44-400000-2442-2-4-4200-2002-2200000000000000000000000000000000023−230000000000
χ4544-4-44-44-400000-2442-2-4-4200-2002-22000000000000000000000000000000000−23230000000000
χ464-44-444-4-4000004-224-42-2-400-200-22200004-400000000000000000000000000000-2200000000
χ474-44-444-4-4000004-224-42-2-400-200-2220000-44000000000000000000000000000002-200000000
χ484-44-444-4-400000-24-4-22-44200-200-222004i−4i000000000000000000000000000−2i2i000000000000
χ494-44-444-4-400000-24-4-22-44200-200-22200−4i4i0000000000000000000000000002i−2i000000000000
χ504-4-444-4-440000044-4-4-44-4400400-4-44000000000000000000000000000000000000000000000
χ514-4-444-4-44000004-22-4-4-22400-2−2i32i322-20000000000000−2i32i3000000000000000000000000000000
χ524-4-444-4-44000004-22-4-4-22400-22i3−2i322-200000000000002i3−2i3000000000000000000000000000000
χ534-4-444-4-4400000-24-4224-4-200-20022-2−2i32i300000000000000−2i32i3000000000000000000000000000
χ544-4-444-4-4400000-24-4224-4-200-20022-22i3−2i3000000000000002i3−2i3000000000000000000000000000
χ554-4-444-4-4400000-2-2222-22-2001−2i32i3-1-11−2i32i30000000003-3i3−i30i3−i3000000000000000000000000000
χ564-4-444-4-4400000-2-2222-22-2001−2i32i3-1-112i3−2i3000000000-33i3−i30−i3i3000000000000000000000000000
χ574-4-444-4-4400000-2-2222-22-20012i3−2i3-1-11−2i32i3000000000-33−i3i30i3−i3000000000000000000000000000
χ584-4-444-4-4400000-2-2222-22-20012i3−2i3-1-112i3−2i30000000003-3−i3i30−i3i3000000000000000000000000000
χ596666-3-3-3-3666-3-300000000-3-3000000000000220000000000020020002-1-1-1-1000000000-1-1000
χ606666-3-3-3-3666-3-300000000-3-3000000000000-2-200000000000-200-2000-2111100000000011000
χ616666-3-3-3-36-6-6-3-300000000330000000000002200000000000-200-20002-1-1-1-100000000011000
χ626666-3-3-3-36-6-6-3-30000000033000000000000-2-2000000000002002000-21111000000000-1-1000
χ636666-3-3-3-3-66-63300000000-330000000000002200000000000200-2000-2-1-111000000000-11000
χ646666-3-3-3-3-66-63300000000-33000000000000-2-200000000000-2002000211-1-10000000001-1000
χ656666-3-3-3-3-6-6633000000003-30000000000002200000000000-2002000-2-1-1110000000001-1000
χ666666-3-3-3-3-6-6633000000003-3000000000000-2-200000000000200-2000211-1-1000000000-11000
χ6788-8-88-88-800000-4-4-44-444400200-22-2000000000000000000000000000000000000000000000
χ688-88-888-8-800000-4-44-444-44002002-2-2000000000000000000000000000000000000000000000
χ691212-12-12-66-660000000000000000000000000000000000000000000000000023−2300000000000000
χ701212-12-12-66-6600000000000000000000000000000000000000000000000000−232300000000000000
χ7112-1212-12-6-6660000000000000000000000000004i−4i0000000000000000000−2i2i0000000000000000
χ7212-1212-12-6-666000000000000000000000000000−4i4i00000000000000000002i−2i0000000000000000
χ7312-12-1212-666-6000−6i36i30000000000000000000000000000000000000000000000000000000000000
χ7412-12-1212-666-60006i3−6i30000000000000000000000000000000000000000000000000000000000000

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