Finite Group Databasebeta

← Group #13151438

Character table — Group #13151438

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order1222366622466336666666123666661212224444666666612121222224444466661212121212121212666121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-111111111111-1-1-1-11-11-11111-1-1-1-1-1-1-1-1-1-1-111-1
χ31111111111111111111111111111111-1-111-1-11111111111-111-1-1-11-1-1-1-1-1-11111-1-1-1-1-111-1-1-1
χ41111111111111111111111111111111-1-1-1-1111111111111-1-1-111-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-11
χ5111111111-1-11111111111-1-11-1-1111-1-111111111-111-1-1-1-1-111-11-1-1-1-1-1111111-1-111-1-111-1-1-1-1
χ6111111111-1-11111111111-1-11-1-1111-1-111-1-1-1-111-111-1-1-1-1-11-11-11-11-111111-1-111-1-111-1-11-1-11
χ7111111111-1-11111111111-1-11-1-1111-1-1-1-111-1-111-111-1-1-1-1-1-11-1-111-111-1-1-1-111-1-1-1-111-11-1111
χ8111111111-1-11111111111-1-11-1-1111-1-1-1-1-1-11111-111-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-11111-1-11-1111-1
χ911111111-11-1-1-1111111111-1111111-1-1111111-1-11-1-111-1-1-1-1-11-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1011111111-11-1-1-1111111111-1111111-1-111-1-1-1-1-1-11-1-111-1-1-1-11-111-111-111-1-1-1-111-1-1-1-111-11-11
χ1111111111-11-1-1-1111111111-1111111-1-1-1-111-1-1-1-11-1-111-1-1-11-11111-1-1-1-1-11111-1-1-1-1-1-11-11-111
χ1211111111-11-1-1-1111111111-1111111-1-1-1-1-1-111-1-11-1-111-1-1-111-1-1-111-11-1-111-1-1111111-11-1-11-1
χ1311111111-1-11-1-111111111-111-1-111111111111-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-111
χ1411111111-1-11-1-111111111-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1111-1111-11-1-1111-1-1-1-1-1-1-1-111111-11-1
χ1511111111-1-11-1-111111111-111-1-111111-1-111-1-1-1-1-1-1-1-1-11111-1-11-1-1111-1-1111111-1-1111-1-11-1-1
χ1611111111-1-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-1-1-1-1111111-11-1-11-1-1-111-1-1-1-111-1-1-1111-11
χ1722222222222222-12-1-1-12222-122-1-1-1-1-10022002-1-1-1-1-1-12-1-10220002000000-1-1-1-100000-1-1000
χ1822222222222222-12-1-1-12222-122-1-1-1-1-100-2-2002-1-1-1-1-1-12-1-10-2-2000-200000011110000011000
χ192222222222222-12-1222-1-122-1-1-1-1-1-122000022-122-1-1-1-1-1-1-100022000200000000-1-1-1-1-10000-1
χ202222222222222-12-1222-1-122-1-1-1-1-1-1220000-2-2-122-1-1-1-1-1-1-1000-2-2000-2000000001111100001
χ21222222222-2-2222-12-1-1-122-2-2-1-2-2-1-1-1110022002-11-1-111-21102-2000-2000000-1-11100000-11000
χ22222222222-2-2222-12-1-1-122-2-2-1-2-2-1-1-11100-2-2002-11-1-111-2110-22000200000011-1-1000001-1000
χ23222222222-2-222-12-1222-1-1-2-2-111-1-1-1-2-2000022-12-2-1-1111110002-2000-200000000-1-111-100001
χ24222222222-2-222-12-1222-1-1-2-2-111-1-1-1-2-20000-2-2-12-2-1-111111000-2200020000000011-1-110000-1
χ2522222222-22-2-2-22-12-1-1-1222-2-122-1-1-111002200-21-111-1-1-2110-22000-2000000-1-111000001-1000
χ2622222222-22-2-2-22-12-1-1-1222-2-122-1-1-11100-2-200-21-111-1-1-21102-2000200000011-1-100000-11000
χ2722222222-22-2-2-2-12-1222-1-12-2-1-1-1-1-1-1-2-20000221-2211-1-1111000-2-2000200000000-1-1-1-1100001
χ2822222222-22-2-2-2-12-1222-1-12-2-1-1-1-1-1-1-2-20000-2-21-2211-1-111100022000-2000000001111-10000-1
χ2922222222-2-22-2-22-12-1-1-122-22-1-2-2-1-1-1-1-1002200-21111112-1-10-2-20002000000-1-1-1-10000011000
χ3022222222-2-22-2-22-12-1-1-122-22-1-2-2-1-1-1-1-100-2-200-21111112-1-1022000-2000000111100000-1-1000
χ3122222222-2-22-2-2-12-1222-1-1-22-111-1-1-1220000221-2-21111-1-1-1000-22000-200000000-1-11110000-1
χ3222222222-2-22-2-2-12-1222-1-1-22-111-1-1-1220000-2-21-2-21111-1-1-10002-200020000000011-1-1-100001
χ332-2-222-22-20000022-2-22-2-22002002-2-2002-22-22-200000000000000000002-2002-2002-200000000
χ342-2-222-22-20000022-2-22-2-22002002-2-2002-2-22-2200000000000000000002-200-2200-2200000000
χ352-2-222-22-20000022-2-22-2-22002002-2-200-222-2-220000000000000000000-22002-200-2200000000
χ362-2-222-22-20000022-2-22-2-22002002-2-200-22-222-20000000000000000000-2200-22002-200000000
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
χ4144-4-444-4-40000044-44-4-44-400400-4-44000000000000000000000000000000000000000000000
χ4244-4-444-4-4000004-2-4-2224-400-20022-2−2i32i300000000000000−2i32i3000000000000000000000000000
χ4344-4-444-4-4000004-2-4-2224-400-20022-22i3−2i3000000000000002i3−2i3000000000000000000000000000
χ4444-4-444-4-400000-2424-4-4-2200-2−2i32i322-20000000000000−2i32i3000000000000000000000000000000
χ4544-4-444-4-400000-2424-4-4-2200-22i3−2i322-200000000000002i3−2i3000000000000000000000000000000
χ4644-4-444-4-400000-2-22-222-22001−2i32i3-1-11−2i32i30000000003-3i3−i30i3−i3000000000000000000000000000
χ4744-4-444-4-400000-2-22-222-22001−2i32i3-1-112i3−2i3000000000-33i3−i30−i3i3000000000000000000000000000
χ4844-4-444-4-400000-2-22-222-220012i3−2i3-1-11−2i32i3000000000-33−i3i30i3−i3000000000000000000000000000
χ4944-4-444-4-400000-2-22-222-220012i3−2i3-1-112i3−2i30000000003-3−i3i30−i3i3000000000000000000000000000
χ504-44-44-4-4400000444-4-44-4-400400-44-4000000000000000000000000000000000000000000000
χ514-44-44-4-44000004-2422-2-4-400-2002-22000000000000000000000000000000000−2i32i30000000000
χ524-44-44-4-44000004-2422-2-4-400-2002-220000000000000000000000000000000002i3−2i30000000000
χ534-44-44-4-4400000-24-2-4-442200-2002-22000000000000000000000000000000000000023−23000000
χ544-44-44-4-4400000-24-2-4-442200-2002-220000000000000000000000000000000000000−2323000000
χ554-4-444-44-4000004-2-42-22-4400-200-22200004-40000000000000000000000000-22000000000000
χ564-4-444-44-4000004-2-42-22-4400-200-2220000-4400000000000000000000000002-2000000000000
χ574-4-444-44-400000-242-44-42-200-200-2220000004-4000000000000000000000000000-2200000000
χ584-4-444-44-400000-242-44-42-200-200-222000000-440000000000000000000000000002-200000000
χ596666-3-3-3-3666-3-300000000-3-3000000002200000000000000200002020-1-1-1-100000000000-1-10
χ606666-3-3-3-3666-3-300000000-3-300000000-2-200000000000000-20000-20-20111100000000000110
χ616666-3-3-3-36-6-6-3-3000000003300000000220000000000000020000-20-20-1-1-1-100000000000110
χ626666-3-3-3-36-6-6-3-3000000003300000000-2-200000000000000-200002020111100000000000-1-10
χ636666-3-3-3-3-66-63300000000-33000000002200000000000000-20000-2020-1-11100000000000-110
χ646666-3-3-3-3-66-63300000000-3300000000-2-2000000000000002000020-2011-1-1000000000001-10
χ656666-3-3-3-3-6-6633000000003-3000000002200000000000000-2000020-20-1-111000000000001-10
χ666666-3-3-3-3-6-6633000000003-300000000-2-20000000000000020000-202011-1-100000000000-110
χ678-88-88-8-8800000-4-4-444-44400200-22-2000000000000000000000000000000000000000000000
χ688-8-888-88-800000-4-444-444-4002002-2-2000000000000000000000000000000000000000000000
χ691212-12-12-6-666000−6i36i30000000000000000000000000000000000000000000000000000000000000
χ701212-12-12-6-6660006i3−6i30000000000000000000000000000000000000000000000000000000000000
χ7112-1212-12-666-600000000000000000000000000000000000000000000000000−2i32i300000000000000
χ7212-1212-12-666-6000000000000000000000000000000000000000000000000002i3−2i300000000000000
χ7312-12-1212-66-66000000000000000000000004-400000000000000000000000-220000000000000000
χ7412-12-1212-66-6600000000000000000000000-44000000000000000000000002-20000000000000000

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