Finite Group Databasebeta

← Group #13151500

Character table — Group #13151500

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order1222366622466336666666123666661212444444666666612121222244444466121212121212121212126612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-1
χ31111111111111111111111111111111-1-111-1-11111111111-11-1-1-1-111-111-1-1-1-111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111-1-1-1-1111111111111-1-11-1-11-1-11-1-11111-1-1-1-1-1-11-11-1-1-1
χ5111111111-1-11111111111-1-11-1-1111-1-111111111-111-1-1-1-1-11-1-1-1-1-11-11-1-111111111-1-1-11-1-11-1
χ6111111111-1-11111111111-1-11-1-1111-1-111-1-1-1-111-111-1-1-1-1-1111-1-11-11-111-1-1-1-1-1-111-1-1111-1-11
χ7111111111-1-11111111111-1-11-1-1111-1-1-1-111-1-111-111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1111-1111-1
χ8111111111-1-11111111111-1-11-1-1111-1-1-1-1-1-11111-111-1-1-1-1-1-11-111-1-111111111-1-1-1-111-1-1-11-11
χ911111111-11-1-1-1111111111-1111111-1-1111111-1-11-1-111-1-1-1-1-1-11-11-11-1-1-111-1-1111111-1-11-1-11
χ1011111111-11-1-1-1111111111-1111111-1-111-1-1-1-1-1-11-1-111-1-1-1-1111-1-11-1111-1-111-1-111111-1-1-11-1
χ1111111111-11-1-1-1111111111-1111111-1-1-1-111-1-1-1-11-1-111-1-1-11-11-11-1-111-1-1-1-11111-1-1-1-111-11-11
χ1211111111-11-1-1-1111111111-1111111-1-1-1-1-1-111-1-11-1-111-1-1-111-1-1111-1-11111-1-1-1-1-1-1-1-1-11111-1
χ1311111111-1-11-1-111111111-111-1-111111111111-1-1-1-1-1-1-1111-111-11-1-1-1-11111-1-11111-1-11-1-11-1-1
χ1411111111-1-11-1-111111111-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-111-1-1-1-11111
χ1511111111-1-11-1-111111111-111-1-111111-1-111-1-1-1-1-1-1-1-1-111111-11-11-1-1111-1-11111-1-111-111-1-1-1
χ1611111111-1-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-1-1-1-11111-111-1-111-1-1-111-1-1-1-1-1-11111-1-111
χ1722222222222222-12-12-12-122-122-1-1-1-1-10022002-1-1-1-1-1-12-1-1020000220-1-10000-1-100000000-1-1
χ1822222222222222-12-12-12-122-122-1-1-1-1-100-2-2002-1-1-1-1-1-12-1-10-20000-2-20110000110000000011
χ192222222222222-12-12-12-1222-1-1-1-1-1-122220000-122-1-1-1-1-1-1-120022000000000000-1-1-1-10-10-100
χ202222222222222-12-12-12-1222-1-1-1-1-1-122-2-20000-122-1-1-1-1-1-1-1-200-2-20000000000001111010100
χ21222222222-2-2222-12-12-12-1-2-2-1-2-2-1-1-1110022002-11-1-111-2110-200002-20110000-1-100000000-11
χ22222222222-2-2222-12-12-12-1-2-2-1-2-2-1-1-11100-2-2002-11-1-111-211020000-220-1-1000011000000001-1
χ23222222222-2-222-12-12-12-12-2-2-111-1-1-1-2-2220000-12-2-1-111111200-2-2000000000000-1-1110-10100
χ24222222222-2-222-12-12-12-12-2-2-111-1-1-1-2-2-2-20000-12-2-1-111111-2002200000000000011-1-1010-100
χ2522222222-22-2-2-22-12-12-12-12-2-122-1-1-111002200-21-111-1-1-2110-20000-220110000-1-1000000001-1
χ2622222222-22-2-2-22-12-12-12-12-2-122-1-1-11100-2-200-21-111-1-1-2110200002-20-1-100001100000000-11
χ2722222222-22-2-2-2-12-12-12-122-2-1-1-1-1-1-1-2-22200001-2211-1-1111-2002-2000000000000-1-1-1-1010100
χ2822222222-22-2-2-2-12-12-12-122-2-1-1-1-1-1-1-2-2-2-200001-2211-1-1111200-2200000000000011110-10-100
χ2922222222-2-22-2-22-12-12-12-1-22-1-2-2-1-1-1-1-1002200-21111112-1-1020000-2-20-1-10000-1-10000000011
χ3022222222-2-22-2-22-12-12-12-1-22-1-2-2-1-1-1-1-100-2-200-21111112-1-10-200002201100001100000000-1-1
χ3122222222-2-22-2-2-12-12-12-12-22-111-1-1-1222200001-2-21111-1-1-1-200-22000000000000-1-111010-100
χ3222222222-2-22-2-2-12-12-12-12-22-111-1-1-122-2-200001-2-21111-1-1-12002-200000000000011-1-10-10100
χ3322-2-222-2-20000022-22-2-22-2002002-2-2002-22i−2i2i−2i0000000000000000000002i−2i002i−2i2-200000000
χ3422-2-222-2-20000022-22-2-22-2002002-2-2002-2−2i2i−2i2i000000000000000000000−2i2i00−2i2i2-200000000
χ3522-2-222-2-20000022-22-2-22-2002002-2-200-222i−2i−2i2i000000000000000000000−2i2i002i−2i-2200000000
χ3622-2-222-2-20000022-22-2-22-2002002-2-200-22−2i2i2i−2i0000000000000000000002i−2i00−2i2i-2200000000
χ374444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2000000-2-2-21111-211000000000000000000000000000
χ38444444444-4-444-2-2-2-2-2-2-2-2-4-412211122000000-2-2211-1-12-1-1000000000000000000000000000
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
χ4144-4-444-4-4000004-2-4-2-424200-200-22200004i−4i000000000000000000000000000−2i2i0000000000
χ4244-4-444-4-4000004-2-4-2-424200-200-2220000−4i4i0000000000000000000000000002i−2i0000000000
χ4344-4-444-4-400000-24242-4-2-400-200-222004-40000000000000000000000000000000-2200000000
χ4444-4-444-4-400000-24242-4-2-400-200-22200-4400000000000000000000000000000002-200000000
χ454-44-44-44-40000044-4-444-4-400400-4-44000000000000000000000000000000000000000000000
χ464-44-44-44-4000004-2-424-2-4200-20022-2−2i32i300000000000000−2i32i3000000000000000000000000000
χ474-44-44-44-4000004-2-424-2-4200-20022-22i3−2i3000000000000002i3−2i3000000000000000000000000000
χ484-44-44-44-400000-242-4-242-400-2−2i32i322-20000000000000−2i32i3000000000000000000000000000000
χ494-44-44-44-400000-242-4-242-400-22i3−2i322-200000000000002i3−2i3000000000000000000000000000000
χ504-44-44-44-400000-2-222-2-222001−2i32i3-1-11−2i32i30000000003-3i3−i30i3−i3000000000000000000000000000
χ514-44-44-44-400000-2-222-2-222001−2i32i3-1-112i3−2i3000000000-33i3−i30−i3i3000000000000000000000000000
χ524-44-44-44-400000-2-222-2-2220012i3−2i3-1-11−2i32i3000000000-33−i3i30i3−i3000000000000000000000000000
χ534-44-44-44-400000-2-222-2-2220012i3−2i3-1-112i3−2i30000000003-3−i3i30−i3i3000000000000000000000000000
χ544-4-444-4-4400000444-4-4-4-4400400-44-4000000000000000000000000000000000000000000000
χ554-4-444-4-44000004-242-42-4-200-2002-22000000000000000000000000000−2i32i30000000000000000
χ564-4-444-4-44000004-242-42-4-200-2002-220000000000000000000000000002i3−2i30000000000000000
χ574-4-444-4-4400000-24-2-42-42400-2002-22000000000000000000000000000000000000023−23000000
χ584-4-444-4-4400000-24-2-42-42400-2002-220000000000000000000000000000000000000−2323000000
χ596666-3-3-3-3666-3-300000000-3-300000000000022000000000000200200200-1-1-1-1000000-10-1000
χ606666-3-3-3-3666-3-300000000-3-3000000000000-2-2000000000000-200-200-2001111000000101000
χ616666-3-3-3-36-6-6-3-3000000003300000000000022000000000000-200-200200-1-1-1-1000000101000
χ626666-3-3-3-36-6-6-3-30000000033000000000000-2-2000000000000200200-2001111000000-10-1000
χ636666-3-3-3-3-66-63300000000-3300000000000022000000000000-200200-200-1-11100000010-1000
χ646666-3-3-3-3-66-63300000000-33000000000000-2-2000000000000200-20020011-1-1000000-101000
χ656666-3-3-3-3-6-6633000000003-300000000000022000000000000200-200-200-1-111000000-101000
χ666666-3-3-3-3-6-6633000000003-3000000000000-2-2000000000000-20020020011-1-100000010-1000
χ6788-8-888-8-800000-4-44-444-44002002-2-2000000000000000000000000000000000000000000000
χ688-8-888-8-8800000-4-4-44444-400200-22-2000000000000000000000000000000000000000000000
χ691212-12-12-6-6660000000000000000000000000004i−4i000000000000000000000−2i2i00000000000000
χ701212-12-12-6-666000000000000000000000000000−4i4i0000000000000000000002i−2i00000000000000
χ7112-1212-12-66-66000−6i36i30000000000000000000000000000000000000000000000000000000000000
χ7212-1212-12-66-660006i3−6i30000000000000000000000000000000000000000000000000000000000000
χ7312-12-1212-666-60000000000000000000000000000000000000000000000000000−2i32i3000000000000
χ7412-12-1212-666-600000000000000000000000000000000000000000000000000002i3−2i3000000000000

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