Finite Group Databasebeta

← Group #13151318

Character table — Group #13151318

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order1222366622412123366666666366666664444446666661212121224444444412121212121212121212121261212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-11111111111-1-11-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1
χ31111111111111111111111111111111-1-111-1-111111111111-1-11-1-1-11-1-1-1-1-11111-1-1-1-11-1-1-1-11
χ41111111111111111111111111111111-1-1-1-1111111111111-11-1-11-1-1-11-1-1-1-1-1-1-1-11111-1-1-111-1
χ5111111111-1-1-1-1111111111-1111-1-1111111111-1111-1-1-1-1-1-11-1-1-1-11-1-1111-1-111-1-1111111-1-1-1-1
χ6111111111-1-1-1-1111111111-1111-1-111111-1-1-1-1-1111-1-1-1-1-1-1-11-1111-11-111-1-1-1-111-1-1-1-1-11-1111
χ7111111111-1-1-1-1111111111-1111-1-1111-1-111-1-1-1111-1-1-1-1-1-1111-11-11-1-1-1-11111-1-1-1-1-1-11-1111-1
χ8111111111-1-1-1-1111111111-1111-1-1111-1-1-1-111-1111-1-1-1-1-1-1-1-111-1-1111-1-111-1-1111111-1-11-1-11
χ911111111-11-1-1-111111111-111-1-1111111111111-1-1-111-1-1-1-1-11-11-1-11-1-111-1-1111111-1-1-1-111-1-1
χ1011111111-11-1-1-111111111-111-1-11111111-1-1-1-11-1-1-111-1-1-1-11-1-1-11-111111-1-1-1-1-1-1-1-1111-11-111
χ1111111111-11-1-1-111111111-111-1-111111-1-111-1-11-1-1-111-1-1-1-1-1-11111-1-11-1-1111111-1-111-11-1-11-1
χ1211111111-11-1-1-111111111-111-1-111111-1-1-1-1111-1-1-111-1-1-1-1111-1-11-11-1-1-111-1-1-1-111-1-111-11-11
χ1311111111-1-111111111111-1-11-1-1-1-1111111111-1-1-1-1-1-11111-1-11-11-1-11-1111111-1-111-1-1-1-1-1-111
χ1411111111-1-111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-111-1-1111-1-11-1-1
χ1511111111-1-111111111111-1-11-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111-11-1-1-11111-1-1-1-111-1-1-1-111-1111-11
χ1611111111-1-111111111111-1-11-1-1-1-1111-1-1-1-111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-11111-1-1111-11-1
χ1722222222222222-1-122-1-1222-122-1-1-1-1-10022002-1-1-1-1-1-12-1-12002000200000-1-1-1-10000-10000-1
χ1822222222222222-1-122-1-1222-122-1-1-1-1-100-2-2002-1-1-1-1-1-12-1-1-200-2000-20000011110000100001
χ192222222222222-122-1-122-122-1-1-122-1-1-1000022-12-1-1-1-12-1-1-102002000200000000-1-1-1-1000-1-10
χ202222222222222-122-1-122-122-1-1-122-1-1-10000-2-2-12-1-1-1-12-1-1-10-200-2000-2000000001111000110
χ21222222222-2-2-2-22-1-122-1-122-2-12211-1-1-1002200-2-1-1-1111-211200-2000-200000-1-1110000-100001
χ22222222222-2-2-2-22-1-122-1-122-2-12211-1-1-100-2-200-2-1-1-1111-211-200200020000011-1-1000010000-1
χ23222222222-2-2-2-2-122-1-122-12-2-1-1-1-2-2-1-1-100002212-1-111-21110-200-2000200000000-1-1-1-1000110
χ24222222222-2-2-2-2-122-1-122-12-2-1-1-1-2-2-1-1-10000-2-212-1-111-211102002000-2000000001111000-1-10
χ2522222222-22-2-2-22-1-122-1-12-22-1-2-2-1-1-1-1-10022002111-1-11-211-2002000-200000-1-1-1-10000100001
χ2622222222-22-2-2-22-1-122-1-12-22-1-2-2-1-1-1-1-100-2-2002111-1-11-211200-200020000011110000-10000-1
χ2722222222-22-2-2-2-122-1-122-1-22-11122-1-1-1000022-1-211-1-1-21110200-2000-200000000-1-111000-110
χ2822222222-22-2-2-2-122-1-122-1-22-11122-1-1-10000-2-2-1-211-1-1-21110-200200020000000011-1-10001-10
χ2922222222-2-22222-1-122-1-12-2-2-1-2-211-1-1-1002200-211111-12-1-1-200-2000200000-1-111000010000-1
χ3022222222-2-22222-1-122-1-12-2-2-1-2-211-1-1-100-2-200-211111-12-1-12002000-20000011-1-10000-100001
χ3122222222-2-2222-122-1-122-1-2-2-111-2-2-1-1-10000221-211112-1-1-10-2002000-200000000-1-1110001-10
χ3222222222-2-2222-122-1-122-1-2-2-111-2-2-1-1-10000-2-21-211112-1-1-10200-200020000000011-1-1000-110
χ332-22-222-2-20000022-22-2-22-200200002-2-22i−2i2-22i−2i00000000000000000002i−2i002-2002i−2i00000000
χ342-22-222-2-20000022-22-2-22-200200002-2-22i−2i-22−2i2i00000000000000000002i−2i00-2200−2i2i00000000
χ352-22-222-2-20000022-22-2-22-200200002-2-2−2i2i2-2−2i2i0000000000000000000−2i2i002-200−2i2i00000000
χ362-22-222-2-20000022-22-2-22-200200002-2-2−2i2i-222i−2i0000000000000000000−2i2i00-22002i−2i00000000
χ374444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111000000-2-21111-2-211000000000000000000000000000
χ38444444444-4-4-4-4-2-2-2-2-2-2-2-24-41-2-2221110000002-211-1-122-1-1000000000000000000000000000
χ3944444444-44-4-4-4-2-2-2-2-2-2-2-2-44122-2-2111000000-22-1-11122-1-1000000000000000000000000000
χ4044444444-4-4444-2-2-2-2-2-2-2-2-4-41222211100000022-1-1-1-1-2-211000000000000000000000000000
χ4144-4-44-44-400000444-44-4-4-40040000-44-40000000000000000000000000000000000000000000
χ4244-4-44-44-4000004-2-2-4422-400-200002-22000000000000000000000000000000023−230000000000
χ4344-4-44-44-4000004-2-2-4422-400-200002-220000000000000000000000000000000−23230000000000
χ4444-4-44-44-400000-2442-2-4-4200-200002-220000000000000000000000000000000000023−23000000
χ4544-4-44-44-400000-2442-2-4-4200-200002-2200000000000000000000000000000000000−2323000000
χ464-44-444-4-4000004-224-42-2-400-20000-222004-40000000000000000000000000-22000000000000
χ474-44-444-4-4000004-224-42-2-400-20000-22200-4400000000000000000000000002-2000000000000
χ484-44-444-4-400000-24-4-22-44200-20000-22200004i−4i000000000000000000000000000−2i2i00000000
χ494-44-444-4-400000-24-4-22-44200-20000-2220000−4i4i0000000000000000000000000002i−2i00000000
χ504-4-444-4-440000044-4-4-44-440040000-4-440000000000000000000000000000000000000000000
χ514-4-444-4-44000004-22-4-4-22400-200−2i32i322-20000000000−2i32i30000000000000000000000000000000
χ524-4-444-4-44000004-22-4-4-22400-2002i3−2i322-200000000002i3−2i30000000000000000000000000000000
χ534-4-444-4-4400000-24-4224-4-200-2−2i32i30022-200000000−2i32i3000000000000000000000000000000000
χ544-4-444-4-4400000-24-4224-4-200-22i3−2i30022-2000000002i3−2i3000000000000000000000000000000000
χ554-4-444-4-4400000-2-2222-22-2001−2i32i3−2i32i3-1-1100000000i3−i3i3−i3003-3000000000000000000000000000
χ564-4-444-4-4400000-2-2222-22-2001−2i32i32i3−2i3-1-1100000000i3−i3−i3i300-33000000000000000000000000000
χ574-4-444-4-4400000-2-2222-22-20012i3−2i3−2i32i3-1-1100000000−i3i3i3−i300-33000000000000000000000000000
χ584-4-444-4-4400000-2-2222-22-20012i3−2i32i3−2i3-1-1100000000−i3i3−i3i3003-3000000000000000000000000000
χ596666-3-3-3-3666-3-300000000-3-3000000002200000000000000002002200-1-1-1-1000000000-1-1000
χ606666-3-3-3-3666-3-300000000-3-300000000-2-20000000000000000-200-2-200111100000000011000
χ616666-3-3-3-36-6-63300000000-3300000000220000000000000000-2002-200-1-111000000000-11000
χ626666-3-3-3-36-6-63300000000-3300000000-2-20000000000000000200-220011-1-10000000001-1000
χ636666-3-3-3-3-66-633000000003-300000000220000000000000000-200-2200-1-1110000000001-1000
χ646666-3-3-3-3-66-633000000003-300000000-2-200000000000000002002-20011-1-1000000000-11000
χ656666-3-3-3-3-6-66-3-3000000003300000000220000000000000000200-2-200-1-1-1-100000000011000
χ666666-3-3-3-3-6-66-3-3000000003300000000-2-20000000000000000-20022001111000000000-1-1000
χ6788-8-88-88-800000-4-4-44-44440020000-22-20000000000000000000000000000000000000000000
χ688-88-888-8-800000-4-44-444-4400200002-2-20000000000000000000000000000000000000000000
χ691212-12-12-66-660000000000000000000000000000000000000000000000000023−2300000000000000
χ701212-12-12-66-6600000000000000000000000000000000000000000000000000−232300000000000000
χ7112-1212-12-6-666000000000000000000000004i−4i00000000000000000000000−2i2i0000000000000000
χ7212-1212-12-6-66600000000000000000000000−4i4i000000000000000000000002i−2i0000000000000000
χ7312-12-1212-666-6000−6i36i30000000000000000000000000000000000000000000000000000000000000
χ7412-12-1212-666-60006i3−6i30000000000000000000000000000000000000000000000000000000000000

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