Finite Group Databasebeta

← Group #13149452

Character table — Group #13149452

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order1222366644412123366666612123666121212124444441212121212121212121222222444466661212121212121212666121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-111
χ31111111111111111111111111111111-1-111-1-1111111111111-1-1-11-1-1-111-1-111-1-1-1-1-1-11-1-11-1-1
χ41111111111111111111111111111111-1-1-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-111-1-1-1
χ5111111111-1-11111111111-1-11111-1-1-1-11111111-11-1-1-111-1-11-11-1-1-11-1-111-1-1111111-1-1-11-1-11-1
χ6111111111-1-11111111111-1-11111-1-1-1-111-1-1-1-11-11-1-1-111-1-1-11-11111-1-1-1-111-1-111-1-1-1-11-1111-1
χ7111111111-1-11111111111-1-11111-1-1-1-1-1-111-1-11-11-1-1-111-1-11-1-111-1-111111111-1-1-1-111-1-11-1-11
χ8111111111-1-11111111111-1-11111-1-1-1-1-1-1-1-1111-11-1-1-111-1-1-111-1-11-111-1-1-1-1-1-1-1-1111111-11-11
χ911111111-11-1-1-111111111-111111-1-111111111-11-1-1-1-1-1-111-1-1-11-11-11-1-1-1-1-111111111-1-111-1-1
χ1011111111-11-1-1-111111111-111111-1-11111-1-1-1-1-11-1-1-1-1-1-111111-11-1-11-11111-1-111-1-11111-1-1-1-1
χ1111111111-11-1-1-111111111-111111-1-111-1-111-1-1-11-1-1-1-1-1-111-1-11-1111-11-1-11111-1-1-1-1-1-1-11-1111
χ1211111111-11-1-1-111111111-111111-1-111-1-1-1-111-11-1-1-1-1-1-11111-11-1-11-1111-1-1-1-1-1-111-1-11-11-111
χ1311111111-1-11-1-1111111111-1111111-1-1111111-1-1-1111-1-1-1-1-11-1-11-1-1-11-1-111111111-1-11-1-1-1-11
χ1411111111-1-11-1-1111111111-1111111-1-111-1-1-1-1-1-1-1111-1-1-1-11-111-11-1-1111-1-1-1-111-1-1-1-1-1111-11
χ1511111111-1-11-1-1111111111-1111111-1-1-1-111-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-111-1-1-1-111111-11-1
χ1611111111-1-11-1-1111111111-1111111-1-1-1-1-1-111-1-1-1111-1-1-1-11-1-1-11111-11111-1-1-1-11111-1-1-111-1
χ1722222222222222-1-1-12-12222-1-1-1-1-1-122000022-1-122-1-1-1-1-1-100222000000-1-10000-1-1000-1-1000
χ1822222222222222-1-1-12-12222-1-1-1-1-1-1220000-2-2-1-122-1-1-1-1-1-100-2-2-20000001100001100011000
χ192222222222222-1222-12-1-122-1-1-1-122-1-122000022-1-1-1-1-1-1-1-1000000222000000-1-100-1-10000-1-1
χ202222222222222-1222-12-1-122-1-1-1-122-1-1-2-2000022-1-1-1-1-1-1-1-1000000-2-2-2000000110011000011
χ21222222222-2-2222-1-1-12-122-2-2-1-1-1-111-2-2000022-112-211-1-111002-2-2000000110000-1-1000-11000
χ22222222222-2-2222-1-1-12-122-2-2-1-1-1-111-2-20000-2-2-112-211-1-11100-222000000-1-10000110001-1000
χ23222222222-2-222-1222-12-1-1-2-2-1-1-1-1-2-2112200002-2-1111-1-1110000002-2-2000000-1-100110000-11
χ24222222222-2-222-1222-12-1-1-2-2-1-1-1-1-2-211-2-200002-2-1111-1-111000000-2220000001100-1-100001-1
χ2522222222-22-2-2-22-1-1-12-122-22-1-1-1-111220000221-1-2-21111-1-100-22-2000000110000-1-10001-1000
χ2622222222-22-2-2-22-1-1-12-122-22-1-1-1-111220000-2-21-1-2-21111-1-1002-22000000-1-1000011000-11000
χ2722222222-22-2-2-2-1222-12-1-1-22-1-1-1-1-2-2-1-1220000-22111111-1-1000000-22-2000000-1-100-1-1000011
χ2822222222-22-2-2-2-1222-12-1-1-22-1-1-1-1-2-2-1-1-2-20000-22111111-1-10000002-220000001100110000-1-1
χ2922222222-2-22-2-22-1-1-12-1222-2-1-1-1-1-1-1-2-200002211-22-1-1111100-2-22000000-1-10000-1-100011000
χ3022222222-2-22-2-22-1-1-12-1222-2-1-1-1-1-1-1-2-20000-2-211-22-1-111110022-200000011000011000-1-1000
χ3122222222-2-22-2-2-1222-12-1-12-2-1-1-1-12211220000-2-21-1-1-11111000000-2-22000000-1-1001100001-1
χ3222222222-2-22-2-2-1222-12-1-12-2-1-1-1-12211-2-20000-2-21-1-1-1111100000022-20000001100-1-10000-11
χ3322-2-22-22-200000222-22-2-2-20022-2-200002-22i−2i2i−2i000000000000000000000002i−2i2-22i−2i00000000
χ3422-2-22-22-200000222-22-2-2-20022-2-200002-2−2i2i−2i2i00000000000000000000000−2i2i2-2−2i2i00000000
χ3522-2-22-22-200000222-22-2-2-20022-2-20000-222i−2i−2i2i000000000000000000000002i−2i-22−2i2i00000000
χ3622-2-22-22-200000222-22-2-2-20022-2-20000-22−2i2i2i−2i00000000000000000000000−2i2i-222i−2i00000000
χ374444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2000000-2-2-2-2111111000000000000000000000000000
χ38444444444-4-444-2-2-2-2-2-2-2-2-4-411112222000000-22-22-1-111-1-1000000000000000000000000000
χ3944444444-44-4-4-4-2-2-2-2-2-2-2-2-44111122-2-20000002-222-1-1-1-111000000000000000000000000000
χ4044444444-4-44-4-4-2-2-2-2-2-2-2-24-41111-2-222000000222-211-1-1-1-1000000000000000000000000000
χ4144-4-44-44-4000004-2-2242-4-400-2-222000000004i−4i000000000000000000000000000−2i2i00000000
χ4244-4-44-44-4000004-2-2242-4-400-2-22200000000−4i4i0000000000000000000000000002i−2i00000000
χ4344-4-44-44-400000-244-4-2-42200-2-22200004-400000000000000000000000000000-220000000000
χ4444-4-44-44-400000-244-4-2-42200-2-2220000-44000000000000000000000000000002-20000000000
χ454-44-44-4-440000044-44-4-44-4004-4-4400000000000000000000000000000000000000000000000
χ464-44-44-4-44000004-22-2-424-400-222-20000000000000000000000000000000−2i32i300000000000000
χ474-44-44-4-44000004-22-2-424-400-222-200000000000000000000000000000002i3−2i300000000000000
χ484-44-44-4-4400000-24-442-4-2200-222-200000000000000000000000000000000000000023−23000000
χ494-44-44-4-4400000-24-442-4-2200-222-2000000000000000000000000000000000000000−2323000000
χ504-4-4444-4-40000044-4-4-44-44004-44-400000000000000000000000000000000000000000000000
χ514-4-4444-4-4000004-222-4-2-4400-22-22−2i32i3000000000000−2i32i30000000000000000000000000000000
χ524-4-4444-4-4000004-222-4-2-4400-22-222i3−2i30000000000002i3−2i30000000000000000000000000000000
χ534-4-4444-4-400000-24-4-4242-200-22-220023−230000000000000023−23000000000000000000000000000
χ544-4-4444-4-400000-24-4-4242-200-22-2200−232300000000000000−2323000000000000000000000000000
χ554-4-4444-4-400000-2-2222-22-2001-11-1−2i32i323−230000000000i3−i33i−3i−33000000000000000000000000000
χ564-4-4444-4-400000-2-2222-22-2001-11-1−2i32i3−23230000000000i3−i3−3i3i3−3000000000000000000000000000
χ574-4-4444-4-400000-2-2222-22-2001-11-12i3−2i323−230000000000−i3i3−3i3i−33000000000000000000000000000
χ584-4-4444-4-400000-2-2222-22-2001-11-12i3−2i3−23230000000000−i3i33i−3i3−3000000000000000000000000000
χ596666-3-3-3-3666-3-300000000-3-3000000000022000000000000220002000-1-100-1-1000000-100-100
χ606666-3-3-3-3666-3-300000000-3-30000000000-2-2000000000000-2-2000-2000110011000000100100
χ616666-3-3-3-36-6-6-3-300000000330000000000220000000000002-2000-2000-1-100-1-1000000100100
χ626666-3-3-3-36-6-6-3-300000000330000000000-2-2000000000000-220002000110011000000-100-100
χ636666-3-3-3-3-66-633000000003-3000000000022000000000000-2-200020001100-1-1000000100-100
χ646666-3-3-3-3-66-633000000003-30000000000-2-200000000000022000-2000-1-10011000000-100100
χ656666-3-3-3-3-6-663300000000-33000000000022000000000000-22000-20001100-1-1000000-100100
χ666666-3-3-3-3-6-663300000000-330000000000-2-20000000000002-20002000-1-10011000000100-100
χ6788-8-88-88-800000-4-4-44-44440022-2-200000000000000000000000000000000000000000000000
χ688-88-88-8-8800000-4-44-444-44002-2-2200000000000000000000000000000000000000000000000
χ691212-12-12-66-6600000000000000000000000004i−4i0000000000000000000000000−2i2i000000000000
χ701212-12-12-66-660000000000000000000000000−4i4i00000000000000000000000002i−2i000000000000
χ7112-1212-12-666-6000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ7212-1212-12-666-60000000000000000000000000000000000000000000000002i3−2i30000000000000000
χ7312-12-1212-6-66600063−630000000000000000000000000000000000000000000000000000000000000
χ7412-12-1212-6-666000−63630000000000000000000000000000000000000000000000000000000000000

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