Finite Group Databasebeta

← Group #13148697

Character table — Group #13148697

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444446666666688121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order1222366624412123366666661236666612122244446661212121212121224444444466661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-11111111111-11-111-1-1-1-1-1-111-1-111-1-1-1-1-1-11-11-1
χ31111111111111111111111111111111-1-111-1-111111111111-11-1-1-11-1-111-1-111-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-11-111-1-1-1-1-1-1-1-11111-1-1-11-11
χ5111111111-1-1-1-1111111111-1111111-1-1111111111-1-1-1-1-1-1-1-1-111-1-1-11-1-1-11111-1-111111-1-1-11-1
χ6111111111-1-1-1-1111111111-1111111-1-111-1-1-1-1111-1-1-1-1-1-1-11-1-11-111-111111-1-1-1-1-1-1-1-1-11-1111
χ7111111111-1-1-1-1111111111-1111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-111-111-1-11-1-1-1-11111-1-1-1-11-111-11
χ8111111111-1-1-1-1111111111-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-111-1-11-111-111-1-1-1-1111111-111-1-1-1
χ911111111-11-1-1-111111111-111-1-111111111111-1-1-1-11-111-1-1-1-1-1-11-11-11-1-111111111-1-1-11-1-1-11
χ1011111111-11-1-1-111111111-111-1-11111111-1-1-1-1-1-1-1-11-111-1-11-11-111-11-11111-1-111-1-1111-1-11-1-1
χ1111111111-11-1-1-111111111-111-1-111111-1-111-1-1-1-1-1-11-111-1-1-11-11-1111-1-1-1-1-111-1-1-1-111-11111-1
χ1211111111-11-1-1-111111111-111-1-111111-1-1-1-111-1-1-1-11-111-1-11111-1-1-1-1111-1-1-1-1-1-111-1-11-11-111
χ1311111111-1-111111111111-1-11-1-1111-1-1111111-1-1-11-11-1-11111-1-1-11-1-1-1111111-1-111-1-1-1-111-1-1
χ1411111111-1-111111111111-1-11-1-1111-1-111-1-1-1-1-1-1-11-11-1-111-111-1-1-1111-1-111-1-1-1-1-1-111111-1-11
χ1511111111-1-111111111111-1-11-1-1111-1-1-1-111-1-1-1-1-11-11-1-1111-1-111-1-11111-1-11111-1-111-1-1-1-111
χ1611111111-1-111111111111-1-11-1-1111-1-1-1-1-1-111-1-1-11-11-1-111-1-111111-1-1-1-1-1-1-1-11111-1-111-111-1
χ1722222222222222-12-1-12-1222-122-1-1-1-1-1220000-1-1-1-122-1-1-1-102022000000-1-100-1-1000000-10-10
χ1822222222222222-12-1-12-1222-122-1-1-1-1-1-2-20000-1-1-1-122-1-1-1-10-20-2-20000001100110000001010
χ192222222222222-12-122-12-122-1-1-1-1-1-1220000222-1-12-1-1-1-1-1-100000202200000000-1-1-1-1000-10-1
χ202222222222222-12-122-12-122-1-1-1-1-1-1220000-2-22-1-12-1-1-1-1-1-100000-20-2-2000000001111000101
χ21222222222-2-2-2-22-12-1-12-122-2-122-1-1-111220000-1-1-11-2-211110-202-2000000-1-1001100000010-10
χ22222222222-2-2-2-22-12-1-12-122-2-122-1-1-111-2-20000-1-1-11-2-21111020-220000001100-1-1000000-1010
χ23222222222-2-2-2-2-12-122-12-12-2-1-1-1-1-1-1-2-20000222-1-1-211111100000-202-200000000-1-1-1-1000101
χ24222222222-2-2-2-2-12-122-12-12-2-1-1-1-1-1-1-2-20000-2-22-1-1-21111110000020-22000000001111000-10-1
χ2522222222-22-2-2-22-12-1-12-12-22-1-2-2-1-1-1-1-122000011112-2-1-1110-20-22000000-1-100-1-10000001010
χ2622222222-22-2-2-22-12-1-12-12-22-1-2-2-1-1-1-1-1-2-2000011112-2-1-1110202-2000000110011000000-10-10
χ2722222222-22-2-2-2-12-122-12-1-22-111-1-1-122000022-211-2-11-1-11100000-20-2200000000-1-11100010-1
χ2822222222-22-2-2-2-12-122-12-1-22-111-1-1-1220000-2-2-211-2-11-1-11100000202-20000000011-1-1000-101
χ2922222222-2-22222-12-1-12-12-2-2-1-2-2-1-1-111220000111-1-2211-1-1020-2-2000000-1-10011000000-1010
χ3022222222-2-22222-12-1-12-12-2-2-1-2-2-1-1-111-2-20000111-1-2211-1-10-20220000001100-1-100000010-10
χ3122222222-2-2222-12-122-12-1-2-2-111-1-1-1-2-2000022-21121-111-1-10000020-2-200000000-1-111000-101
χ3222222222-2-2222-12-122-12-1-2-2-111-1-1-1-2-20000-2-2-21121-111-1-100000-20220000000011-1-100010-1
χ332-22-222-2-20000022-2-2-222-200200-22-2002-22i−2i2i−2i0000000000000000000002-22i−2i002i−2i00000000
χ342-22-222-2-20000022-2-2-222-200200-22-2002-2−2i2i−2i2i0000000000000000000002-2−2i2i00−2i2i00000000
χ352-22-222-2-20000022-2-2-222-200200-22-200-222i−2i−2i2i000000000000000000000-222i−2i00−2i2i00000000
χ362-22-222-2-20000022-2-2-222-200200-22-200-22−2i2i2i−2i000000000000000000000-22−2i2i002i−2i00000000
χ374444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2000000-211-2-2-21111000000000000000000000000000
χ38444444444-4-4-4-4-2-2-2-2-2-2-2-24-41-2-211122000000-211222-1-1-1-1000000000000000000000000000
χ3944444444-44-4-4-4-2-2-2-2-2-2-2-2-44122111-2-20000002-1-12-2211-1-1000000000000000000000000000
χ4044444444-4-4444-2-2-2-2-2-2-2-2-4-4122111220000002-1-1-22-2-1-111000000000000000000000000000
χ4144-4-44-44-400000444-44-4-4-4004004-4-4000000000000000000000000000000000000000000000
χ4244-4-44-44-4000004-242-2-42-400-200-22223−2300000000000023−2300000000000000000000000000000
χ4344-4-44-44-4000004-242-2-42-400-200-222−2323000000000000−232300000000000000000000000000000
χ4444-4-44-44-400000-24-2-442-4200-2−2i32i3-222000000000−2i32i30000000000000000000000000000000000
χ4544-4-44-44-400000-24-2-442-4200-22i3−2i3-2220000000002i3−2i30000000000000000000000000000000000
χ4644-4-44-44-400000-2-2-22-2222001−2i32i31-1-123−230000000i3−i3000−333i−3i000000000000000000000000000
χ4744-4-44-44-400000-2-2-22-2222001−2i32i31-1-1−23230000000i3−i30003−3−3i3i000000000000000000000000000
χ4844-4-44-44-400000-2-2-22-22220012i3−2i31-1-123−230000000−i3i3000−33−3i3i000000000000000000000000000
χ4944-4-44-44-400000-2-2-22-22220012i3−2i31-1-1−23230000000−i3i30003−33i−3i000000000000000000000000000
χ504-44-444-4-4000004-2-4224-2-400-2002-22004-40000000000000000000000000-2200000000000000
χ514-44-444-4-4000004-2-4224-2-400-2002-2200-4400000000000000000000000002-200000000000000
χ524-44-444-4-400000-242-4-4-24200-2002-220000004i−4i000000000000000000000000000−2i2i00000000
χ534-44-444-4-400000-242-4-4-24200-2002-22000000−4i4i0000000000000000000000000002i−2i00000000
χ544-4-444-4-440000044-44-4-4-4400400-4-44000000000000000000000000000000000000000000000
χ554-4-444-4-44000004-2-4-22-42400-20022-200000000000000000000000000000000023−230000000000
χ564-4-444-4-44000004-2-4-22-42400-20022-2000000000000000000000000000000000−23230000000000
χ574-4-444-4-4400000-2424-42-4-200-20022-20000000000000000000000000000000000000−2i32i3000000
χ584-4-444-4-4400000-2424-42-4-200-20022-200000000000000000000000000000000000002i3−2i3000000
χ596666-3-3-3-3666-3-300000000-3-3000000000022000000000000202000200-1-100-1-1000000-1-10000
χ606666-3-3-3-3666-3-300000000-3-30000000000-2-2000000000000-20-2000-200110011000000110000
χ616666-3-3-3-36-6-63300000000-33000000000022000000000000-202000-2001100-1-1000000-110000
χ626666-3-3-3-36-6-63300000000-330000000000-2-200000000000020-2000200-1-100110000001-10000
χ636666-3-3-3-3-66-633000000003-3000000000022000000000000-20-20002001100-1-10000001-10000
χ646666-3-3-3-3-66-633000000003-30000000000-2-2000000000000202000-200-1-10011000000-110000
χ656666-3-3-3-3-6-66-3-3000000003300000000002200000000000020-2000-200-1-100-1-1000000110000
χ666666-3-3-3-3-6-66-3-300000000330000000000-2-2000000000000-202000200110011000000-1-10000
χ678-88-888-8-800000-4-4444-4-4400200-22-2000000000000000000000000000000000000000000000
χ688-8-888-8-8800000-4-44-4444-400200-2-22000000000000000000000000000000000000000000000
χ691212-12-12-66-6600063−630000000000000000000000000000000000000000000000000000000000000
χ701212-12-12-66-66000−63630000000000000000000000000000000000000000000000000000000000000
χ7112-1212-12-6-66600000000000000000000000004i−4i0000000000000000000000000−2i2i000000000000
χ7212-1212-12-6-6660000000000000000000000000−4i4i00000000000000000000000002i−2i000000000000
χ7312-12-1212-666-6000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ7412-12-1212-666-60000000000000000000000000000000000000000000000002i3−2i30000000000000000

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