Finite Group Databasebeta

← Group #13140529

Character table — Group #13140529

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size112222244444666666889912121212121212121212121212181818181818182424242424242424363636363636363636363636363636367272727272727272
order122223624666336666612443666666666612124441212121266666121212244444444466121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-11111111111111-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-11111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111111111-1-1111111-1-111111-1-11111111-111-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-1
χ61111111-1-1111111111-1-1111111-1-111111-1-11111111-111-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111
χ71111111-1-1111111111-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111
χ81111111-1-1111111111-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-111-1-111-1-11111-1-1
χ9111-1-1111-11-1-11111111-11111-1-111111-1-1-1-11-1-111111-1-111-1-1-1-11i−ii−ii−ii−i-1-1-1-111i−ii−ii−ii−i
χ10111-1-1111-11-1-11111111-11111-1-111111-1-1-1-11-1-111111-1-111-1-1-1-11−ii−ii−ii−ii-1-1-1-111−ii−ii−ii−ii
χ11111-1-1111-11-1-11111111-1-1-111-1-111111-1-1-1-1-111-1-1-1-11-1-111-1-1-11-1i−ii−i−ii−ii1111-1-1i−ii−i−ii−ii
χ12111-1-1111-11-1-11111111-1-1-111-1-111111-1-1-1-1-111-1-1-1-11-1-111-1-1-11-1−ii−iii−ii−i1111-1-1−ii−iii−ii−i
χ13111-1-111-111-1-1111111-111111-1-1-1-1111-1-1111-1-11111-1-1-1-1-11111-1i−i−iii−i−ii11-1-1-1-1i−i−iii−i−ii
χ14111-1-111-111-1-1111111-111111-1-1-1-1111-1-1111-1-11111-1-1-1-1-11111-1−iii−i−iii−i11-1-1-1-1−iii−i−iii−i
χ15111-1-111-111-1-1111111-11-1-111-1-1-1-1111-1-111-111-1-1-1-1-1-1-1-1-1111-11i−i−ii−iii−i-1-11111i−i−ii−iii−i
χ16111-1-111-111-1-1111111-11-1-111-1-1-1-1111-1-111-111-1-1-1-1-1-1-1-1-1111-11−iii−ii−i−ii-1-11111−iii−ii−i−ii
χ172222222222222-1-1-12-12222-12-1-1-1-1-1-1-122-1-1222-1-1-1-12-1-1-1-12-1-12200000000-1-1-1-1-1-100000000
χ182222222222222-1-1-12-122-2-2-12-1-1-1-1-1-1-122-1-1-2-2-211112-1-1-1-12-1-1-2-20000000011111100000000
χ19222222222222-1222-122200-1-12222-1-1-1-1-1220000000-1-1-1-1-1-1-1-100000022220000000000-1-1-1-1
χ20222222222222-1222-122200-1-12222-1-1-1-1-1220000000-1-1-1-1-1-1-1-1000000-2-2-2-200000000001111
χ212222222-2-22222-1-1-12-1-2-222-12-1-111-1-1-12211222-1-1-1-1-2-1-111-211-2-20000000011-1-11100000000
χ222222222-2-22222-1-1-12-1-2-2-2-2-12-1-111-1-1-12211-2-2-21111-2-1-111-2112200000000-1-111-1-100000000
χ232222222-2-2222-1222-12-2-200-1-122-2-2-1-1-1-1-1-2-200000001-1-11111100000022-2-20000000000-1-111
χ242222222-2-2222-1222-12-2-200-1-122-2-2-1-1-1-1-1-2-200000001-1-111111000000-2-222000000000011-1-1
χ25222-2-2222-22-2-22-1-1-12-12-222-1211-1-1-1-1-1-2-2112-2-2-1-1-1-1211-1-1-211-22000000001111-1-100000000
χ26222-2-2222-22-2-22-1-1-12-12-2-2-2-1211-1-1-1-1-1-2-211-2221111211-1-1-2112-200000000-1-1-1-11100000000
χ27222-2-2222-22-2-2-1222-122-200-1-1-2-222-1-1-111-2-20000000-111-1-11110000002i−2i2i−2i0000000000−ii−ii
χ28222-2-2222-22-2-2-1222-122-200-1-1-2-222-1-1-111-2-20000000-111-1-1111000000−2i2i−2i2i0000000000i−ii−i
χ29222-2-222-222-2-22-1-1-12-1-2222-121111-1-1-1-2-2-1-12-2-2-1-1-1-1-211112-1-12-200000000-1-1111100000000
χ30222-2-222-222-2-22-1-1-12-1-22-2-2-121111-1-1-1-2-2-1-1-2221111-211112-1-1-220000000011-1-1-1-100000000
χ31222-2-222-222-2-2-1222-12-2200-1-1-2-2-2-2-1-1-11122000000011111-1-1-10000002i−2i−2i2i0000000000−iii−i
χ32222-2-222-222-2-2-1222-12-2200-1-1-2-2-2-2-1-1-11122000000011111-1-1-1000000−2i2i2i−2i0000000000i−i−ii
χ3322-22-22200-22-222-2-22200222-22-200-2-222-200-22-222-2-202-2000000000000000002-20000000000
χ3422-22-22200-22-222-2-22200-2-22-22-200-2-222-2002-22-2-22202-200000000000000000-220000000000
χ3522-22-22200-22-22-1112-10022-1-2-11−i3i311-12-2−i3i3-22-2-1-1110-11−i3i30−i3i30000000000−i3i3-11−i3i300000000
χ3622-22-22200-22-22-1112-10022-1-2-11i3−i311-12-2i3−i3-22-2-1-1110-11i3−i30i3−i30000000000i3−i3-11i3−i300000000
χ3722-22-22200-22-22-1112-100-2-2-1-2-11−i3i311-12-2−i3i32-2211-1-10-11−i3i30−i3i30000000000i3−i31-1i3−i300000000
χ3822-22-22200-22-22-1112-100-2-2-1-2-11i3−i311-12-2i3−i32-2211-1-10-11i3−i30i3−i30000000000−i3i31-1−i3i300000000
χ3922-2-222200-2-2222-2-22200222-2-2200-2-22-2200-2-2222-2-20-2200000000000000000-220000000000
χ4022-2-222200-2-2222-2-22200-2-22-2-2200-2-22-220022-2-2-2220-22000000000000000002-20000000000
χ4122-2-222200-2-222-1112-10022-1-21-1−i3i311-1-22i3−i3-2-22-1-11101-1−i3i30i3−i30000000000i3−i31-1−i3i300000000
χ4222-2-222200-2-222-1112-10022-1-21-1i3−i311-1-22−i3i3-2-22-1-11101-1i3−i30−i3i30000000000−i3i31-1i3−i300000000
χ4322-2-222200-2-222-1112-100-2-2-1-21-1−i3i311-1-22i3−i322-211-1-101-1−i3i30i3−i30000000000−i3i3-11i3−i300000000
χ4422-2-222200-2-222-1112-100-2-2-1-21-1i3−i311-1-22−i3i322-211-1-101-1i3−i30−i3i30000000000i3−i3-11−i3i300000000
χ45444444444444-2-2-2-2-2-244001-2-2-2-2-2111-2-2-2-20000000-21111-211000000000000000000000000
χ464444444-4-4444-2-2-2-2-2-2-4-4001-2-2-222111-2-2220000000211-1-12-1-1000000000000000000000000
χ47444-4-4444-44-4-4-2-2-2-2-2-24-4001-222-2-211122220000000-2-1-1112-1-1000000000000000000000000
χ48444-4-444-444-4-4-2-2-2-2-2-2-44001-2222211122-2-200000002-1-1-1-1-211000000000000000000000000
χ4944-44-44400-44-4-24-4-4-240000-224-40022-2-220000000000-2200000000000000000000000000000
χ5044-44-44400-44-4-2-222-2-2000012-22−2i32i3-1-11-22−2i32i3000000001-1i3−i30i3−i3000000000000000000000000
χ5144-44-44400-44-4-2-222-2-2000012-222i3−2i3-1-11-222i3−2i3000000001-1−i3i30−i3i3000000000000000000000000
χ5244-4-444400-4-44-24-4-4-240000-22-440022-22-200000000002-200000000000000000000000000000
χ5344-4-444400-4-44-2-222-2-20000122-2−2i32i3-1-112-22i3−2i300000000-11i3−i30−i3i3000000000000000000000000
χ5444-4-444400-4-44-2-222-2-20000122-22i3−2i3-1-112-2−2i32i300000000-11−i3i30i3−i3000000000000000000000000
χ554-40004-4000004400-4-4004i−4i40000000-400000004i−4i0000000000000000000000000000000000
χ564-40004-4000004400-4-400−4i4i40000000-40000000−4i4i0000000000000000000000000000000000
χ574-40004-4000004-2−2i32i3-42004i−4i-200000−2i32i320000000−2i2i23−2300000000000000000000000000000000
χ584-40004-4000004-2−2i32i3-4200−4i4i-200000−2i32i3200000002i−2i−232300000000000000000000000000000000
χ594-40004-4000004-22i3−2i3-42004i−4i-2000002i3−2i320000000−2i2i−232300000000000000000000000000000000
χ604-40004-4000004-22i3−2i3-4200−4i4i-2000002i3−2i3200000002i−2i23−2300000000000000000000000000000000
χ6166666-3-366-3-3-3000000-3-30000000000000000000000000000000022220000000000-1-1-1-10000
χ6266666-3-366-3-3-3000000-3-300000000000000000000000000000000-2-2-2-2000000000011110000
χ6366666-3-3-6-6-3-3-3000000330000000000000000000000000000000022-2-20000000000-1-1110000
χ6466666-3-3-6-6-3-3-30000003300000000000000000000000000000000-2-222000000000011-1-10000
χ65666-6-6-3-36-6-333000000-33000000000000000000000000000000002i−2i2i−2i0000000000−ii−ii0000
χ66666-6-6-3-36-6-333000000-3300000000000000000000000000000000−2i2i−2i2i0000000000i−ii−i0000
χ67666-6-6-3-3-66-3330000003-3000000000000000000000000000000002i−2i−2i2i0000000000−iii−i0000
χ68666-6-6-3-3-66-3330000003-300000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii0000
χ698-80008-800000-48004-80000-4000000040000000000000000000000000000000000000000000
χ708-80008-800000-4-4−4i34i34400002000002i3−2i3-20000000000000000000000000000000000000000000
χ718-80008-800000-4-44i3−4i3440000200000−2i32i3-20000000000000000000000000000000000000000000
χ721212-1212-12-6-6006-6600000000000000000000000000000000000000000000000000000000000000
χ731212-12-1212-6-60066-600000000000000000000000000000000000000000000000000000000000000
χ7424-24000-12120000000000000000000000000000000000000000000000000000000000000000000

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