Finite Group Databasebeta

← Group #13137922

Character table — Group #13137922

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order122234466612123366666641212366612121212441212121212121212121222444888812121212242424242424242446612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111
χ31111111111111111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1
χ41111111111111111111111111111111-1-11111111111-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1
χ511111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111111-1-11111
χ92222222222222-1-12-1-122222-1-1-1-122-1-100-1-122-1-1-1-1-1-122000220000000000-1-1-1-10-1-10000
χ102222222222222-1-12-1-122222-1-1-1-122-1-100-1-122-1-1-1-1-1-1-2-2000-2-2000000000011110110000
χ112222222222222-1-12-1-122-2-2-2-1-1-1-122-1-10011-2-2-1-1111122000-2-2000000000011110-1-10000
χ122222222222222-1-12-1-122-2-2-2-1-1-1-122-1-10011-2-2-1-11111-2-2000220000000000-1-1-1-10110000
χ13222222222222-122-122-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1000020000-1-1-1-10000000020000-1-1
χ14222222222222-122-122-1-1222-1-1-1-1-1-122-2-222-1-1-1-1-1-1-1-10000-20000111100000000-2000011
χ15222222222222-122-122-1-1-2-2-2-1-1-1-1-1-12222-2-211-1-11111000020000-1-1-1-100000000-2000011
χ16222222222222-122-122-1-1-2-2-2-1-1-1-1-1-122-2-2-2-211-1-111110000-2000011110000000020000-1-1
χ1722222-2-2222-2-2222222220002222-2-2-2-2220000-2-200000000-2000022-2-2000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-20000-2-20000000020000-2-222000000000000000
χ1922222-2-2222-2-2-122-122-1-1000-1-1-1-111-2-22200−i3i311−i3−i3i3i30000-20000-1-1110000000000000−i3i3
χ2022222-2-2222-2-2-122-122-1-1000-1-1-1-111-2-22200i3−i311i3i3−i3−i30000-20000-1-1110000000000000i3−i3
χ2122222-2-2222-2-2-122-122-1-1000-1-1-1-111-2-2-2-200−i3i311−i3−i3i3i300002000011-1-10000000000000i3−i3
χ2222222-2-2222-2-2-122-122-1-1000-1-1-1-111-2-2-2-200i3−i311i3i3−i3−i300002000011-1-10000000000000−i3i3
χ2322-2-222-22-2-22-222-222-2-2-20002-22-22-22-20000002-200002-2000000000000000000002-20000
χ2422-2-222-22-2-22-222-222-2-2-20002-22-22-22-20000002-20000-2200000000000000000000-220000
χ2522-2-222-22-2-22-22-112-11-2-2000-11-112-2-11003−300-113−33−32-200000000000000033−3−30-110000
χ2622-2-222-22-2-22-22-112-11-2-2000-11-112-2-11003−300-113−33−3-22000000000000000−3−33301-10000
χ2722-2-222-22-2-22-22-112-11-2-2000-11-112-2-1100−3300-11−33−332-2000000000000000−3−3330-110000
χ2822-2-222-22-2-22-22-112-11-2-2000-11-112-2-1100−3300-11−33−33-2200000000000000033−3−301-10000
χ2922-2-22-222-2-2-2222-222-2-2-20002-22-2-22-22000000-220000002i−2i000000000000000000002i−2i00
χ3022-2-22-222-2-2-2222-222-2-2-20002-22-2-22-22000000-22000000−2i2i00000000000000000000−2i2i00
χ312-22-2200-2-2200222-2-2-22-200022-2-200002-2000000000000000−i2i2−i2i22-200−i2−i2i2i2−i2i2−i2i20000000
χ322-22-2200-2-2200222-2-2-22-200022-2-200002-2000000000000000i2−i2i2−i22-200i2i2−i2−i2i2−i2i2−i20000000
χ332-22-2200-2-2200222-2-2-22-200022-2-20000-22000000000000000−i2i2i2−i2-2200i2i2−i2−i2−i2i2−i2i20000000
χ342-22-2200-2-2200222-2-2-22-200022-2-20000-22000000000000000i2−i2−i2i2-2200−i2−i2i2i2i2−i2i2−i20000000
χ35444444444444-2-2-2-2-2-2-2-24441111-2-2-2-200-2-2-2-21111110000000000000000000000000000
χ36444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-200222211-1-1-1-10000000000000000000000000000
χ3744444-4-4444-4-44-2-24-2-244000-2-2-2-2-4-4220000002200000000000000000000000000000000
χ3844444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000−2i32i3-1-1i3i3−i3−i30000000000000000000000000000
χ3944444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200002i3−2i3-1-1−i3−i3i3i30000000000000000000000000000
χ4044-4-444-44-4-44-4-24-4-24-422000-22-22-224-4000000-2200000000000000000000000000000000
χ4144-4-444-44-4-44-4-2-22-2-22220001-11-1-22-220023−23001-1−33−330000000000000000000000000000
χ4244-4-444-44-4-44-4-2-22-2-22220001-11-1-22-2200−2323001-13−33−30000000000000000000000000000
χ4344-4-44-444-4-4-444-224-22-4-4000-22-22-442-20000002-200000000000000000000000000000000
χ4444-4-44-444-4-4-44-24-4-24-422000-22-222-2-440000002-200000000000000000000000000000000
χ4544-4-44-444-4-4-44-2-22-2-22220001-11-12-22-2000000-113i−3i−3i3i0000000000000000000000000000
χ4644-4-44-444-4-4-44-2-22-2-22220001-11-12-22-2000000-11−3i3i3i−3i0000000000000000000000000000
χ474-44-4400-4-44004-2-2-4224-4000-2-222000000000000000000000−2i22i20000000000i2−i2i2−i20000000
χ484-44-4400-4-44004-2-2-4224-4000-2-2220000000000000000000002i2−2i20000000000−i2i2−i2i20000000
χ494-44-4400-4-4400-2442-4-4-22000-2-22200004-40000000000000000000-2200000000000000000
χ504-44-4400-4-4400-2442-4-4-22000-2-2220000-4400000000000000000002-200000000000000000
χ514-4-44400-44-40044-4-4-44-440004-4-4400000000000000000000000000000000000000000000
χ524-4-44400-44-4004-22-42-2-44000-222-2000000000000000000000000000000000i6−i6−i6i60000000
χ534-4-44400-44-4004-22-42-2-44000-222-2000000000000000000000000000000000−i6i6i6−i60000000
χ544-4-44400-44-400-24-42-442-2000-222-2000000000000000000000000000−2i32i3000000000000000
χ554-4-44400-44-400-24-42-442-2000-222-20000000000000000000000000002i3−2i3000000000000000
χ566666-366-3-3-3-3-3000000006-3-3000000000000000000000022000220000-1-1-1-10000000-1-100
χ576666-366-3-3-3-3-3000000006-3-30000000000000000000000-2-2000-2-20000111100000001100
χ586666-366-3-3-3-3-300000000-633000000000000000000000022000-2-2000011110000000-1-100
χ596666-366-3-3-3-3-300000000-6330000000000000000000000-2-2000220000-1-1-1-100000001100
χ6066-6-6-3-66-3333-300000000033−3300000000000000000000002i−2i000000000−i3i3−i3i30000000−ii00
χ6166-6-6-3-66-3333-300000000033−330000000000000000000000−2i2i000000000i3−i3i3−i30000000i−i00
χ6266-6-6-3-66-3333-3000000000−333300000000000000000000002i−2i000000000i3−i3i3−i30000000−ii00
χ6366-6-6-3-66-3333-3000000000−33330000000000000000000000−2i2i000000000−i3i3−i3i30000000i−i00
χ648-88-8800-8-8800-4-4-4444-4400022-2-200000000000000000000000000000000000000000000
χ658-8-88800-88-800-4-4444-44-40002-2-2200000000000000000000000000000000000000000000
χ6612121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-612-12-666-6600000000000000000000000000000000000000000000000000000000000
χ6812-1212-12-60066-60000000000000000000000000000000000000000−2i22i20000i2i2−i2−i200000000000
χ6912-1212-12-60066-600000000000000000000000000000000000000002i2−2i20000−i2−i2i2i200000000000
χ7012-12-1212-6006-6600000000000000000000000000000000000000000000006−6−6600000000000
χ7112-12-1212-6006-660000000000000000000000000000000000000000000000−666−600000000000

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