Finite Group Databasebeta

← Group #13140585

Character table — Group #13140585

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222224444444466666666121212121212121218181818181818182424242424242424242436363636363636363636363636363636363636363636363672727272
order122234466622666612123366666636661212121222446666666666661212224444666688881212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ51111111111-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ61111111111-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ71111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1111111-1-1
χ81111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ911-1-111-1-1-111-111-1-11-111-1-111-1-11-1-1111-1-11-11-111-1-111-1-111-1-11-11-1i−ii−i11-1-1i−ii−i1-1ii−i−iii−i−ii−ii−i
χ1011-1-111-1-1-111-111-1-11-111-1-111-1-11-1-1111-1-11-11-111-1-111-1-111-1-11-11-1−ii−ii11-1-1−ii−ii1-1−i−iii−i−iii−ii−ii
χ1111-1-111-1-1-111-111-1-11-111-1-111-1-11-1-1111-1-1-11-11-1-11111-1-111-1-11-1-11i−i−ii-1-111i−i−ii-11ii−i−i−i−iiii−i−ii
χ1211-1-111-1-1-111-111-1-11-111-1-111-1-11-1-1111-1-1-11-11-1-11111-1-111-1-11-1-11−iii−i-1-111−iii−i-11−i−iiiii−i−i−iii−i
χ1311-1-111-1-1-11-11-1-1111-111-1-111-1-11-1-1111-1-11-11-111-1-1-1-111-1-1111-1-11i−ii−i-1-111−ii−ii1-1−i−iii−i−iiii−ii−i
χ1411-1-111-1-1-11-11-1-1111-111-1-111-1-11-1-1111-1-11-11-111-1-1-1-111-1-1111-1-11−ii−ii-1-111i−ii−i1-1ii−i−iii−i−i−ii−ii
χ1511-1-111-1-1-11-11-1-1111-111-1-111-1-11-1-1111-1-1-11-11-1-111-1-111-1-1111-11-1i−i−ii11-1-1−iii−i-11−i−iiiii−i−ii−i−ii
χ1611-1-111-1-1-11-11-1-1111-111-1-111-1-11-1-1111-1-1-11-11-1-111-1-111-1-1111-11-1−iii−i11-1-1i−i−ii-11ii−i−i−i−iii−iii−i
χ172222222222222222222-12-12-12-1-1-1-1-12-12-1000000002-12-1-1-1-1-1-1-100002200000022000000-1-1-1-100-1-1
χ182222222222222222222-12-12-12-1-1-1-1-12-12-1000000002-12-1-1-1-1-1-1-10000-2-2000000-2-200000011110011
χ19222222222222222222-12-12-12-12-1-1-1-1-12-1200000000-12-12-1-1-1-1-1-10022000000220000-1-1-1-10000-1-100
χ20222222222222222222-12-12-12-12-1-1-1-1-12-1200000000-12-12-1-1-1-1-1-100-2-2000000-2-20000111100001100
χ212222222222-2-2-2-2-2-2222-12-12-12-1-1-1-1-12-12-100000000-21-211111-1-1000022000000-2-2000000111100-1-1
χ222222222222-2-2-2-2-2-2222-12-12-12-1-1-1-1-12-12-100000000-21-211111-1-10000-2-200000022000000-1-1-1-10011
χ232222222222-2-2-2-2-2-222-12-12-12-12-1-1-1-1-12-12000000001-21-21111-1-10022000000-2-2000011110000-1-100
χ242222222222-2-2-2-2-2-222-12-12-12-12-1-1-1-1-12-12000000001-21-21111-1-100-2-2000000220000-1-1-1-100001100
χ2522222-2-2222000000-2-2222222222222-2-2-2-222-2-2222200000000-2-200000000000000-2-2000000000000
χ2622222-2-2222000000-2-2222222222222-2-2-2-2-2-222-2-2-2-200000000-2-20000000000000022000000000000
χ2722-2-222-2-2-222-222-2-22-22-1-212-1-21-111-12-1-21000000002-1-21-1-111-1100002i−2i0000002i−2i000000−i−iii00−ii
χ2822-2-222-2-2-222-222-2-22-22-1-212-1-21-111-12-1-21000000002-1-21-1-111-110000−2i2i000000−2i2i000000ii−i−i00i−i
χ2922-2-222-2-2-222-222-2-22-2-121-2-121-2-111-1-121-200000000-121-2-1-111-11002i−2i0000002i−2i0000−i−iii0000−ii00
χ3022-2-222-2-2-222-222-2-22-2-121-2-121-2-111-1-121-200000000-121-2-1-111-1100−2i2i000000−2i2i0000ii−i−i0000i−i00
χ3122-2-222-2-2-22-22-2-2222-22-1-212-1-21-111-12-1-2100000000-212-111-1-1-1100002i−2i000000−2i2i000000ii−i−i00−ii
χ3222-2-222-2-2-22-22-2-2222-22-1-212-1-21-111-12-1-2100000000-212-111-1-1-110000−2i2i0000002i−2i000000−i−iii00i−i
χ3322-2-222-2-2-22-22-2-2222-2-121-2-121-2-111-1-121-2000000001-2-1211-1-1-11002i−2i000000−2i2i0000ii−i−i0000−ii00
χ3422-2-222-2-2-22-22-2-2222-2-121-2-121-2-111-1-121-2000000001-2-1211-1-1-1100−2i2i0000002i−2i0000−i−iii0000i−i00
χ3522-2-22-22-2-22000000-2222-2-222-2-22-2-22-2-2222-2-2222-2-200000000-2200000000000000-22000000000000
χ3622-2-22-22-2-22000000-2222-2-222-2-22-2-22-2-222-222-2-2-22200000000-22000000000000002-2000000000000
χ37444444444444444444-2-2-2-2-2-2-2-21111-2-2-2-200000000-2-2-2-21111110000000000000000000000000000
χ384444444444-4-4-4-4-4-444-2-2-2-2-2-2-2-21111-2-2-2-2000000002222-1-1-1-1110000000000000000000000000000
χ3944444-4-4444000000-4-44-24-24-24-2-2-2-2-2-42-420000000000000000220000000000000000000000000000
χ4044444-4-4444000000-4-4-24-24-24-24-2-2-2-22-42-40000000000000000220000000000000000000000000000
χ4144444-4-4444000000-4-4-2-2-2-2-2-2-2-2111122220000000000003-33-3-1-10000000000000000000000000000
χ4244444-4-4444000000-4-4-2-2-2-2-2-2-2-211112222000000000000-33-33-1-10000000000000000000000000000
χ4344-4-444-4-4-444-444-4-44-4-2-222-2-2221-1-11-2-22200000000-2-22211-1-11-10000000000000000000000000000
χ4444-4-444-4-4-44-44-4-4444-4-2-222-2-2221-1-11-2-2220000000022-2-2-1-1111-10000000000000000000000000000
χ4544-4-44-44-4-44000000-444-2-424-2-42-222-2-424-200000000000000002-20000000000000000000000000000
χ4644-4-44-44-4-44000000-44-242-4-242-4-222-22-4-2400000000000000002-20000000000000000000000000000
χ4744-4-44-44-4-44000000-44-2-222-2-2221-1-1122-2-20000000000003-3-33-110000000000000000000000000000
χ4844-4-44-44-4-44000000-44-2-222-2-2221-1-1122-2-2000000000000-333-3-110000000000000000000000000000
χ494-44-44004-4-400000000444-4-4-4-4444-4-400000000000000000000000000000000000000000000000000
χ504-44-44004-4-4000000004-242-42-4-2-2-222000000000000000000000000000000000000000000i6−i6i6−i60000
χ514-44-44004-4-4000000004-242-42-4-2-2-222000000000000000000000000000000000000000000−i6i6−i6i60000
χ524-44-44004-4-400000000-24-2-42-424-2-222000000000000000000000000000000000000006−66−600000000
χ534-44-44004-4-400000000-24-2-42-424-2-22200000000000000000000000000000000000000−66−6600000000
χ544-4-44400-44-40000000044-44-4-44-44-44-400000000000000000000000000000000000000000000000000
χ554-4-44400-44-4000000004-2-4-2-4242-22-220000000000000000000000000000000000000000006−6−660000
χ564-4-44400-44-4000000004-2-4-2-4242-22-22000000000000000000000000000000000000000000−666−60000
χ574-4-44400-44-400000000-24242-4-2-4-22-2200000000000000000000000000000000000000i6−i6−i6i600000000
χ584-4-44400-44-400000000-24242-4-2-4-22-2200000000000000000000000000000000000000−i6i6i6−i600000000
χ596666-366-3-3-366-3-3-3-3-3-300000000000000002222-1-1-1-10000000000220000-1-1-1-10000-1-1000000000000
χ606666-366-3-3-366-3-3-3-3-3-30000000000000000-2-2-2-211110000000000-2-200001111000011000000000000
χ616666-366-3-3-3-6-63333-3-300000000000000002222-1-1-1-10000000000-2-2000011110000-1-1000000000000
χ626666-366-3-3-3-6-63333-3-30000000000000000-2-2-2-211110000000000220000-1-1-1-1000011000000000000
χ636666-3-6-6-3-3-300−3i33i3−3i33i333000000000000000022-2-2-1-1-1-10000000000000000−i3i3−i3i3000011000000000000
χ646666-3-6-6-3-3-300−3i33i3−3i33i3330000000000000000-2-22211110000000000000000i3−i3i3−i30000-1-1000000000000
χ656666-3-6-6-3-3-3003i3−3i33i3−3i333000000000000000022-2-2-1-1-1-10000000000000000i3−i3i3−i3000011000000000000
χ666666-3-6-6-3-3-3003i3−3i33i3−3i3330000000000000000-2-22211110000000000000000−i3i3−i3i30000-1-1000000000000
χ6766-6-6-36-633-36-6-3-333-3300000000000000002-22-2-1-11100000000002-20000-1-1110000-11000000000000
χ6866-6-6-36-633-36-6-3-333-330000000000000000-22-2211-1-10000000000-22000011-1-100001-1000000000000
χ6966-6-6-36-633-3-6633-3-3-3300000000000000002-22-2-1-1110000000000-22000011-1-10000-11000000000000
χ7066-6-6-36-633-3-6633-3-3-330000000000000000-22-2211-1-100000000002-20000-1-11100001-1000000000000
χ7166-6-6-3-6633-300−3i33i33i3−3i33-300000000000000002-2-22-1-1110000000000000000−i3i3i3−i300001-1000000000000
χ7266-6-6-3-6633-300−3i33i33i3−3i33-30000000000000000-222-211-1-10000000000000000i3−i3−i3i30000-11000000000000
χ7366-6-6-3-6633-3003i3−3i3−3i33i33-300000000000000002-2-22-1-1110000000000000000i3−i3−i3i300001-1000000000000
χ7466-6-6-3-6633-3003i3−3i3−3i33i33-30000000000000000-222-211-1-10000000000000000−i3i3i3−i30000-11000000000000
χ758-88-88008-8-800000000-4-4-44444-422-2-200000000000000000000000000000000000000000000000000
χ768-8-88800-88-800000000-4-44-444-442-22-200000000000000000000000000000000000000000000000000
χ7712-1212-12-600-6660000000000000000000000000000−2i32i3−2i32i300000000000000000000000000000000000000
χ7812-1212-12-600-66600000000000000000000000000002i3−2i32i3−2i300000000000000000000000000000000000000
χ7912-12-1212-6006-660000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ8012-12-1212-6006-6600000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000

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