Finite Group Databasebeta

← Group #13140564

Character table — Group #13140564

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order122234466622121233666666663666666612121212224466666666661212224444666688881212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ51111111111-1-11111111111-1-11-1-1-1-1111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-11-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ71111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ911-1-111-1-11-11-11-111-1-1-111-11-1111-1-1-1-1111-1-11-11-111-1-11-111-1-11-11-1i−ii−i11-1-1i−ii−i1-1ii−i−iii−i−ii−ii−i
χ1011-1-111-1-11-11-11-111-1-1-111-11-1111-1-1-1-1111-1-11-11-111-1-11-111-1-11-11-1−ii−ii11-1-1−ii−ii1-1−i−iii−i−iii−ii−ii
χ1111-1-111-1-11-11-11-111-1-1-111-11-1111-1-1-1-1111-1-1-11-11-1-1111-111-1-11-1-11i−i−ii-1-111i−i−ii-11ii−i−i−i−iiii−i−ii
χ1211-1-111-1-11-11-11-111-1-1-111-11-1111-1-1-1-1111-1-1-11-11-1-1111-111-1-11-1-11−iii−i-1-111−iii−i-11−i−iiiii−i−i−iii−i
χ1311-1-111-1-11-1-111-111-1-1-111-1-111-1-111-1-1111-1-11-11-111-1-1-11-1-1111-1-11i−ii−i-1-111−ii−ii1-1−i−iii−i−iiii−ii−i
χ1411-1-111-1-11-1-111-111-1-1-111-1-111-1-111-1-1111-1-11-11-111-1-1-11-1-1111-1-11−ii−ii-1-111i−ii−i1-1ii−i−iii−i−i−ii−ii
χ1511-1-111-1-11-1-111-111-1-1-111-1-111-1-111-1-1111-1-1-11-11-1-111-11-1-1111-11-1i−i−ii11-1-1−iii−i-11−i−iiiii−i−ii−i−ii
χ1611-1-111-1-11-1-111-111-1-1-111-1-111-1-111-1-1111-1-1-11-11-1-111-11-1-1111-11-1−iii−i11-1-1i−i−ii-11ii−i−i−i−iii−iii−i
χ17222222222222222-12-1-12-1222-1-1-1-1-1-1-1-12-1-122222-1-1-1-122-1-1-1-1-1-1220000-1-1-1-10000-1-1000000000000
χ18222222222222222-12-1-12-1222-1-1-1-1-1-1-1-12-1-12-2-2-2-2111122-1-1-1-1-1-1-2-200001111000011000000000000
χ1922222222222222-12-122-12-122-12222-1-1-1-122-100000000-1-1-1-1-1-1-1-100002200000022000000-1-1-1-100-1-1
χ2022222222222222-12-122-12-122-12222-1-1-1-122-100000000-1-1-1-1-1-1-1-10000-2-2000000-2-200000011110011
χ212222222222-2-2222-12-1-12-12-2-2-11111-1-1-12-1-122222-1-1-1-1-2-21111-1-1-2-2000011110000-1-1000000000000
χ222222222222-2-2222-12-1-12-12-2-2-11111-1-1-12-1-12-2-2-2-21111-2-21111-1-1220000-1-1-1-1000011000000000000
χ232222222222-2-222-12-122-12-1-2-2-1-2-2-2-2-1-1-1-122-100000000111111-1-1000022000000-2-2000000111100-1-1
χ242222222222-2-222-12-122-12-1-2-2-1-2-2-2-2-1-1-1-122-100000000111111-1-10000-2-200000022000000-1-1-1-10011
χ2522222-2-222200-2-2222222220020000222-2-2-2-222-2-22222000000-2-200000000000000-2-2000000000000
χ2622222-2-222200-2-2222222220020000222-2-2-2-2-2-222-2-2-2-2000000-2-20000000000000022000000000000
χ2722222-2-222200-2-22-12-1-12-1200-1−i3i3−i3i3-1-1-1-211-222-2-2-1-1-1-100−i3i3−i3i311000000−i3i3−i3i3000011000000000000
χ2822222-2-222200-2-22-12-1-12-1200-1−i3i3−i3i3-1-1-1-211-2-2-222111100−i3i3−i3i311000000i3−i3i3−i30000-1-1000000000000
χ2922222-2-222200-2-22-12-1-12-1200-1i3−i3i3−i3-1-1-1-211-222-2-2-1-1-1-100i3−i3i3−i311000000i3−i3i3−i3000011000000000000
χ3022222-2-222200-2-22-12-1-12-1200-1i3−i3i3−i3-1-1-1-211-2-2-222111100i3−i3i3−i311000000−i3i3−i3i30000-1-1000000000000
χ3122-2-222-2-22-22-22-22-1-2112-1-22-2-1-1-11111-12-11-22-22-2-1-1112-2-1-111-112-20000-1-1110000-11000000000000
χ3222-2-222-2-22-22-22-22-1-2112-1-22-2-1-1-11111-12-11-2-22-2211-1-12-2-1-111-11-22000011-1-100001-1000000000000
χ3322-2-222-2-22-22-22-2-121-2-2-1212-2-122-2-211-1-12-2100000000-11-1-111-1100002i−2i0000002i−2i000000−i−iii00−ii
χ3422-2-222-2-22-22-22-2-121-2-2-1212-2-122-2-211-1-12-2100000000-11-1-111-110000−2i2i000000−2i2i000000ii−i−i00i−i
χ3522-2-222-2-22-2-222-22-1-2112-1-2-22-111-1-111-12-11-22-22-2-1-111-2211-1-1-11-22000011-1-10000-11000000000000
χ3622-2-222-2-22-2-222-22-1-2112-1-2-22-111-1-111-12-11-2-22-2211-1-1-2211-1-1-112-20000-1-11100001-1000000000000
χ3722-2-222-2-22-2-222-2-121-2-2-121-22-1-2-22211-1-12-21000000001-111-1-1-1100002i−2i000000−2i2i000000ii−i−i00−ii
χ3822-2-222-2-22-2-222-2-121-2-2-121-22-1-2-22211-1-12-21000000001-111-1-1-110000−2i2i0000002i−2i000000−i−iii00i−i
χ3922-2-22-22-22-200-2222-2-2-222-20020000-2-22-2-2222-2-2222-2-2000000-2200000000000000-22000000000000
χ4022-2-22-22-22-200-2222-2-2-222-20020000-2-22-2-222-222-2-2-222000000-22000000000000002-2000000000000
χ4122-2-22-22-22-200-222-1-2112-1-200-1−i3i3i3−i311-1-21-122-2-22-1-11100−i3i3i3−i31-1000000−i3i3i3−i300001-1000000000000
χ4222-2-22-22-22-200-222-1-2112-1-200-1−i3i3i3−i311-1-21-12-222-211-1-100−i3i3i3−i31-1000000i3−i3−i3i30000-11000000000000
χ4322-2-22-22-22-200-222-1-2112-1-200-1i3−i3−i3i311-1-21-122-2-22-1-11100i3−i3−i3i31-1000000i3−i3−i3i300001-1000000000000
χ4422-2-22-22-22-200-222-1-2112-1-200-1i3−i3−i3i311-1-21-12-222-211-1-100i3−i3−i3i31-1000000−i3i3i3−i30000-11000000000000
χ4544444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-412222111-2-2-2-20000000022-1-1-1-1110000000000000000000000000000
χ4744444-4-444400-4-4-24-244-24-200-20000-2-2-22-4-4200000000000000220000000000000000000000000000
χ4844444-4-444400-4-4-2-2-2-2-2-2-2-2001−2i32i3−2i32i311122220000000000i3−i3i3−i3-1-10000000000000000000000000000
χ4944444-4-444400-4-4-2-2-2-2-2-2-2-20012i3−2i32i3−2i311122220000000000−i3i3−i3i3-1-10000000000000000000000000000
χ5044-4-444-4-44-44-44-4-2-2222-2-224-41-2-222-1-11-2-22200000000-2211-1-11-10000000000000000000000000000
χ5144-4-444-4-44-4-444-4-2-2222-2-22-44122-2-2-1-11-2-222000000002-2-1-1111-10000000000000000000000000000
χ5244-4-44-44-44-400-44-242-4-4-24200-2000022-22-44-2000000000000002-20000000000000000000000000000
χ5344-4-44-44-44-400-44-2-2222-2-22001−2i32i32i3−2i3-1-1122-2-20000000000i3−i3−i3i3-110000000000000000000000000000
χ5444-4-44-44-44-400-44-2-2222-2-220012i3−2i3−2i32i3-1-1122-2-20000000000−i3i3i3−i3-110000000000000000000000000000
χ554-44-44004-4-4000044-44-4-4-4400400004-4-4000000000000000000000000000000000000000000000000
χ564-44-44004-4-400004-2-4-22-42400-20000-22200000000−2i32i3−2i32i3000000000000000000000000000000000000
χ574-44-44004-4-400004-2-4-22-42400-20000-222000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ584-44-44004-4-40000-2424-42-4-200-20000-2220000000000000000000000000000000000000000i6−i6i6−i60000
χ594-44-44004-4-40000-2424-42-4-200-20000-2220000000000000000000000000000000000000000−i6i6−i6i60000
χ604-4-44400-4-440000444-44-4-4-40040000-44-4000000000000000000000000000000000000000000000000
χ614-4-44400-4-4400004-242-2-42-400-200002-2200000000−2i32i32i3−2i3000000000000000000000000000000000000
χ624-4-44400-4-4400004-242-2-42-400-200002-22000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ634-4-44400-4-440000-24-2-442-4200-200002-2200000000000000000000000000000000000000006−6−660000
χ644-4-44400-4-440000-24-2-442-4200-200002-220000000000000000000000000000000000000000−666−60000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000000022000000220000-1-1-1-10000-1-100
χ666666-366-3-3-366-3-300000000-3-3000000000000000000000000000000-2-2000000-2-20000111100001100
χ676666-366-3-3-3-6-6-3-3000000003300000000000000000000000000000022000000-2-2000011110000-1-100
χ686666-366-3-3-3-6-6-3-30000000033000000000000000000000000000000-2-2000000220000-1-1-1-100001100
χ6966-6-6-36-63-336-6-3300000000-330000000000000000000000000000002i−2i0000002i−2i0000−i−iii0000−ii00
χ7066-6-6-36-63-336-6-3300000000-33000000000000000000000000000000−2i2i000000−2i2i0000ii−i−i0000i−i00
χ7166-6-6-36-63-33-66-33000000003-30000000000000000000000000000002i−2i000000−2i2i0000ii−i−i0000−ii00
χ7266-6-6-36-63-33-66-33000000003-3000000000000000000000000000000−2i2i0000002i−2i0000−i−iii0000i−i00
χ738-88-88008-8-80000-4-44-4444-400200002-2-2000000000000000000000000000000000000000000000000
χ748-8-88800-8-880000-4-4-44-44440020000-22-2000000000000000000000000000000000000000000000000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-6-12126-66006-6000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212-12-600-66600000000000000000000000000000000000000000000000000000000006−66−600000000
χ7812-1212-12-600-6660000000000000000000000000000000000000000000000000000000000−66−6600000000
χ7912-12-1212-60066-60000000000000000000000000000000000000000000000000000000000i6−i6−i6i600000000
χ8012-12-1212-60066-60000000000000000000000000000000000000000000000000000000000−i6i6i6−i600000000

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