Finite Group Databasebeta

← Group #13140924

Character table — Group #13140924

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order1222344666441212336666661212366612121212121212122244666612121212121212124444448888121212121212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-11111111111-1-11111111-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-11111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ71111111111-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111
χ91-1-1111-1-11-11-11-111-1-1-11-111-11-1-1111-111-1-1-11-11-111-1-11-11-111-1-1i−ii−i1-1i−ii−i1-111-1-1ii−i−iii−i−ii−ii−i
χ101-1-1111-1-11-11-11-111-1-1-11-111-11-1-1111-111-1-1-11-11-111-1-11-11-111-1-1−ii−ii1-1−ii−ii1-111-1-1−i−iii−i−iii−ii−ii
χ111-1-1111-1-11-11-11-111-1-1-11-111-11-1-1111-111-1-1-1-11-11-1-1111-11-111-1-1i−i−ii-11i−i−ii-11-1-111ii−i−i−i−iiii−i−ii
χ121-1-1111-1-11-11-11-111-1-1-11-111-11-1-1111-111-1-1-1-11-11-1-1111-11-111-1-1−iii−i-11−iii−i-11-1-111−i−iiiii−i−i−iii−i
χ131-1-1111-1-11-1-111-111-1-1-11-11-111-1-1111-1-1-111-11-11-111-1-1-111-1-1-111i−ii−i-11−ii−ii1-1-1-111−i−iii−i−iiii−ii−i
χ141-1-1111-1-11-1-111-111-1-1-11-11-111-1-1111-1-1-111-11-11-111-1-1-111-1-1-111−ii−ii-11i−ii−i1-1-1-111ii−i−iii−i−i−ii−ii
χ151-1-1111-1-11-1-111-111-1-1-11-11-111-1-1111-1-1-111-1-11-11-1-111-111-1-1-111i−i−ii1-1−iii−i-1111-1-1−i−iiiii−i−ii−i−ii
χ161-1-1111-1-11-1-111-111-1-1-11-11-111-1-1111-1-1-111-1-11-11-1-111-111-1-1-111−iii−i1-1i−i−ii-1111-1-1ii−i−i−i−iii−iii−i
χ17222222222222222-12-1-122-122-1-1-1-12-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-10000220000-1-1-1-1-1-1000000000000
χ18222222222222222-12-1-122-122-1-1-1-12-1-1-1-1-1-12-2-2-2-2111122-1-1-1-1-1-10000-2-20000111111000000000000
χ1922222222222222-12-122-1-1222-1-1-1-1-1222222-100000000-1-1-1-1-1-1-1-100220000220000000000-1-1-1-100-1-1
χ2022222222222222-12-122-1-1222-1-1-1-1-1222222-100000000-1-1-1-1-1-1-1-100-2-20000-2-2000000000011110011
χ212222222222-2-2222-12-1-122-1-2-2-1-1-1-12-1-1111122222-1-1-1-1-2-2-1-111110000-2-20000-1-11111000000000000
χ222222222222-2-2222-12-1-122-1-2-2-1-1-1-12-1-111112-2-2-2-21111-2-2-1-11111000022000011-1-1-1-1000000000000
χ232222222222-2-222-12-122-1-12-2-2-1-1-1-1-122-2-2-2-2-10000000011-1-1111100220000-2-20000000000111100-1-1
χ242222222222-2-222-12-122-1-12-2-2-1-1-1-1-122-2-2-2-2-10000000011-1-1111100-2-20000220000000000-1-1-1-10011
χ2522222-2-222200-2-222222222002222-2-2-20000-222-2-2222200-2-200000000000000-2-20000000000000000
χ2622222-2-222200-2-222222222002222-2-2-20000-2-2-222-2-2-2-200-2-200000000000000220000000000000000
χ2722222-2-222200-2-22-12-1-122-100-1-1-1-1-211−i3i3−i3i3-222-2-2-1-1-1-10011−i3i3−i3i3000000000011−i3i3−i3i3000000000000
χ2822222-2-222200-2-22-12-1-122-100-1-1-1-1-211−i3i3−i3i3-2-2-22211110011−i3i3−i3i30000000000-1-1i3−i3i3−i3000000000000
χ2922222-2-222200-2-22-12-1-122-100-1-1-1-1-211i3−i3i3−i3-222-2-2-1-1-1-10011i3−i3i3−i3000000000011i3−i3i3−i3000000000000
χ3022222-2-222200-2-22-12-1-122-100-1-1-1-1-211i3−i3i3−i3-2-2-22211110011i3−i3i3−i30000000000-1-1−i3i3−i3i3000000000000
χ312-2-2222-2-22-22-22-22-1-2112-2-12-2-111-12-11-1-111-22-22-2-1-1112-2-11-1-11100002-20000-11-1-111000000000000
χ322-2-2222-2-22-22-22-22-1-2112-2-12-2-111-12-11-1-111-2-22-2211-1-12-2-11-1-1110000-2200001-111-1-1000000000000
χ332-2-2222-2-22-22-22-2-121-2-2-1122-2-111-1-12-222-2-2100000000-11-11-1-111002i−2i00002i−2i0000000000−i−iii00−ii
χ342-2-2222-2-22-22-22-2-121-2-2-1122-2-111-1-12-222-2-2100000000-11-11-1-11100−2i2i0000−2i2i0000000000ii−i−i00i−i
χ352-2-2222-2-22-2-222-22-1-2112-2-1-22-111-12-1111-1-1-22-22-2-1-111-22-1111-1-10000-220000-1111-1-1000000000000
χ362-2-2222-2-22-2-222-22-1-2112-2-1-22-111-12-1111-1-1-2-22-2211-1-1-22-1111-1-100002-200001-1-1-111000000000000
χ372-2-2222-2-22-2-222-2-121-2-2-112-22-111-1-12-2-2-2221000000001-1-1111-1-1002i−2i0000−2i2i0000000000ii−i−i00−ii
χ382-2-2222-2-22-2-222-2-121-2-2-112-22-111-1-12-2-2-2221000000001-1-1111-1-100−2i2i00002i−2i0000000000−i−iii00i−i
χ392-2-222-22-22-200-2222-2-2-22-22002-2-22-2-22000022-2-2222-2-200-2200000000000000-220000000000000000
χ402-2-222-22-22-200-2222-2-2-22-22002-2-22-2-2200002-222-2-2-22200-22000000000000002-20000000000000000
χ412-2-222-22-22-200-222-1-2112-2-100-111-1-21-1−i3i3i3−i322-2-22-1-111001-1−i3i3i3−i300000000001-1−i3i3i3−i3000000000000
χ422-2-222-22-22-200-222-1-2112-2-100-111-1-21-1−i3i3i3−i32-222-211-1-1001-1−i3i3i3−i30000000000-11i3−i3−i3i3000000000000
χ432-2-222-22-22-200-222-1-2112-2-100-111-1-21-1i3−i3−i3i322-2-22-1-111001-1i3−i3−i3i300000000001-1i3−i3−i3i3000000000000
χ442-2-222-22-22-200-222-1-2112-2-100-111-1-21-1i3−i3−i3i32-222-211-1-1001-1i3−i3−i3i30000000000-11−i3i3i3−i3000000000000
χ4544444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41111-2-2-22222-2000000002211-1-1-1-10000000000000000000000000000
χ4744444-4-444400-4-4-24-244-2-2400-2-2-2-22-4-40000200000000002200000000000000000000000000000000
χ4844444-4-444400-4-4-2-2-2-2-2-2-2-2001111222−2i32i3−2i32i320000000000-1-1i3−i3i3−i30000000000000000000000000000
χ4944444-4-444400-4-4-2-2-2-2-2-2-2-20011112222i3−2i32i3−2i320000000000-1-1−i3i3−i3i30000000000000000000000000000
χ5044-4-44004-4-4000044-44-4-44-40044-4-40000000000000000000000000000000000000000000000000000
χ5144-4-44004-4-400004-2-4-22-44200-2-222000000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ5244-4-44004-4-400004-2-4-22-44200-2-2220000000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ5344-4-44004-4-40000-2424-42-2-400-2-222000000000000000000000000000000000000000000006−66−60000
χ5444-4-44004-4-40000-2424-42-2-400-2-22200000000000000000000000000000000000000000000−66−660000
χ554-44-4400-4-440000444-44-4-4-4004-44-40000000000000000000000000000000000000000000000000000
χ564-44-4400-4-4400004-242-2-4-4200-22-22000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ574-44-4400-4-4400004-242-2-4-4200-22-220000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ584-44-4400-4-440000-24-2-4422-400-22-2200000000000000000000000000000000000000000000i6−i6−i6i60000
χ594-44-4400-4-440000-24-2-4422-400-22-2200000000000000000000000000000000000000000000−i6i6i6−i60000
χ604-4-4444-4-44-44-44-4-2-2222-22-24-41-1-11-2-22-2-222200000000-221-111-1-10000000000000000000000000000
χ614-4-4444-4-44-4-444-4-2-2222-22-2-441-1-11-2-2222-2-22000000002-21-1-1-1110000000000000000000000000000
χ624-4-444-44-44-400-44-242-4-4-22400-222-22-440000-200000000002-200000000000000000000000000000000
χ634-4-444-44-44-400-44-2-2222-22-2001-1-1122-2−2i32i32i3−2i3-20000000000-11i3−i3−i3i30000000000000000000000000000
χ644-4-444-44-44-400-44-2-2222-22-2001-1-1122-22i3−2i3−2i32i3-20000000000-11−i3i3i3−i30000000000000000000000000000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000002200002200000000-1-1-1-10000-1-100
χ666666-366-3-3-366-3-300000000-3-30000000000000000000000000000-2-20000-2-200000000111100001100
χ676666-366-3-3-3-6-6-3-300000000330000000000000000000000000000220000-2-20000000011110000-1-100
χ686666-366-3-3-3-6-6-3-300000000330000000000000000000000000000-2-200002200000000-1-1-1-100001100
χ696-6-66-36-63-336-6-3300000000-3300000000000000000000000000002i−2i00002i−2i00000000−i−iii0000−ii00
χ706-6-66-36-63-336-6-3300000000-330000000000000000000000000000−2i2i0000−2i2i00000000ii−i−i0000i−i00
χ716-6-66-36-63-33-66-33000000003-300000000000000000000000000002i−2i0000−2i2i00000000ii−i−i0000−ii00
χ726-6-66-36-63-33-66-33000000003-30000000000000000000000000000−2i2i00002i−2i00000000−i−iii0000i−i00
χ7388-8-88008-8-80000-4-44-444-440022-2-20000000000000000000000000000000000000000000000000000
χ748-88-8800-8-880000-4-4-44-4444002-22-20000000000000000000000000000000000000000000000000000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-600-6660000000000000000000000000000000000000000000000000000000000i6−i6i6−i600000000
χ771212-12-12-600-6660000000000000000000000000000000000000000000000000000000000−i6i6−i6i600000000
χ7812-1212-12-60066-600000000000000000000000000000000000000000000000000000000006−6−6600000000
χ7912-1212-12-60066-60000000000000000000000000000000000000000000000000000000000−666−600000000
χ8012-12-1212-6-12126-66006-6000000000000000000000000000000000000000000000000000000000000000000

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