Finite Group Databasebeta

← Group #13149608

Character table — Group #13149608

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order1222344666441212336666661212366612121212121212124444121212121212121212121212222444444466121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-11-1-1-1111-1-1-1-111-1-1-1-1-1-111-1-111
χ51111111111-1-11111111111-1-1111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-11-1-1111111111-1-1-1-111-1-1-1-1
χ71111111111-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1111-1-1-11-1-1-1-111-1-111111111-1-1
χ81111111111-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111111-11111-1-1-1-11111-1-1-1-111
χ911111-1-11111-1-1-1111111111-11111-1-111-1-1-1-111-1-111111-1-1-111-1-11-11-11-1-11-1111-1-1-1-1-1-111-1-1111-11-1
χ1011111-1-11111-1-1-1111111111-11111-1-111-1-1-1-111-1-111111-1-1-111-1-1-11-111-11-11-1-1-11111-1-111-1-1-1-1-11-11
χ1111111-1-11111-1-1-1111111111-11111-1-111-1-1-1-1-1-111-1-1-1-11-1-1-111-1-11-111-11-1-11-111-1-11111-1-111-1-11-1-11
χ1211111-1-11111-1-1-1111111111-11111-1-111-1-1-1-1-1-111-1-1-1-11-1-1-111-1-1-11-1-1-1111-11-1-111-1-111-1-11111-111-1
χ1311111-1-1111-11-1-111111111-111111-1-1-1-111-1-111-1-11111-11-1-1-1-1111-1-11-1111-1-1-1-11111-1-1-1-111-1-11-11-1
χ1411111-1-1111-11-1-111111111-111111-1-1-1-111-1-111-1-11111-11-1-1-1-111-111-1-11-1-11111-1-1-1-1-1-1-1-11111-11-11
χ1511111-1-1111-11-1-111111111-111111-1-1-1-111-1-1-1-111-1-1-1-1-11-1-1-1-1111-1-1-11-11-111-1-111-1-11111-1-1111-1-11
χ1611111-1-1111-11-1-111111111-111111-1-1-1-111-1-1-1-111-1-1-1-1-11-1-1-1-111-11111-1-11-1-111-1-1111111-1-1-1-1-111-1
χ17222222222222222-122-1-1-1222-1-1-1-122-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-10000220000000000-1-1-1-1-1-1000000
χ18222222222222222-122-1-1-1222-1-1-1-122-1-1-1-1-1-1-2-2-2-2111122-1-1-1-1-1-10000-2-20000000000111111000000
χ1922222222222222-12-1-1222-122-1-1-1-1-1-122222200000000-1-1-1-1-1-1-1-100020002220000-1-1000000-1-100-1-1
χ2022222222222222-12-1-1222-122-1-1-1-1-1-122222200000000-1-1-1-1-1-1-1-1000-2000-2-2-2000011000000110011
χ212222222222-2-2222-122-1-1-12-2-2-1-1-1-1221111-1-12222-1-1-1-1-2-2-1-111110000-2-20000000000-1-11111000000
χ222222222222-2-2222-122-1-1-12-2-2-1-1-1-1221111-1-1-2-2-2-21111-2-2-1-11111000022000000000011-1-1-1-1000000
χ232222222222-2-222-12-1-1222-1-2-2-1-1-1-1-1-1-2-2-2-2220000000011-1-111110002000-2-220000-1-1000000-1-10011
χ242222222222-2-222-12-1-1222-1-2-2-1-1-1-1-1-1-2-2-2-2220000000011-1-11111000-200022-20000110000001100-1-1
χ2522222-2-22222-2-2-22-122-1-1-122-2-1-1-1-1-2-2-1-1111122-2-2-1-1-1-12-211-1-11100002-2000000000011-1-111000000
χ2622222-2-22222-2-2-22-122-1-1-122-2-1-1-1-1-2-2-1-11111-2-22211112-211-1-1110000-220000000000-1-111-1-1000000
χ2722222-2-22222-2-2-2-12-1-1222-12-2-1-1-1-11122-2-2-2-200000000-1111-1-1110002000-22-20000-1-100000011001-1
χ2822222-2-22222-2-2-2-12-1-1222-12-2-1-1-1-11122-2-2-2-200000000-1111-1-111000-20002-22000011000000-1-100-11
χ2922222-2-2222-22-2-22-122-1-1-12-22-1-1-1-1-2-211-1-11122-2-2-1-1-1-1-221111-1-10000-2200000000001111-1-1000000
χ3022222-2-2222-22-2-22-122-1-1-12-22-1-1-1-1-2-211-1-111-2-2221111-221111-1-100002-20000000000-1-1-1-111000000
χ3122222-2-2222-22-2-2-12-1-1222-1-22-1-1-1-111-2-222-2-2000000001-11111-1-100020002-2-20000-1-10000001100-11
χ3222222-2-2222-22-2-2-12-1-1222-1-22-1-1-1-111-2-222-2-2000000001-11111-1-1000-2000-222000011000000-1-1001-1
χ332-22-222-2-2-22002-2222-2-2-22-2002-22-22-200002-22i−2i2i−2i2i2i−2i−2i002-2000000000000000000002i−2i0000000000
χ342-22-222-2-2-22002-2222-2-2-22-2002-22-22-200002-2−2i2i−2i2i−2i−2i2i2i002-200000000000000000000−2i2i0000000000
χ352-22-222-2-2-22002-22-12-211-1-200-11-112-23−33−3-112i−2i2i−2i−i−iii00-113−33−30000000000000000−ii−i3i3−i3i3000000
χ362-22-222-2-2-22002-22-12-211-1-200-11-112-23−33−3-11−2i2i−2i2iii−i−i00-113−33−30000000000000000i−ii3−i3i3−i3000000
χ372-22-222-2-2-22002-22-12-211-1-200-11-112-2−33−33-112i−2i2i−2i−i−iii00-11−33−330000000000000000−iii3−i3i3−i3000000
χ382-22-222-2-2-22002-22-12-211-1-200-11-112-2−33−33-11−2i2i−2i2iii−i−i00-11−33−330000000000000000i−i−i3i3−i3i3000000
χ392-22-22-22-2-2200-22222-2-2-22-2002-22-2-220000-222i−2i−2i2i2i2i−2i−2i00-2200000000000000000000−2i2i0000000000
χ402-22-22-22-2-2200-22222-2-2-22-2002-22-2-220000-22−2i2i2i−2i−2i−2i2i2i00-22000000000000000000002i−2i0000000000
χ412-22-22-22-2-2200-222-12-211-1-200-11-11-223−3−331-12i−2i−2i2i−i−iii001-13−3−330000000000000000i−i−i3i3i3−i3000000
χ422-22-22-22-2-2200-222-12-211-1-200-11-11-223−3−331-1−2i2i2i−2iii−i−i001-13−3−330000000000000000−iii3−i3−i3i3000000
χ432-22-22-22-2-2200-222-12-211-1-200-11-11-22−333−31-12i−2i−2i2i−i−iii001-1−333−30000000000000000i−ii3−i3−i3i3000000
χ442-22-22-22-2-2200-222-12-211-1-200-11-11-22−333−31-1−2i2i2i−2iii−i−i001-1−333−30000000000000000−ii−i3i3i3−i3000000
χ4544444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41111-2-22222-2-2000000002211-1-1-1-10000000000000000000000000000
χ4744444-4-44444-4-4-4-2-2-2-2-2-2-2-24-4111122-2-2222200000000-22-1-111-1-10000000000000000000000000000
χ4844444-4-4444-44-4-4-2-2-2-2-2-2-2-2-4411112222-2-222000000002-2-1-1-1-1110000000000000000000000000000
χ4944-4-44004-4-4000044-444-4-4-40044-4-40000000000000000000000000000000000000000000000000000
χ5044-4-44004-4-400004-2-44-222-400-2-222000000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ5144-4-44004-4-400004-2-44-222-400-2-2220000000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ5244-4-44004-4-40000-242-24-4-4200-2-22200000000000000000000000000000000000000−2i32i3000000000000
χ5344-4-44004-4-40000-242-24-4-4200-2-222000000000000000000000000000000000000002i3−2i3000000000000
χ544-44-444-4-4-44004-4-24-22-4-44200-22-22-2200004-40000000000-2200000000000000000000000000000000
χ554-44-444-4-4-44004-4-2-2-2222-22001-11-1-2223−2323−23-2200000000001-1−33−330000000000000000000000000000
χ564-44-444-4-4-44004-4-2-2-2222-22001-11-1-22−2323−2323-2200000000001-13−33−30000000000000000000000000000
χ574-44-44-44-4-4400-44-24-22-4-44200-22-222-20000-4400000000002-200000000000000000000000000000000
χ584-44-44-44-4-4400-44-2-2-2222-22001-11-12-223−23−23232-20000000000-11−333−30000000000000000000000000000
χ594-44-44-44-4-4400-44-2-2-2222-22001-11-12-2−232323−232-20000000000-113−3−330000000000000000000000000000
χ604-4-44400-44-4000044-4-4-44-44004-4-440000000000000000000000000000000000000000000000000000
χ614-4-44400-44-400004-2-4-42-22400-222-200000000000023−23−2323000000000000000000000000000000000000
χ624-4-44400-44-400004-2-4-42-22400-222-2000000000000−232323−23000000000000000000000000000000000000
χ634-4-44400-44-40000-2422-44-4-200-222-20000000000000000000000000000000000000000000000−2i32i30000
χ644-4-44400-44-40000-2422-44-4-200-222-200000000000000000000000000000000000000000000002i3−2i30000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000002220002000-1-1-1-10000000000-1-100
χ666666-366-3-3-366-3-300000000-3-30000000000000000000000000000-2-2-2000-2000111100000000001100
χ676666-366-3-3-3-6-6-3-30000000033000000000000000000000000000022-2000-200011110000000000-1-100
χ686666-366-3-3-3-6-6-3-300000000330000000000000000000000000000-2-220002000-1-1-1-100000000001100
χ696666-3-6-6-3-3-36-63300000000-3300000000000000000000000000002-22000-2000-1-1110000000000-1100
χ706666-3-6-6-3-3-36-63300000000-330000000000000000000000000000-22-2000200011-1-100000000001-100
χ716666-3-6-6-3-3-3-6633000000003-300000000000000000000000000002-2-2000200011-1-10000000000-1100
χ726666-3-6-6-3-3-3-6633000000003-30000000000000000000000000000-222000-2000-1-11100000000001-100
χ7388-8-88008-8-80000-4-44-4-44440022-2-20000000000000000000000000000000000000000000000000000
χ748-8-88800-88-80000-4-4444-44-4002-2-220000000000000000000000000000000000000000000000000000
χ751212-12-12-600-66600000000000000000000000000000000000000000000000000000023−2300000000000000
χ761212-12-12-600-666000000000000000000000000000000000000000000000000000000−232300000000000000
χ7712-1212-12-612-1266-600-66000000000000000000000000000000000000000000000000000000000000000000
χ7812-1212-12-6-121266-6006-6000000000000000000000000000000000000000000000000000000000000000000
χ7912-12-1212-6006-660000000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ8012-12-1212-6006-6600000000000000000000000000000000000000000000000000002i3−2i30000000000000000

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