Finite Group Databasebeta

← Group #13151496

Character table — Group #13151496

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order1222344666221212336666666636666666121212124444121212126666661212222444444466121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
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
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111-1-11111111111-1-11-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-11-1-1-1-1111111111111111-1-1-1-1-1-111-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1
χ71111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-111
χ911111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-111-1-111111-111-1-1-1-11-11-11-11-11-111-1-1-1-111-1-111-1-11-11-1
χ1011111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-111-1-111111-111-1-1-1-1-11-111-1-11-11-1-111-1-1-1-11111-1-1-11-11
χ1111111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-1-1-111-1-1-1-11-111-1-1-1-11-1-11-111-1-11-1-1111111-1-1-1-1111-1-11
χ1211111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-1-1-111-1-1-1-11-111-1-1-1-1-111-1-11-111-111-1-111-1-111-1-111-111-1
χ1311111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-11111-11-1-111-1-11-1-11-11-111-1-1-111-1-1-1-111-1-1111-11-1
χ1411111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-11111-11-1-111-1-1-111-1-111-1-1111-1-1-1-111-1-1-1-111-11-11
χ1511111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-11-11-11-1-11-1111-1-111-1-11111-1-11-1-11
χ1611111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1-11-111-11-11-1-1-1111111-1-111-1-1-111-1
χ17222222222222222-12-12-1-1222-12222-1-1-122-1-100000000-1-1-1-1-1-1-1-12200002200000000-1-1-1-10000-1-100
χ18222222222222222-12-12-1-1222-12222-1-1-122-1-100000000-1-1-1-1-1-1-1-1-2-20000-2-200000000111100001100
χ1922222222222222-12-12-122-122-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-100002200000000-1-10000-1-1-1-10000
χ2022222222222222-12-12-122-122-1-1-1-1-1-1-1-1-1-122-2-2-2-2111122-1-1-1-1-1-10000-2-20000000011000011110000
χ212222222222-2-2222-12-12-1-12-2-2-1-2-2-2-2-1-1-122-1-100000000111111-1-1220000-2-20000000011110000-1-100
χ222222222222-2-2222-12-12-1-12-2-2-1-2-2-2-2-1-1-122-1-100000000111111-1-1-2-200002200000000-1-1-1-100001100
χ232222222222-2-222-12-12-122-1-2-2-11111-1-1-1-1-1222222-1-1-1-1-2-21111-1-10000-2-200000000-1-1000011110000
χ242222222222-2-222-12-12-122-1-2-2-11111-1-1-1-1-122-2-2-2-21111-2-21111-1-100002200000000110000-1-1-1-10000
χ2522222-2-22222-2-2-22-12-12-1-122-2-122-2-2-1-1-1-2-21100000000-11-1-111112-200002-200000000-1-1110000-1100
χ2622222-2-22222-2-2-22-12-12-1-122-2-122-2-2-1-1-1-2-21100000000-11-1-11111-220000-220000000011-1-100001-100
χ2722222-2-22222-2-2-2-12-12-122-12-2-1-1-111-1-1-111-2-222-2-2-1-1-1-12-2-1-1111100002-200000000110000-1-1110000
χ2822222-2-22222-2-2-2-12-12-122-12-2-1-1-111-1-1-111-2-2-2-22211112-2-1-111110000-2200000000-1-1000011-1-10000
χ2922222-2-2222-22-2-22-12-12-1-12-22-1-2-222-1-1-1-2-211000000001-111-1-1112-20000-220000000011-1-10000-1100
χ3022222-2-2222-22-2-22-12-12-1-12-22-1-2-222-1-1-1-2-211000000001-111-1-111-2200002-200000000-1-11100001-100
χ3122222-2-2222-22-2-2-12-12-122-1-22-111-1-1-1-1-111-2-222-2-2-1-1-1-1-2211-1-1110000-220000000011000011-1-10000
χ3222222-2-2222-22-2-2-12-12-122-1-22-111-1-1-1-1-111-2-2-2-2221111-2211-1-11100002-200000000-1-10000-1-1110000
χ3322-2-222-2-22-2002-22222-2-2-2-20020000-2-222-22-22i−2i2i−2i2i2i−2i−2i0000002-2000000000000002i−2i000000000000
χ3422-2-222-2-22-2002-22222-2-2-2-20020000-2-222-22-2−2i2i−2i2i−2i−2i2i2i0000002-200000000000000−2i2i000000000000
χ3522-2-222-2-22-2002-2-12-121-2-2100-1−i3i3−i3i311-1-112-22i−2i2i−2i−i−iii00−i3i3−i3i3-1100000000000000−ii00003−33−30000
χ3622-2-222-2-22-2002-2-12-121-2-2100-1−i3i3−i3i311-1-112-2−2i2i−2i2iii−i−i00−i3i3−i3i3-1100000000000000i−i0000−33−330000
χ3722-2-222-2-22-2002-2-12-121-2-2100-1i3−i3i3−i311-1-112-22i−2i2i−2i−i−iii00i3−i3i3−i3-1100000000000000−ii0000−33−330000
χ3822-2-222-2-22-2002-2-12-121-2-2100-1i3−i3i3−i311-1-112-2−2i2i−2i2iii−i−i00i3−i3i3−i3-1100000000000000i−i00003−33−30000
χ3922-2-22-22-22-200-222222-2-2-2-20020000-2-22-22-222i−2i−2i2i2i2i−2i−2i000000-2200000000000000−2i2i000000000000
χ4022-2-22-22-22-200-222222-2-2-2-20020000-2-22-22-22−2i2i2i−2i−2i−2i2i2i000000-22000000000000002i−2i000000000000
χ4122-2-22-22-22-200-22-12-121-2-2100-1−i3i3i3−i311-11-1-222i−2i−2i2i−i−iii00−i3i3i3−i31-100000000000000i−i00003−3−330000
χ4222-2-22-22-22-200-22-12-121-2-2100-1−i3i3i3−i311-11-1-22−2i2i2i−2iii−i−i00−i3i3i3−i31-100000000000000−ii0000−333−30000
χ4322-2-22-22-22-200-22-12-121-2-2100-1i3−i3−i3i311-11-1-222i−2i−2i2i−i−iii00i3−i3−i3i31-100000000000000i−i0000−333−30000
χ4422-2-22-22-22-200-22-12-121-2-2100-1i3−i3−i3i311-11-1-22−2i2i2i−2iii−i−i00i3−i3−i3i31-100000000000000−ii00003−3−330000
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
χ4744444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-222111222200000000-2211-1-1-1-10000000000000000000000000000
χ4844444-4-4444-44-4-4-2-2-2-2-2-2-2-2-44122-2-21112222000000002-2-1-111-1-10000000000000000000000000000
χ4944-4-444-4-44-4004-44-24-2-422-400-2000022-24-4-2200000000000000-220000000000000000000000000000
χ5044-4-444-4-44-4004-4-2-2-2-22222001−2i32i3−2i32i3-1-11-22-220000000000i3−i3i3−i31-10000000000000000000000000000
χ5144-4-444-4-44-4004-4-2-2-2-222220012i3−2i32i3−2i3-1-11-22-220000000000−i3i3−i3i31-10000000000000000000000000000
χ5244-4-44-44-44-400-444-24-2-422-400-2000022-2-442-2000000000000002-20000000000000000000000000000
χ5344-4-44-44-44-400-44-2-2-2-22222001−2i32i32i3−2i3-1-112-22-20000000000i3−i3−i3i3-110000000000000000000000000000
χ5444-4-44-44-44-400-44-2-2-2-222220012i3−2i3−2i32i3-1-112-22-20000000000−i3i3i3−i3-110000000000000000000000000000
χ554-44-44004-4-4000044-4-4-44-4400400004-4-4000000000000000000000000000000000000000000000000
χ564-44-44004-4-400004-2-42-4-22400-20000-22200000000000000000000000000000000000000−2i32i300000000
χ574-44-44004-4-400004-2-42-4-22400-20000-222000000000000000000000000000000000000002i3−2i300000000
χ584-44-44004-4-40000-242-424-4-200-20000-22200000000−2i32i3−2i32i3000000000000000000000000000000000000
χ594-44-44004-4-40000-242-424-4-200-20000-222000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ604-4-44400-4-44000044-4-44-44-40040000-44-4000000000000000000000000000000000000000000000000
χ614-4-44400-4-4400004-2-4242-2-400-200002-22000000000000000000000000000000000000−2i32i30000000000
χ624-4-44400-4-4400004-2-4242-2-400-200002-220000000000000000000000000000000000002i3−2i30000000000
χ634-4-44400-4-440000-242-4-2-44200-200002-220000000023−23−2323000000000000000000000000000000000000
χ644-4-44400-4-440000-242-4-2-44200-200002-2200000000−232323−23000000000000000000000000000000000000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000000022000022-1-1-1-1000000000000-1-1
χ666666-366-3-3-366-3-300000000-3-3000000000000000000000000000000-2-20000-2-2111100000000000011
χ676666-366-3-3-3-6-6-3-30000000033000000000000000000000000000000220000-2-2-1-1-1-100000000000011
χ686666-366-3-3-3-6-6-3-30000000033000000000000000000000000000000-2-20000221111000000000000-1-1
χ696666-3-6-6-3-3-36-63300000000-330000000000000000000000000000002-200002-2-1-111000000000000-11
χ706666-3-6-6-3-3-36-63300000000-33000000000000000000000000000000-220000-2211-1-10000000000001-1
χ716666-3-6-6-3-3-3-6633000000003-30000000000000000000000000000002-20000-22-1-1110000000000001-1
χ726666-3-6-6-3-3-3-6633000000003-3000000000000000000000000000000-2200002-211-1-1000000000000-11
χ738-88-88008-8-80000-4-4444-44-400200002-2-2000000000000000000000000000000000000000000000000
χ748-8-88800-8-880000-4-444-44-440020000-22-2000000000000000000000000000000000000000000000000
χ751212-12-12-612-126-6600-66000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-6-12126-66006-6000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212-12-600-66600000000000000000000000000000000000000000000000000000023−2300000000000000
χ7812-1212-12-600-666000000000000000000000000000000000000000000000000000000−232300000000000000
χ7912-12-1212-60066-60000000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ8012-12-1212-60066-600000000000000000000000000000000000000000000000000002i3−2i30000000000000000

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