Finite Group Databasebeta

← Group #13148473

Character table — Group #13148473

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order122222366644661212121233666666444436666666444444444412121212661212121212121212444444121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-11
χ51111111111-1-111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-11-11
χ81111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111-11-1
χ91111-1-111111-1-1-111-1-11111111111111-1-1-1-1111-1-111-1-111-1-11111-1-11-11-111-1-11-11-11-111-1-1-1-111-1-111-1-111-1-1
χ101111-1-111111-1-1-111-1-11111111111111-1-1-1-1111-1-1-1-111-1-1111111-1-11-11-111-1-11-1-11-1111-1-1-1-1-1-111-1-111-1-111
χ111111-1-111111-1-1-111-1-111111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11-11-111-1-1-111-1-11-1-1111111-1-1-1-1111-1-11
χ121111-1-111111-1-1-111-1-111111111-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1-1-1-11-11-111-1-1-11-111-1-1-11111-1-11111-1-1-111-1
χ131111-1-11111-11-1-1-1-1111111111111111-1-1-1-1111-1-111-1-111-1-11111-1-1-11-11-1-111-11-11-11-1-111-1-111-1-111-1-1-1-111
χ141111-1-11111-11-1-1-1-1111111111111111-1-1-1-1111-1-1-1-111-1-1111111-1-1-11-11-1-111-111-11-1-1-111-1-1-1-111-1-11111-1-1
χ151111-1-11111-11-1-1-1-11111111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-11-11-1-1111-1-111-111-1-11111-1-1-1-111-111-1
χ161111-1-11111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-11-11-1-1111-11-1-1111-1-111-1-11111-1-11-1-11
χ172222222222222222222-12-12-12-10000-122-1-1-1-1-100000022220000-1-12-1-12-1-1-1-10000220000000000-1-1-1-10-10-1
χ182222222222222222222-12-12-12-10000-122-1-1-1-1-1000000-2-2-2-20000-1-12-1-12-1-1-1-10000-2-2000000000011110101
χ19222222222222222222-12-12-12-120000-1-1-122-1-1-100222200000000-1-1-122-1-1-1-1-1002200000000-1-1-1-10000-10-10
χ20222222222222222222-12-12-12-120000-1-1-122-1-1-100-2-2-2-200000000-1-1-122-1-1-1-1-100-2-200000000111100001010
χ212222222222-2-222-2-2-2-22-12-12-12-10000-122-1-1-1-1-100000022220000-1-1-211-211110000-2-20000000000-1-1-1-10101
χ222222222222-2-222-2-2-2-22-12-12-12-10000-122-1-1-1-1-1000000-2-2-2-20000-1-1-211-21111000022000000000011110-10-1
χ232222222222-2-222-2-2-2-2-12-12-12-120000-1-1-122-1-1-100222200000000-1-11-2-21111100-2-200000000-1-1-1-100001010
χ242222222222-2-222-2-2-2-2-12-12-12-120000-1-1-122-1-1-100-2-2-2-200000000-1-11-2-21111100220000000011110000-10-10
χ252222-2-222222-2-2-222-2-22-12-12-12-10000-1-2-211-1-1-100000022-2-200001121-1-2-1-11100002-20000000000-1-1110-101
χ262222-2-222222-2-2-222-2-22-12-12-12-10000-1-2-211-1-1-1000000-2-22200001121-1-2-1-1110000-22000000000011-1-1010-1
χ272222-2-222222-2-2-222-2-2-12-12-12-120000-111-2-2-1-1-10022-2-20000000011-1-221-1-111002-200000000-1-1110000-1010
χ282222-2-222222-2-2-222-2-2-12-12-12-120000-111-2-2-1-1-100-2-2220000000011-1-221-1-11100-220000000011-1-1000010-10
χ292222-2-22222-22-2-2-2-2222-12-12-12-10000-1-2-211-1-1-100000022-2-2000011-2-11211-1-10000-220000000000-1-111010-1
χ302222-2-22222-22-2-2-2-2222-12-12-12-10000-1-2-211-1-1-1000000-2-222000011-2-11211-1-100002-2000000000011-1-10-101
χ312222-2-22222-22-2-2-2-222-12-12-12-120000-111-2-2-1-1-10022-2-2000000001112-2-111-1-100-2200000000-1-111000010-10
χ322222-2-22222-22-2-2-2-222-12-12-12-120000-111-2-2-1-1-100-2-222000000001112-2-111-1-1002-20000000011-1-10000-1010
χ3322-2-22-22-2-22002-200002222-2-2-2-222-2-222-22-22-2-22-20000000022-2-22-20000000000000000002-2000000000000
χ3422-2-22-22-2-22002-200002222-2-2-2-2-2-22222-22-22-2-2-2200000000-2-2222-2000000000000000000-22000000000000
χ3522-2-2-222-2-2200-2200002222-2-2-2-222-2-22-22-222-2-2-220000000022-2-2-22000000000000000000-22000000000000
χ3622-2-2-222-2-2200-2200002222-2-2-2-2-2-2222-22-222-2-22-200000000-2-222-220000000000000000002-2000000000000
χ372-22-20022-2-20000000022-2-22-2-222i−2i2i−2i20000-22-200002i−2i002-22i−2i2i−2i0000000000000000000000002i−2i002-20000
χ382-22-20022-2-20000000022-2-22-2-222i−2i2i−2i20000-22-20000−2i2i00-222i−2i2i−2i000000000000000000000000−2i2i00-220000
χ392-22-20022-2-20000000022-2-22-2-22−2i2i−2i2i20000-22-200002i−2i00-22−2i2i−2i2i0000000000000000000000002i−2i00-220000
χ402-22-20022-2-20000000022-2-22-2-22−2i2i−2i2i20000-22-20000−2i2i002-2−2i2i−2i2i000000000000000000000000−2i2i002-20000
χ412-2-22002-22-20000000022-2-2-222-22i−2i−2i2i20000-2-22002-2002i−2i002i−2i−2i2i00000000000000000000002-2002i−2i000000
χ422-2-22002-22-20000000022-2-2-222-22i−2i−2i2i20000-2-2200-2200−2i2i002i−2i−2i2i0000000000000000000000-2200−2i2i000000
χ432-2-22002-22-20000000022-2-2-222-2−2i2i2i−2i20000-2-22002-200−2i2i00−2i2i2i−2i00000000000000000000002-200−2i2i000000
χ442-2-22002-22-20000000022-2-2-222-2−2i2i2i−2i20000-2-2200-22002i−2i00−2i2i2i−2i0000000000000000000000-22002i−2i000000
χ45444444444444444444-2-2-2-2-2-2-2-200001-2-2-2-21110000000000000011-2-2-2-21111000000000000000000000000
χ464444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-200001-2-2-2-211100000000000000112222-1-1-1-1000000000000000000000000
χ474444-4-444444-4-4-444-4-4-2-2-2-2-2-2-2-200001222211100000000000000-1-1-22-2211-1-1000000000000000000000000
χ484444-4-44444-44-4-4-4-444-2-2-2-2-2-2-2-200001222211100000000000000-1-12-22-2-1-111000000000000000000000000
χ4944-4-44-44-4-44004-400004-24-2-42-420000-24-4-22-22200000000000000-2200000000000000000000000000000000
χ5044-4-44-44-4-44004-40000-24-242-42-40000-2-224-4-22200000000000000-2200000000000000000000000000000000
χ5144-4-44-44-4-44004-40000-2-2-2-2222200001-22-221-1-1000000000000001-100003i−3i3i−3i000000000000000000000000
χ5244-4-44-44-4-44004-40000-2-2-2-2222200001-22-221-1-1000000000000001-10000−3i3i−3i3i000000000000000000000000
χ5344-4-4-444-4-4400-4400004-24-2-42-420000-2-442-2-222000000000000002-200000000000000000000000000000000
χ5444-4-4-444-4-4400-440000-24-242-42-40000-22-2-44-222000000000000002-200000000000000000000000000000000
χ5544-4-4-444-4-4400-440000-2-2-2-22222000012-22-21-1-100000000000000-1100003i−3i−3i3i000000000000000000000000
χ5644-4-4-444-4-4400-440000-2-2-2-22222000012-22-21-1-100000000000000-110000−3i3i3i−3i000000000000000000000000
χ574-44-40044-4-4000000004-2-4242-4-20000-200002-22000000004-400000000000000000000000000000000-220000
χ584-44-40044-4-4000000004-2-4242-4-20000-200002-2200000000-44000000000000000000000000000000002-20000
χ594-44-40044-4-400000000-242-4-2-4240000-200002-2200004i−4i00000000000000000000000000000000−2i2i00000000
χ604-44-40044-4-400000000-242-4-2-4240000-200002-220000−4i4i000000000000000000000000000000002i−2i00000000
χ614-4-44004-44-4000000004-2-42-4-2420000-2000022-20000004i−4i00000000000000000000000000000000−2i2i000000
χ624-4-44004-44-4000000004-2-42-4-2420000-2000022-2000000−4i4i000000000000000000000000000000002i−2i000000
χ634-4-44004-44-400000000-242-424-2-40000-2000022-2004-400000000000000000000000000000000-220000000000
χ644-4-44004-44-400000000-242-424-2-40000-2000022-200-44000000000000000000000000000000002-20000000000
χ65666666-3-3-3-366-3-3-3-3-3-3000000002222000000002200000000-1-1-1-10000000000220000-1-1-1-1-1-1000000000000
χ66666666-3-3-3-366-3-3-3-3-3-300000000-2-2-2-200000000-2-20000000011110000000000-2-20000111111000000000000
χ67666666-3-3-3-3-6-6-3-33333000000002222000000002200000000-1-1-1-10000000000-2-200001111-1-1000000000000
χ68666666-3-3-3-3-6-6-3-3333300000000-2-2-2-200000000-2-20000000011110000000000220000-1-1-1-111000000000000
χ696666-6-6-3-3-3-36-633-3-33300000000222200000000-2-200000000-1-1-1-100000000002-20000-1-11111000000000000
χ706666-6-6-3-3-3-36-633-3-33300000000-2-2-2-200000000220000000011110000000000-22000011-1-1-1-1000000000000
χ716666-6-6-3-3-3-3-663333-3-300000000222200000000-2-200000000-1-1-1-10000000000-22000011-1-111000000000000
χ726666-6-6-3-3-3-3-663333-3-300000000-2-2-2-2000000002200000000111100000000002-20000-1-111-1-1000000000000
χ7366-6-66-6-333-300-3333−3333−330000000022-2-2000000002-200000000-1-11100000000000000003−33−3-11000000000000
χ7466-6-66-6-333-300-3333−3333−3300000000-2-22200000000-220000000011-1-10000000000000000−33−331-1000000000000
χ7566-6-66-6-333-300-33−3333−33330000000022-2-2000000002-200000000-1-1110000000000000000−33−33-11000000000000
χ7666-6-66-6-333-300-33−3333−333300000000-2-22200000000-220000000011-1-100000000000000003−33−31-1000000000000
χ7766-6-6-66-333-3003-333−33−33330000000022-2-200000000-2200000000-1-11100000000000000003−3−331-1000000000000
χ7866-6-6-66-333-3003-333−33−333300000000-2-222000000002-20000000011-1-10000000000000000−333−3-11000000000000
χ7966-6-6-66-333-3003-3−333333−330000000022-2-200000000-2200000000-1-1110000000000000000−333−31-1000000000000
χ8066-6-6-66-333-3003-3−333333−3300000000-2-222000000002-20000000011-1-100000000000000003−3−33-11000000000000
χ818-88-80088-8-800000000-4-444-444-4000020000-22-2000000000000000000000000000000000000000000000000
χ828-8-88008-88-800000000-4-4444-4-44000020000-2-22000000000000000000000000000000000000000000000000
χ8312-1212-1200-6-66600000000000000004i−4i4i−4i000000000000000000−2i2i−2i2i0000000000000000000000000000000000
χ8412-1212-1200-6-6660000000000000000−4i4i−4i4i0000000000000000002i−2i2i−2i0000000000000000000000000000000000
χ8512-12-121200-66-6600000000000000004i−4i−4i4i000000000000000000−2i2i2i−2i0000000000000000000000000000000000
χ8612-12-121200-66-660000000000000000−4i4i4i−4i0000000000000000002i−2i−2i2i0000000000000000000000000000000000

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