Finite Group Databasebeta

← Group #13151317

Character table — Group #13151317

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order12222236662466661212336666664444366666664444444444121212126666661212121224444412121212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ51111111111-1-111-1-1-1-11111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ61111111111-1-111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111-1-11
χ81111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-111-1
χ91111-1-111111-1-1-111-1-11111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-111-1-1-1-11-11-11-1-1-1-1-11111-1-111-1-111-1-1
χ101111-1-111111-1-1-111-1-11111111111111-1-1-1-1111-1-111-1-1-1-111111111-1-111-1-1-1-1-111-1-11-1-1-1-111-1-111-1-111-1-111
χ111111-1-111111-1-1-111-1-111111111-1-1-1-11-1-1-1-111111-1-111-1-111-1-1-1-111-1-111-1-1-1-1-11-111-11111-1-1-1-11111-1-1-11-11
χ121111-1-111111-1-1-111-1-111111111-1-1-1-11-1-1-1-1111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11-1-11-111111-1-111-1-1-1-1111-11-1
χ131111-1-11111-11-1-1-1-1111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-11111-11-11-1111-1-1-1-111-1-111-1-1-1-111
χ141111-1-11111-11-1-1-1-1111111111111111-1-1-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-111111-1-111-111-1-1-1-1-1-111-1-11111-1-1
χ151111-1-11111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-11111-1-11111-1-11-11-1
χ161111-1-11111-11-1-1-1-11111111111-1-1-1-11-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-11-1-1-1111111-1-1-1-111-11-11
χ172222222222222222222-1-122-1-120000-122-1-1-1-1-1000000222200002-1-1-1-1-1-12-1-1220000000000-1-1-1-10000-100-1
χ182222222222222222222-1-122-1-120000-122-1-1-1-1-1000000-2-2-2-200002-1-1-1-1-1-12-1-1-2-20000000000111100001001
χ19222222222222222222-122-1-122-10000-1-1-122-1-1-122220000000000-12-1-1-1-12-1-1-10000220000000000-1-1-1-10-1-10
χ20222222222222222222-122-1-122-10000-1-1-122-1-1-1-2-2-2-20000000000-12-1-1-1-12-1-1-10000-2-2000000000011110110
χ212222222222-2-222-2-2-2-22-1-122-1-120000-122-1-1-1-1-100000022220000-21-1-1111-211-2-20000000000-1-1-1-100001001
χ222222222222-2-222-2-2-2-22-1-122-1-120000-122-1-1-1-1-1000000-2-2-2-20000-21-1-1111-21122000000000011110000-100-1
χ232222222222-2-222-2-2-2-2-122-1-122-10000-1-1-122-1-1-1222200000000001-2-1-111-21110000-2-20000000000-1-1-1-10110
χ242222222222-2-222-2-2-2-2-122-1-122-10000-1-1-122-1-1-1-2-2-2-200000000001-2-1-111-2111000022000000000011110-1-10
χ252222-2-222222-2-2-222-2-22-1-122-1-120000-1-2-211-1-1-100000022-2-200002-111-1-11-2112-20000000000-1-1110000-1001
χ262222-2-222222-2-2-222-2-22-1-122-1-120000-1-2-211-1-1-1000000-2-22200002-111-1-11-211-22000000000011-1-10000100-1
χ272222-2-222222-2-2-222-2-2-122-1-122-10000-111-2-2-1-1-122-2-20000000000-1211-1-1-211100002-20000000000-1-1110-110
χ282222-2-222222-2-2-222-2-2-122-1-122-10000-111-2-2-1-1-1-2-2220000000000-1211-1-1-21110000-22000000000011-1-101-10
χ292222-2-22222-22-2-2-2-2222-1-122-1-120000-1-2-211-1-1-100000022-2-20000-211111-12-1-1-220000000000-1-1110000100-1
χ302222-2-22222-22-2-2-2-2222-1-122-1-120000-1-2-211-1-1-1000000-2-2220000-211111-12-1-12-2000000000011-1-10000-1001
χ312222-2-22222-22-2-2-2-222-122-1-122-10000-111-2-2-1-1-122-2-200000000001-211112-1-1-10000-220000000000-1-11101-10
χ322222-2-22222-22-2-2-2-222-122-1-122-10000-111-2-2-1-1-1-2-22200000000001-211112-1-1-100002-2000000000011-1-10-110
χ3322-2-22-222-2-2002-2000022-2-2-22-222i2i−2i−2i22-22-2-2-2200002i−2i00002i2i−2i−2i002-2000000000000002i−2i00000000000000
χ3422-2-22-222-2-2002-2000022-2-2-22-22−2i−2i2i2i22-22-2-2-220000−2i2i0000−2i−2i2i2i002-200000000000000−2i2i00000000000000
χ3522-2-2-2222-2-200-22000022-2-2-22-222i2i−2i−2i2-22-22-2-220000−2i2i00002i2i−2i−2i00-2200000000000000−2i2i00000000000000
χ3622-2-2-2222-2-200-22000022-2-2-22-22−2i−2i2i2i2-22-22-2-2200002i−2i0000−2i−2i2i2i00-22000000000000002i−2i00000000000000
χ372-22-2002-22-20000000022-22-2-22-22i−2i2i−2i200002-2-22i−2i00002-2002i−2i2i−2i00000000000000000000002-2002i−2i000000
χ382-22-2002-22-20000000022-22-2-22-22i−2i2i−2i200002-2-2−2i2i0000-22002i−2i2i−2i0000000000000000000000-2200−2i2i000000
χ392-22-2002-22-20000000022-22-2-22-2−2i2i−2i2i200002-2-22i−2i0000-2200−2i2i−2i2i0000000000000000000000-22002i−2i000000
χ402-22-2002-22-20000000022-22-2-22-2−2i2i−2i2i200002-2-2−2i2i00002-200−2i2i−2i2i00000000000000000000002-200−2i2i000000
χ412-2-22002-2-2200000000222-22-2-2-22-2-2220000-22-2002i−2i00002i−2i2-2-220000000000000000000000002i−2i002i−2i0000
χ422-2-22002-2-2200000000222-22-2-2-22-2-2220000-22-200−2i2i0000−2i2i2-2-22000000000000000000000000−2i2i00−2i2i0000
χ432-2-22002-2-2200000000222-22-2-2-2-222-220000-22-2002i−2i0000−2i2i-222-2000000000000000000000000−2i2i002i−2i0000
χ442-2-22002-2-2200000000222-22-2-2-2-222-220000-22-200−2i2i00002i−2i-222-20000000000000000000000002i−2i00−2i2i0000
χ45444444444444444444-2-2-2-2-2-2-2-200001-2-2-2-211100000000000000-2-21111-2-211000000000000000000000000
χ464444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-200001-2-2-2-2111000000000000002211-1-122-1-1000000000000000000000000
χ474444-4-444444-4-4-444-4-4-2-2-2-2-2-2-2-200001222211100000000000000-2-2-1-11122-1-1000000000000000000000000
χ484444-4-44444-44-4-4-4-444-2-2-2-2-2-2-2-20000122221110000000000000022-1-1-1-1-2-211000000000000000000000000
χ4944-4-44-444-4-4004-400004-22-4-4-2240000-24-4-2222-20000000000000000-22000000000000000000000000000000
χ5044-4-44-444-4-4004-40000-24-4224-4-20000-2-224-422-20000000000000000-22000000000000000000000000000000
χ5144-4-44-444-4-4004-40000-2-2222-22-200001-22-22-1-1100000000000000001-13-3003-3000000000000000000000000
χ5244-4-44-444-4-4004-40000-2-2222-22-200001-22-22-1-1100000000000000001-1-3300-33000000000000000000000000
χ5344-4-4-4444-4-400-4400004-22-4-4-2240000-2-442-222-200000000000000002-2000000000000000000000000000000
χ5444-4-4-4444-4-400-440000-24-4224-4-20000-22-2-4422-200000000000000002-2000000000000000000000000000000
χ5544-4-4-4444-4-400-440000-2-2222-22-2000012-22-2-1-110000000000000000-113-300-33000000000000000000000000
χ5644-4-4-4444-4-400-440000-2-2222-22-2000012-22-2-1-110000000000000000-11-33003-3000000000000000000000000
χ574-44-4004-44-4000000004-224-42-2-40000-20000-2220000004-40000000000000000000000000000-220000000000
χ584-44-4004-44-4000000004-224-42-2-40000-20000-222000000-4400000000000000000000000000002-20000000000
χ594-44-4004-44-400000000-24-4-22-4420000-20000-2224i−4i00000000000000000000000000000000000000−2i2i000000
χ604-44-4004-44-400000000-24-4-22-4420000-20000-222−4i4i000000000000000000000000000000000000002i−2i000000
χ614-4-44004-4-44000000004-2-2-4422-40000-200002-22000000004i−4i0000000000000000000000000000−2i2i00000000
χ624-4-44004-4-44000000004-2-2-4422-40000-200002-2200000000−4i4i00000000000000000000000000002i−2i00000000
χ634-4-44004-4-4400000000-2442-2-4-420000-200002-22004i−4i00000000000000000000000000000000000000−2i2i0000
χ644-4-44004-4-4400000000-2442-2-4-420000-200002-2200−4i4i000000000000000000000000000000000000002i−2i0000
χ65666666-3-3-3-366-3-3-3-3-3-3000000002222000000000000220000-1-1-1-10000000000002200-1-1-1-1-1-1000000000000
χ66666666-3-3-3-366-3-3-3-3-3-300000000-2-2-2-2000000000000-2-200001111000000000000-2-200111111000000000000
χ67666666-3-3-3-3-6-6-3-33333000000002222000000000000220000-1-1-1-1000000000000-2-20011-1-111000000000000
χ68666666-3-3-3-3-6-6-3-3333300000000-2-2-2-2000000000000-2-2000011110000000000002200-1-111-1-1000000000000
χ696666-6-6-3-3-3-36-633-3-333000000002222000000000000-2-20000-1-1-1-10000000000002-2001111-1-1000000000000
χ706666-6-6-3-3-3-36-633-3-33300000000-2-2-2-20000000000002200001111000000000000-2200-1-1-1-111000000000000
χ716666-6-6-3-3-3-3-663333-3-3000000002222000000000000-2-20000-1-1-1-1000000000000-2200-1-11111000000000000
χ726666-6-6-3-3-3-3-663333-3-300000000-2-2-2-200000000000022000011110000000000002-20011-1-1-1-1000000000000
χ7366-6-66-6-3-33300-33−3i33i3−3i33i3000000002i2i−2i−2i0000000000002i−2i0000−i−iii00000000000000003−3−ii3−3000000000000
χ7466-6-66-6-3-33300-33−3i33i3−3i33i300000000−2i−2i2i2i000000000000−2i2i0000ii−i−i0000000000000000−33i−i−33000000000000
χ7566-6-66-6-3-33300-333i3−3i33i3−3i3000000002i2i−2i−2i0000000000002i−2i0000−i−iii0000000000000000−33−ii−33000000000000
χ7666-6-66-6-3-33300-333i3−3i33i3−3i300000000−2i−2i2i2i000000000000−2i2i0000ii−i−i00000000000000003−3i−i3−3000000000000
χ7766-6-6-66-3-333003-3−3i33i33i3−3i3000000002i2i−2i−2i000000000000−2i2i0000−i−iii0000000000000000−33i−i3−3000000000000
χ7866-6-6-66-3-333003-3−3i33i33i3−3i300000000−2i−2i2i2i0000000000002i−2i0000ii−i−i00000000000000003−3−ii−33000000000000
χ7966-6-6-66-3-333003-33i3−3i3−3i33i3000000002i2i−2i−2i000000000000−2i2i0000−i−iii00000000000000003−3i−i−33000000000000
χ8066-6-6-66-3-333003-33i3−3i3−3i33i300000000−2i−2i2i2i0000000000002i−2i0000ii−i−i0000000000000000−33−ii3−3000000000000
χ818-88-8008-88-800000000-4-44-444-440000200002-2-2000000000000000000000000000000000000000000000000
χ828-8-88008-8-8800000000-4-4-44-4444000020000-22-2000000000000000000000000000000000000000000000000
χ8312-1212-1200-66-6600000000000000004i−4i4i−4i000000000000000000−2i2i−2i2i0000000000000000000000000000000000
χ8412-1212-1200-66-660000000000000000−4i4i−4i4i0000000000000000002i−2i2i−2i0000000000000000000000000000000000
χ8512-12-121200-666-600000000000000004-4-44000000000000000000-222-20000000000000000000000000000000000
χ8612-12-121200-666-60000000000000000-444-40000000000000000002-2-220000000000000000000000000000000000

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