Finite Group Databasebeta

← Group #13151440

Character table — Group #13151440

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order12222236662466661212336666662222366666662244444444666666666612121212222444666612121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111111111-11-1-11-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-11111-11-11
χ51111111111-1-111-1-1-1-11111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-11-1-111111111-1-1-1-1-11-11
χ81111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-111-1-1-11111-1-1-1-111111-11-1
χ91111-1-111111-1-1-111-1-11111111111111-1-1-1-1111-1-111-1-111-1-1111111-1-111-1-1-1-1111-1-1-1-1-111-1-111-1-111-1-111-1-1
χ101111-1-111111-1-1-111-1-11111111111111-1-1-1-1111-1-1-1-111-1-111111111-1-111-1-1-1-11-1-1-111-1-111-1-1-1-111-1-111-1-111
χ111111-1-111111-1-1-111-1-111111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-11-11-1111-1-11111-1-1-1-1111-1-11
χ121111-1-111111-1-1-111-1-111111111-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1111-111-1-111-1-11111-1-1-111-1
χ131111-1-11111-11-1-1-1-1111111111111111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1111-1-1-1-11111-1-111-1-1-1-111
χ141111-1-11111-11-1-1-1-1111111111111111-1-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1111-1-1-1-1-1-111-1-111-1-11111-1-1
χ151111-1-11111-11-1-1-1-11111111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-11-11-11111-1-111-1-1-1-111-111-1
χ161111-1-11111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111111-1-1-1-11111-1-11-1-11
χ172222222222222222222-12-12-12-10000-122-1-1-1-1-1000000222200002-1-1-1-1-12-1-1-10020020000000000-1-1-1-10-10-1
χ182222222222222222222-12-12-12-10000-122-1-1-1-1-1000000-2-2-2-200002-1-1-1-1-12-1-1-100-200-2000000000011110101
χ19222222222222222222-12-12-12-120000-1-1-122-1-1-100222200000000-12-1-1-1-1-12-1-1020020000000-1-1-1-10000-10-10
χ20222222222222222222-12-12-12-120000-1-1-122-1-1-100-2-2-2-200000000-12-1-1-1-1-12-1-10-200-20000000111100001010
χ212222222222-2-222-2-2-2-22-12-12-12-10000-122-1-1-1-1-100000022220000-21-1-111-211100-200-20000000000-1-1-1-10101
χ222222222222-2-222-2-2-2-22-12-12-12-10000-122-1-1-1-1-1000000-2-2-2-20000-21-1-111-2111002002000000000011110-10-1
χ232222222222-2-222-2-2-2-2-12-12-12-120000-1-1-122-1-1-1002222000000001-2-1-1111-2110-200-20000000-1-1-1-100001010
χ242222222222-2-222-2-2-2-2-12-12-12-120000-1-1-122-1-1-100-2-2-2-2000000001-2-1-1111-21102002000000011110000-10-10
χ252222-2-222222-2-2-222-2-22-12-12-12-10000-1-2-211-1-1-100000022-2-200002-111-1-1-211100200-20000000000-1-1110-101
χ262222-2-222222-2-2-222-2-22-12-12-12-10000-1-2-211-1-1-1000000-2-22200002-111-1-1-211100-2002000000000011-1-1010-1
χ272222-2-222222-2-2-222-2-2-12-12-12-120000-111-2-2-1-1-10022-2-200000000-1211-1-11-2110200-20000000-1-1110000-1010
χ282222-2-222222-2-2-222-2-2-12-12-12-120000-111-2-2-1-1-100-2-22200000000-1211-1-11-2110-2002000000011-1-1000010-10
χ292222-2-22222-22-2-2-2-2222-12-12-12-10000-1-2-211-1-1-100000022-2-20000-2111112-1-1-100-20020000000000-1-111010-1
χ302222-2-22222-22-2-2-2-2222-12-12-12-10000-1-2-211-1-1-1000000-2-2220000-2111112-1-1-100200-2000000000011-1-10-101
χ312222-2-22222-22-2-2-2-222-12-12-12-120000-111-2-2-1-1-10022-2-2000000001-21111-12-1-10-20020000000-1-111000010-10
χ322222-2-22222-22-2-2-2-222-12-12-12-120000-111-2-2-1-1-100-2-222000000001-21111-12-1-10200-2000000011-1-10000-1010
χ3322-2-20022-2-2000000002222-2-2-2-222-2-2200002-2-200002i−2i002i−2i22-2-20000000000000000000000002i−2i002i−2i0000
χ3422-2-20022-2-2000000002222-2-2-2-222-2-2200002-2-20000−2i2i00−2i2i22-2-2000000000000000000000000−2i2i00−2i2i0000
χ3522-2-20022-2-2000000002222-2-2-2-2-2-222200002-2-200002i−2i00−2i2i-2-2220000000000000000000000002i−2i00−2i2i0000
χ3622-2-20022-2-2000000002222-2-2-2-2-2-222200002-2-20000−2i2i002i−2i-2-222000000000000000000000000−2i2i002i−2i0000
χ372-22-22-22-2-22002-2000022-2-222-2-22-22-222-22-2-2-222-2000000002-22-2002-20000000000002-20000000000000000
χ382-22-22-22-2-22002-2000022-2-222-2-2-22-2222-22-2-2-22-2200000000-22-22002-2000000000000-220000000000000000
χ392-22-2-222-2-2200-22000022-2-222-2-22-22-22-22-22-2-22-22000000002-22-200-22000000000000-220000000000000000
χ402-22-2-222-2-2200-22000022-2-222-2-2-22-222-22-22-2-222-200000000-22-2200-220000000000002-20000000000000000
χ412-2-22002-22-20000000022-2-2-2-2222-2-2220000-22-2002-2002-2002-2-2200000000000000000000002-2002-2000000
χ422-2-22002-22-20000000022-2-2-2-2222-2-2220000-22-200-2200-22002-2-220000000000000000000000-2200-22000000
χ432-2-22002-22-20000000022-2-2-2-222-222-220000-22-2002-200-2200-222-200000000000000000000002-200-22000000
χ442-2-22002-22-20000000022-2-2-2-222-222-220000-22-200-22002-200-222-20000000000000000000000-22002-2000000
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
χ4944-4-40044-4-4000000004-24-2-42-420000-20000-222000000004i−4i00000000000000000000000000000000−2i2i0000
χ5044-4-40044-4-4000000004-24-2-42-420000-20000-22200000000−4i4i000000000000000000000000000000002i−2i0000
χ5144-4-40044-4-400000000-24-242-42-40000-20000-22200004i−4i00000000000000000000000000000000−2i2i00000000
χ5244-4-40044-4-400000000-24-242-42-40000-20000-2220000−4i4i000000000000000000000000000000002i−2i00000000
χ534-44-44-44-4-44004-400004-2-424-2-420000-24-4-2222-20000000000000000-22000000000000000000000000000000
χ544-44-44-44-4-44004-40000-242-4-242-40000-2-224-422-20000000000000000-22000000000000000000000000000000
χ554-44-44-44-4-44004-40000-2-222-2-22200001-22-22-1-1100000000000000001-13-3003-3000000000000000000000000
χ564-44-44-44-4-44004-40000-2-222-2-22200001-22-22-1-1100000000000000001-1-3300-33000000000000000000000000
χ574-44-4-444-4-4400-4400004-2-424-2-420000-2-442-222-200000000000000002-2000000000000000000000000000000
χ584-44-4-444-4-4400-440000-242-4-242-40000-22-2-4422-200000000000000002-2000000000000000000000000000000
χ594-44-4-444-4-4400-440000-2-222-2-222000012-22-2-1-110000000000000000-113-300-33000000000000000000000000
χ604-44-4-444-4-4400-440000-2-222-2-222000012-22-2-1-110000000000000000-11-33003-3000000000000000000000000
χ614-4-44004-44-4000000004-2-42-424-20000-200002-220000004-400000000000000000000000000000000-22000000
χ624-4-44004-44-4000000004-2-42-424-20000-200002-22000000-44000000000000000000000000000000002-2000000
χ634-4-44004-44-400000000-242-42-4-240000-200002-22004-400000000000000000000000000000000-220000000000
χ644-4-44004-44-400000000-242-42-4-240000-200002-2200-44000000000000000000000000000000002-20000000000
χ65666666-3-3-3-366-3-3-3-3-3-3000000002222000000002200000000-1-1-1-10000000000200200-1-1-1-1-1-1000000000000
χ66666666-3-3-3-366-3-3-3-3-3-300000000-2-2-2-200000000-2-20000000011110000000000-200-200111111000000000000
χ67666666-3-3-3-3-6-6-3-33333000000002222000000002200000000-1-1-1-10000000000-200-200-1-11111000000000000
χ68666666-3-3-3-3-6-6-3-3333300000000-2-2-2-200000000-2-2000000001111000000000020020011-1-1-1-1000000000000
χ696666-6-6-3-3-3-36-633-3-33300000000222200000000-2-200000000-1-1-1-10000000000200-20011-1-111000000000000
χ706666-6-6-3-3-3-36-633-3-33300000000-2-2-2-200000000220000000011110000000000-200200-1-111-1-1000000000000
χ716666-6-6-3-3-3-3-663333-3-300000000222200000000-2-200000000-1-1-1-10000000000-2002001111-1-1000000000000
χ726666-6-6-3-3-3-3-663333-3-300000000-2-2-2-200000000220000000011110000000000200-200-1-1-1-111000000000000
χ736-66-66-6-333-300-33−3i33i3−3i33i3000000002-22-2000000002-200000000-11-110000000000000000-11−i3i3−i3i3000000000000
χ746-66-66-6-333-300-33−3i33i3−3i33i300000000-22-2200000000-22000000001-11-100000000000000001-1i3−i3i3−i3000000000000
χ756-66-66-6-333-300-333i3−3i33i3−3i3000000002-22-2000000002-200000000-11-110000000000000000-11i3−i3i3−i3000000000000
χ766-66-66-6-333-300-333i3−3i33i3−3i300000000-22-2200000000-22000000001-11-100000000000000001-1−i3i3−i3i3000000000000
χ776-66-6-66-333-3003-3−3i33i33i3−3i3000000002-22-200000000-2200000000-11-1100000000000000001-1−i3i3i3−i3000000000000
χ786-66-6-66-333-3003-3−3i33i33i3−3i300000000-22-22000000002-2000000001-11-10000000000000000-11i3−i3−i3i3000000000000
χ796-66-6-66-333-3003-33i3−3i3−3i33i3000000002-22-200000000-2200000000-11-1100000000000000001-1i3−i3−i3i3000000000000
χ806-66-6-66-333-3003-33i3−3i3−3i33i300000000-22-22000000002-2000000001-11-10000000000000000-11−i3i3i3−i3000000000000
χ8188-8-80088-8-800000000-4-4-4-444440000200002-2-2000000000000000000000000000000000000000000000000
χ828-8-88008-88-800000000-4-44444-4-4000020000-22-2000000000000000000000000000000000000000000000000
χ831212-12-1200-6-666000000000000000044-4-4000000000000000000-2-2220000000000000000000000000000000000
χ841212-12-1200-6-6660000000000000000-4-44400000000000000000022-2-20000000000000000000000000000000000
χ8512-12-121200-66-6600000000000000004-4-44000000000000000000-222-20000000000000000000000000000000000
χ8612-12-121200-66-660000000000000000-444-40000000000000000002-2-220000000000000000000000000000000000

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