Finite Group Databasebeta

← Group #13151306

Character table — Group #13151306

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order1222223666246633666666612366666666612124444121212126666612121224444444446612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111-1-11111111111-1-111111-1-1111-1-111111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ61111111111-1-11111111111-1-111111-1-1111-1-111111111-111-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1
χ71111111111-1-11111111111-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-11111-1-1-1-11111-1-11111-1-1
χ81111111111-1-11111111111-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111111-1-1111111-1-1-1-1-1-111-1-111
χ91111-1-111111-1-1-1111111111-11-1-1-1-111111-1-111-1-111111-1-111-1-1-1-11-11-111-11-1-1-111-1-111-1-1-1-1111-11-1
χ101111-1-111111-1-1-1111111111-11-1-1-1-111111-1-111-1-111111-1-111-1-1-1-1-11-111-11-11-1-1-1-111-1-111-1-111-11-11
χ111111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1-1-111-1-1-1-11-1-111-1-1-111-1-11-11-1-111111-1-1-1-11111-1-11-1-11
χ121111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1-1-111-1-1-1-11-1-111-1-1-11-111-1-1-111-111-1-11111-1-111-1-1-111-1
χ131111-1-11111-11-1-111111111-111-1-1-1-1-1-11111111-1-11111-1-1-1-1-111111-11-1-1-11-1111-1-111-1-111-1-1-1-11-11-1
χ141111-1-11111-11-1-111111111-111-1-1-1-1-1-11111111-1-11111-1-1-1-1-11111-11-11-11-11-11111-1-111-1-1-1-1-1-1-11-11
χ151111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1111-11-1-111-111-1-1-1-1-11111-1-111111-1-11
χ161111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1111-1-111-111-1-11-1-111-1-1-1-1111111-111-1
χ17222222222222222-1-1-1222-122-122-1-1-1-1-1-1-1-1-12222-1-1-1-12-1-1-1-12-1-12000020000-1-100000000-1-1-1-10000
χ18222222222222222-1-1-1222-122-122-1-1-1-1-1-1-1-1-1-2-2-2-211112-1-1-1-12-1-1-20000-20000110000000011110000
χ1922222222222222-1222-1-1-1222-1-1-12222-1-1-12200000000-1-1-1-1-1-1-1-10002200022000000-1-1-1-1000000-1-1
χ2022222222222222-1222-1-1-1222-1-1-12222-1-1-12200000000-1-1-1-1-1-1-1-1000-2-2000-2-2000000111100000011
χ212222222222-2-2222-1-1-1222-1-2-2-122-1-111-1-1-1112222-1-1-1-1-2-1-111-211-20000-200001100000000-1-1110000
χ222222222222-2-2222-1-1-1222-1-2-2-122-1-111-1-1-111-2-2-2-21111-2-1-111-2112000020000-1-10000000011-1-10000
χ232222222222-2-222-1222-1-1-12-2-2-1-1-122-2-2-1-1-1-2-2000000001-1-11111100022000-2-20000001111000000-1-1
χ242222222222-2-222-1222-1-1-12-2-2-1-1-122-2-2-1-1-1-2-2000000001-1-111111000-2-200022000000-1-1-1-100000011
χ252222-2-222222-2-2-22-1-1-1222-12-2-1-2-211-1-1-1-1-11122-2-2-1-1-1-1211-1-1-211-2000020000110000000011-1-10000
χ262222-2-222222-2-2-22-1-1-1222-12-2-1-2-211-1-1-1-1-111-2-2221111211-1-1-21120000-20000-1-100000000-1-1110000
χ272222-2-222222-2-2-2-1222-1-1-122-2-111-2-222-1-1-1-2-200000000-111-1-11110002-20002-2000000-1-111000000-11
χ282222-2-222222-2-2-2-1222-1-1-122-2-111-2-222-1-1-1-2-200000000-111-1-1111000-22000-2200000011-1-10000001-1
χ292222-2-22222-22-2-22-1-1-1222-1-22-1-2-21111-1-1-1-1-122-2-2-1-1-1-1-211112-1-120000-20000-1-10000000011110000
χ302222-2-22222-22-2-22-1-1-1222-1-22-1-2-21111-1-1-1-1-1-2-2221111-211112-1-1-20000200001100000000-1-1-1-10000
χ312222-2-22222-22-2-2-1222-1-1-12-22-111-2-2-2-2-1-1-1220000000011111-1-1-10002-2000-2200000011-1-1000000-11
χ322222-2-22222-22-2-2-1222-1-1-12-22-111-2-2-2-2-1-1-1220000000011111-1-1-1000-220002-2000000-1-1110000001-1
χ332-2-222-22-2-22002-222-2-2-2-2220022-22-200-2-22002-22-222-2-202-200000000000000000000000002-2000000
χ342-2-222-22-2-22002-222-2-2-2-2220022-22-200-2-2200-22-22-2-22202-20000000000000000000000000-22000000
χ352-2-222-22-2-22002-22-111-2-22-100-12-2-11−i3i311-1−i3i32-22-2-1-1110-11−i3i30−i3i30000000000−i3i300000000-11−i3i30000
χ362-2-222-22-2-22002-22-111-2-22-100-12-2-11−i3i311-1−i3i3-22-2211-1-10-11−i3i30−i3i30000000000i3−i3000000001-1i3−i30000
χ372-2-222-22-2-22002-22-111-2-22-100-12-2-11i3−i311-1i3−i32-22-2-1-1110-11i3−i30i3−i30000000000i3−i300000000-11i3−i30000
χ382-2-222-22-2-22002-22-111-2-22-100-12-2-11i3−i311-1i3−i3-22-2211-1-10-11i3−i30i3−i30000000000−i3i3000000001-1−i3i30000
χ392-2-22-222-2-2200-2222-2-2-2-222002-22-2200-2-22002-2-2222-2-20-220000000000000000000000000-22000000
χ402-2-22-222-2-2200-2222-2-2-2-222002-22-2200-2-2200-222-2-2-2220-2200000000000000000000000002-2000000
χ412-2-22-222-2-2200-222-111-2-22-100-1-221-1−i3i311-1i3−i32-2-22-1-11101-1−i3i30i3−i30000000000i3−i3000000001-1−i3i30000
χ422-2-22-222-2-2200-222-111-2-22-100-1-221-1−i3i311-1i3−i3-222-211-1-101-1−i3i30i3−i30000000000−i3i300000000-11i3−i30000
χ432-2-22-222-2-2200-222-111-2-22-100-1-221-1i3−i311-1−i3i32-2-22-1-11101-1i3−i30−i3i30000000000−i3i3000000001-1i3−i30000
χ442-2-22-222-2-2200-222-111-2-22-100-1-221-1i3−i311-1−i3i3-222-211-1-101-1i3−i30−i3i30000000000i3−i300000000-11−i3i30000
χ4544444444444444-2-2-2-2-2-2-2-2441-2-2-2-2-2-2111-2-200000000-21111-2110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41-2-2-2-2221112200000000211-1-12-1-10000000000000000000000000000
χ474444-4-444444-4-4-4-2-2-2-2-2-2-2-24-412222-2-21112200000000-2-1-1112-1-10000000000000000000000000000
χ484444-4-44444-44-4-4-2-2-2-2-2-2-2-2-441222222111-2-2000000002-1-1-1-1-2110000000000000000000000000000
χ4944-4-40044-4-40000444-44-4-4-40040000004-4-40000000000000000000000000000000000000000000000
χ5044-4-40044-4-400004-2-224-4-4200-2000000-22200000023−2323−23000000000000000000000000000000000000
χ5144-4-40044-4-400004-2-224-4-4200-2000000-222000000−2323−2323000000000000000000000000000000000000
χ5244-4-40044-4-40000-244-4-222-400-2000000-22200000000000000000000000000000000000023−2300000000
χ5344-4-40044-4-40000-244-4-222-400-2000000-222000000000000000000000000000000000000−232300000000
χ544-44-4004-44-4000044-44-44-4-4004000000-44-40000000000000000000000000000000000000000000000
χ554-44-4004-44-400004-22-2-44-4200-20000002-2200000023−23−2323000000000000000000000000000000000000
χ564-44-4004-44-400004-22-2-44-4200-20000002-22000000−232323−23000000000000000000000000000000000000
χ574-44-4004-44-40000-24-442-22-400-20000002-22000000000000000000000000000000000023−230000000000
χ584-44-4004-44-40000-24-442-22-400-20000002-220000000000000000000000000000000000−23230000000000
χ594-4-444-44-4-44004-4-24-4-422-2400-2-224-40022-200000000000-22000000000000000000000000000000000
χ604-4-444-44-4-44004-4-2-22222-2-2001-22-22−2i32i3-1-11−2i32i30000000001-1i3−i30i3−i30000000000000000000000000000
χ614-4-444-44-4-44004-4-2-22222-2-2001-22-222i3−2i3-1-112i3−2i30000000001-1−i3i30−i3i30000000000000000000000000000
χ624-4-44-444-4-4400-44-24-4-422-2400-22-2-440022-2000000000002-2000000000000000000000000000000000
χ634-4-44-444-4-4400-44-2-22222-2-20012-22-2−2i32i3-1-112i3−2i3000000000-11i3−i30−i3i30000000000000000000000000000
χ644-4-44-444-4-4400-44-2-22222-2-20012-22-22i3−2i3-1-11−2i32i3000000000-11−i3i30i3−i30000000000000000000000000000
χ65666666-3-3-3-366-3-300000000-3-30000000000000000000000000000022000220000-1-1-1-100000000-1-100
χ66666666-3-3-3-366-3-300000000-3-300000000000000000000000000000-2-2000-2-200001111000000001100
χ67666666-3-3-3-3-6-6-3-300000000330000000000000000000000000000022000-2-20000111100000000-1-100
χ68666666-3-3-3-3-6-6-3-3000000003300000000000000000000000000000-2-2000220000-1-1-1-1000000001100
χ696666-6-6-3-3-3-36-63300000000-33000000000000000000000000000002-20002-20000-1-11100000000-1100
χ706666-6-6-3-3-3-36-63300000000-3300000000000000000000000000000-22000-22000011-1-1000000001-100
χ716666-6-6-3-3-3-3-6633000000003-3000000000000000000000000000002-2000-22000011-1-100000000-1100
χ726666-6-6-3-3-3-3-6633000000003-300000000000000000000000000000-220002-20000-1-111000000001-100
χ7388-8-80088-8-80000-4-4-44-44440020000002-2-20000000000000000000000000000000000000000000000
χ748-88-8008-88-80000-4-44-44-444002000000-22-20000000000000000000000000000000000000000000000
χ751212-12-1200-6-6660000000000000000000000000000000000000000000000000000000023−23000000000000
χ761212-12-1200-6-66600000000000000000000000000000000000000000000000000000000−2323000000000000
χ7712-1212-1200-66-6600000000000000000000000000000000000000000000000000000023−2300000000000000
χ7812-1212-1200-66-66000000000000000000000000000000000000000000000000000000−232300000000000000
χ7912-12-121212-12-666-600-66000000000000000000000000000000000000000000000000000000000000000000
χ8012-12-1212-1212-666-6006-6000000000000000000000000000000000000000000000000000000000000000000

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