Finite Group Databasebeta

← Group #13151382

Character table — Group #13151382

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12222236662466336666666123666666666121244441212121266666121212244444444412121212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1-1-1-11-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-11-1-1-111-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-111-1-1-111111-1-1-1-1-1-1-1-1-1-1-111-1
χ51111111111-1-11111111111-1-1111-1-111111-1-111111111-111-1-1-1-1-11-111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111
χ61111111111-1-11111111111-1-1111-1-111111-1-111111111-111-1-1-1-1-1-1-1-1-111-111-11111-1-1111111-1-1-1-1-1-1
χ71111111111-1-11111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-11111-1-1-1111111-1-1-1-1-1-1111-1-11
χ81111111111-1-11111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-1-1111111-1-111-111-1
χ91111-1-111111-1-1-1111111111-11-1-111-1-1111-1-111-1-111111-1-111-1-1-11-11-11-111-1-111-1-1-1-111-1-1-1-11111-1-1
χ101111-1-111111-1-1-1111111111-11-1-111-1-1111-1-111-1-111111-1-111-1-1-1-1-1-11-111-111-1-111-1-1-1-111-1-111-1-111
χ111111-1-111111-1-1-1111111111-11-1-111-1-1111-1-1-1-111-1-1-1-11-1-111-1-1-111-1-1-11-11-11-1-1111111-1-111-1-11-11-1
χ121111-1-111111-1-1-1111111111-11-1-111-1-1111-1-1-1-111-1-1-1-11-1-111-1-1-1-11111-1-1-11-111-1-111-1-11111-1-1-11-11
χ131111-1-11111-11-1-111111111-111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1111111-1-11-1-11-1-1-11111-1-111-1-1-1-111-1-1
χ141111-1-11111-11-1-111111111-111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1111-11-111-1-11-1111-1-11111-1-1-1-1-1-1-1-111
χ151111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-11-11-11111-1-1-1-1-1-11111111-11-1
χ161111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1111-1-111-1111-1-1-1-111-1-111-1-11111-11-11
χ17222222222222222-1-122-1-1222-12222-1-1-1-1-12200000000-1-1-1-1-1-1-1-12002000220000000-1-1-1-10000-100-1
χ18222222222222222-1-122-1-1222-12222-1-1-1-1-12200000000-1-1-1-1-1-1-1-1-200-2000-2-20000000111100001001
χ1922222222222222-122-1-122-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-12-1-1-1-12-1-102000020000000-1-10000-1-1-1-10000
χ2022222222222222-122-1-122-122-1-1-1-1-122-1-1-1-1-1-2-2-2-211112-1-1-1-12-1-10-20000-2000000011000011110000
χ212222222222-2-2222-1-122-1-12-2-2-122-2-2-1-1-1-1-1-2-2000000001-1-1111112002000-2-2000000011110000-100-1
χ222222222222-2-2222-1-122-1-12-2-2-122-2-2-1-1-1-1-1-2-2000000001-1-111111-200-2000220000000-1-1-1-100001001
χ232222222222-2-222-122-1-122-1-2-2-1-1-11122-1-1-1112222-1-1-1-1-2-1-111-2110-20000-20000000110000-1-1110000
χ242222222222-2-222-122-1-122-1-2-2-1-1-11122-1-1-111-2-2-2-21111-2-1-111-21102000020000000-1-1000011-1-10000
χ252222-2-222222-2-2-22-1-122-1-122-2-1-2-22211-1-1-1-2-200000000-111-1-1111200-20002-20000000-1-1110000-1001
χ262222-2-222222-2-2-22-1-122-1-122-2-1-2-22211-1-1-1-2-200000000-111-1-1111-2002000-22000000011-1-10000100-1
χ272222-2-222222-2-2-2-122-1-122-12-2-111-1-1-2-2-1-1-11122-2-2-1-1-1-1211-1-1-2110-200002000000011000011-1-10000
χ282222-2-222222-2-2-2-122-1-122-12-2-111-1-1-2-2-1-1-111-2-2221111211-1-1-211020000-20000000-1-10000-1-1110000
χ292222-2-22222-22-2-22-1-122-1-12-22-1-2-2-2-211-1-1-1220000000011111-1-1-1200-2000-22000000011-1-10000-1001
χ302222-2-22222-22-2-22-1-122-1-12-22-1-2-2-2-211-1-1-1220000000011111-1-1-1-20020002-20000000-1-1110000100-1
χ312222-2-22222-22-2-2-122-1-122-1-22-11111-2-2-1-1-1-1-122-2-2-1-1-1-1-211112-1-1020000-20000000-1-1000011110000
χ322222-2-22222-22-2-2-122-1-122-1-22-11111-2-2-1-1-1-1-1-2-2221111-211112-1-10-2000020000000110000-1-1-1-10000
χ332-22-22-22-2-22002-222-22-22-2-20022-2002-2-2-22002i−2i2i−2i2i2i−2i−2i02-200000000000000000000000002i−2i000000
χ342-22-22-22-2-22002-222-22-22-2-20022-2002-2-2-2200−2i2i−2i2i−2i−2i2i2i02-20000000000000000000000000−2i2i000000
χ352-22-22-22-2-22002-2-12-2-112-2100-1-11−i3i32-211-1−i3i32i−2i2i−2i−i−iii0-11−i3i30−i3i3000000000000003−30000−ii3−30000
χ362-22-22-22-2-22002-2-12-2-112-2100-1-11−i3i32-211-1−i3i3−2i2i−2i2iii−i−i0-11−i3i30−i3i300000000000000−330000i−i−330000
χ372-22-22-22-2-22002-2-12-2-112-2100-1-11i3−i32-211-1i3−i32i−2i2i−2i−i−iii0-11i3−i30i3−i300000000000000−330000−ii−330000
χ382-22-22-22-2-22002-2-12-2-112-2100-1-11i3−i32-211-1i3−i3−2i2i−2i2iii−i−i0-11i3−i30i3−i3000000000000003−30000i−i3−30000
χ392-22-2-222-2-2200-2222-22-22-2-2002-2200-22-2-22002i−2i−2i2i2i2i−2i−2i0-220000000000000000000000000−2i2i000000
χ402-22-2-222-2-2200-2222-22-22-2-2002-2200-22-2-2200−2i2i2i−2i−2i−2i2i2i0-2200000000000000000000000002i−2i000000
χ412-22-2-222-2-2200-22-12-2-112-2100-11-1−i3i3-2211-1i3−i32i−2i−2i2i−i−iii01-1−i3i30i3−i300000000000000−330000i−i3−30000
χ422-22-2-222-2-2200-22-12-2-112-2100-11-1−i3i3-2211-1i3−i3−2i2i2i−2iii−i−i01-1−i3i30i3−i3000000000000003−30000−ii−330000
χ432-22-2-222-2-2200-22-12-2-112-2100-11-1i3−i3-2211-1−i3i32i−2i−2i2i−i−iii01-1i3−i30−i3i3000000000000003−30000i−i−330000
χ442-22-2-222-2-2200-22-12-2-112-2100-11-1i3−i3-2211-1−i3i3−2i2i2i−2iii−i−i01-1i3−i30−i3i300000000000000−330000−ii3−30000
χ4544444444444444-2-2-2-2-2-2-2-2441-2-2-2-2-2-2111-2-200000000-21111-2110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41-2-222-2-21112200000000211-1-12-1-10000000000000000000000000000
χ474444-4-444444-4-4-4-2-2-2-2-2-2-2-24-4122-2-2221112200000000-2-1-1112-1-10000000000000000000000000000
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
χ5044-4-40044-4-400004-2-2-4422-400-2000000-22200000000000000000000000000000000000023−2300000000
χ5144-4-40044-4-400004-2-2-4422-400-2000000-222000000000000000000000000000000000000−232300000000
χ5244-4-40044-4-40000-2442-2-4-4200-2000000-22200000023−2323−23000000000000000000000000000000000000
χ5344-4-40044-4-40000-2442-2-4-4200-2000000-222000000−2323−2323000000000000000000000000000000000000
χ544-44-44-44-4-44004-44-224-4-22-400-24-400-2222-200000000000-22000000000000000000000000000000000
χ554-44-44-44-4-44004-4-2-22-22-222001-22−2i32i3-22-1-11−2i32i30000000001-1i3−i30i3−i30000000000000000000000000000
χ564-44-44-44-4-44004-4-2-22-22-222001-222i3−2i3-22-1-112i3−2i30000000001-1−i3i30−i3i30000000000000000000000000000
χ574-44-4-444-4-4400-444-224-4-22-400-2-44002-222-2000000000002-2000000000000000000000000000000000
χ584-44-4-444-4-4400-44-2-22-22-2220012-2−2i32i32-2-1-112i3−2i3000000000-11i3−i30−i3i30000000000000000000000000000
χ594-44-4-444-4-4400-44-2-22-22-2220012-22i3−2i32-2-1-11−2i32i3000000000-11−i3i30i3−i30000000000000000000000000000
χ604-4-44004-44-4000044-4-4-4-444004000000-44-40000000000000000000000000000000000000000000000
χ614-4-44004-44-400004-22-4-42-2400-20000002-220000000000000000000000000000000000−2i32i30000000000
χ624-4-44004-44-400004-22-4-42-2400-20000002-2200000000000000000000000000000000002i3−2i30000000000
χ634-4-44004-44-40000-24-422-44-200-20000002-22000000−2i32i32i3−2i3000000000000000000000000000000000000
χ644-4-44004-44-40000-24-422-44-200-20000002-220000002i3−2i3−2i32i3000000000000000000000000000000000000
χ65666666-3-3-3-366-3-300000000-3-300000000000000000000000000000020220002-1-1-1-100000000000-1-10
χ66666666-3-3-3-366-3-300000000-3-3000000000000000000000000000000-20-2-2000-2111100000000000110
χ67666666-3-3-3-3-6-6-3-3000000003300000000000000000000000000000020-2-20002111100000000000-1-10
χ68666666-3-3-3-3-6-6-3-30000000033000000000000000000000000000000-2022000-2-1-1-1-100000000000110
χ696666-6-6-3-3-3-36-63300000000-33000000000000000000000000000000202-2000-2-1-11100000000000-110
χ706666-6-6-3-3-3-36-63300000000-33000000000000000000000000000000-20-22000211-1-1000000000001-10
χ716666-6-6-3-3-3-3-6633000000003-300000000000000000000000000000020-22000-211-1-100000000000-110
χ726666-6-6-3-3-3-3-6633000000003-3000000000000000000000000000000-202-20002-1-111000000000001-10
χ7388-8-80088-8-80000-4-4-44-44440020000002-2-20000000000000000000000000000000000000000000000
χ748-8-88008-88-80000-4-44444-4-4002000000-22-20000000000000000000000000000000000000000000000
χ751212-12-1200-6-66600000000000000000000000000000000000000000000000000000023−2300000000000000
χ761212-12-1200-6-666000000000000000000000000000000000000000000000000000000−232300000000000000
χ7712-1212-1212-12-666-600-66000000000000000000000000000000000000000000000000000000000000000000
χ7812-1212-12-1212-666-6006-6000000000000000000000000000000000000000000000000000000000000000000
χ7912-12-121200-66-66000000000000000000000000000000000000000000000000000023−230000000000000000
χ8012-12-121200-66-660000000000000000000000000000000000000000000000000000−23230000000000000000

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