Finite Group Databasebeta

← Group #13137969

Character table — Group #13137969

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222224466666666888121212121212121224242424242424242424363636363636363636363636363636363636727272727272727272
order122234466612123366666641212366612121212121212121212121212122466888812122424242424242424444121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-111-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-1-1-1-111
χ511111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-11-1-11111
χ711111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-11111-1-1
χ92222222222222-12-12-1-12222-1-1-1-1-12-1222-1-1-1-1-1-1-1-10000220000-1-1-1-1000020000-1-100
χ102222222222222-12-12-1-12222-1-1-1-1-12-1222-1-1-1-1-1-1-1-10000-2-2000011110000-200001100
χ112222222222222-12-12-1-12-2-2-2-1-1-1-1-12-12-2-211-1-111110000220000-1-1-1-10000-200001100
χ122222222222222-12-12-1-12-2-2-2-1-1-1-1-12-12-2-211-1-111110000-2-200001111000020000-1-100
χ13222222222222-12-12-122-1222-1-1-1-12-12-1-1-122-1-1-1-1-1-100000022000000-1-1-1-10020000-1-1
χ14222222222222-12-12-122-1222-1-1-1-12-12-1-1-122-1-1-1-1-1-1000000-2-2000000111100-2000011
χ15222222222222-12-12-122-1-2-2-2-1-1-1-12-12-111-2-2-1-1111100000022000000-1-1-1-100-2000011
χ16222222222222-12-12-122-1-2-2-2-1-1-1-12-12-111-2-2-1-11111000000-2-200000011110020000-1-1
χ1722222-2-2222-2-2222222220002222-2-2-2-20000-2-200002-2220000-2-200000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-20000-2-20000-22-2-200002200000000000000000
χ192-2-2222-2-2-222-222-22-2-2-220002-22-222-2-200002-200000000002i−2i0000002i2i−2i−2i000000000
χ202-2-2222-2-2-222-222-22-2-2-220002-22-222-2-200002-20000000000−2i2i000000−2i−2i2i2i000000000
χ212-2-2222-2-2-222-2-12121-2-2-1000-11-112-1-213−300-1133−3−30000002i−2i000000−i−iii0000000−i3i3
χ222-2-2222-2-2-222-2-12121-2-2-1000-11-112-1-213−300-1133−3−3000000−2i2i000000ii−i−i0000000i3−i3
χ232-2-2222-2-2-222-2-12121-2-2-1000-11-112-1-21−3300-11−3−3330000002i−2i000000−i−iii0000000i3−i3
χ242-2-2222-2-2-222-2-12121-2-2-1000-11-112-1-21−3300-11−3−333000000−2i2i000000ii−i−i0000000−i3i3
χ252-2-222-22-2-22-2222-22-2-2-220002-22-2-2-2220000-22000000002-2000022-2-20000000000000
χ262-2-222-22-2-22-2222-22-2-2-220002-22-2-2-2220000-2200000000-220000-2-2220000000000000
χ272-2-222-22-2-22-222-1-2-1-2112000-11-111-2-12003−31-13−33−300002-20000-1-1110000000003−300
χ282-2-222-22-2-22-222-1-2-1-2112000-11-111-2-12003−31-13−33−30000-22000011-1-1000000000−3300
χ292-2-222-22-2-22-222-1-2-1-2112000-11-111-2-1200−331-1−33−3300002-20000-1-111000000000−3300
χ302-2-222-22-2-22-222-1-2-1-2112000-11-111-2-1200−331-1−33−330000-22000011-1-10000000003−300
χ31444444444444-2-2-2-2-2-2-2-24441111-2-2-2-2-2-2-2-2111111000000000000000000000000000
χ32444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-2222211-1-1-1-1000000000000000000000000000
χ3344444-4-4444-4-44-24-24-2-24000-2-2-2-22-42-40000220000000000000000000000000000000
χ3444444-4-4444-4-4-24-24-244-2000-2-2-2-2-42-420000220000000000000000000000000000000
χ3544444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000-1-13-3-33000000000000000000000000000
χ3644444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000-1-1-333-3000000000000000000000000000
χ3744-4-4400-44-40044-4-444-4-40004-4-4400000000000000000000000000000000000000000
χ3844-4-4400-44-4004-2-424-22-4000-222-20000000000000000000000006−66−60000000000000
χ3944-4-4400-44-4004-2-424-22-4000-222-2000000000000000000000000−66−660000000000000
χ4044-4-4400-44-400-242-4-24-42000-222-200000000000000000000000000006−66−6000000000
χ4144-4-4400-44-400-242-4-24-42000-222-20000000000000000000000000000−66−66000000000
χ424-44-44004-4-400444-4-4-44-400044-4-400000000000000000000000000000000000000000
χ434-44-44004-4-4004-242-42-2-4000-2-2220000000000000000000000006−6−660000000000000
χ444-44-44004-4-4004-242-42-2-4000-2-222000000000000000000000000−666−60000000000000
χ454-44-44004-4-400-24-2-42-442000-2-2220000000000000000000000000000i6−i6−i6i6000000000
χ464-44-44004-4-400-24-2-42-442000-2-2220000000000000000000000000000−i6i6i6−i6000000000
χ474-4-4444-4-4-444-44-2-4-2-4224000-22-22-242-40000-220000000000000000000000000000000
χ484-4-4444-4-4-444-4-2-22-2222-20001-11-1-2-22223−23001-1−3−333000000000000000000000000000
χ494-4-4444-4-4-444-4-2-22-2222-20001-11-1-2-222−2323001-133−3−3000000000000000000000000000
χ504-4-444-44-4-44-44-24242-4-4-2000-22-22-424-200002-20000000000000000000000000000000
χ514-4-444-44-4-44-44-2-22-2222-20001-11-122-2-20023−23-11−33−33000000000000000000000000000
χ524-4-444-44-4-44-44-2-22-2222-20001-11-122-2-200−2323-113−33−3000000000000000000000000000
χ536666-366-3-3-3-3-3000000006-3-300000000000000000022-1-10000-1-100000000020-1-10000
χ546666-366-3-3-3-3-3000000006-3-3000000000000000000-2-211000011000000000-20110000
χ556666-366-3-3-3-3-300000000-63300000000000000000022-1-10000-1-1000000000-20110000
χ566666-366-3-3-3-3-300000000-633000000000000000000-2-21100001100000000020-1-10000
χ576666-3-6-6-3-3-333000000000−3i33i30000000000000000002-2-1-100001100000000000−i3i30000
χ586666-3-6-6-3-3-333000000000−3i33i3000000000000000000-22110000-1-100000000000i3−i30000
χ596666-3-6-6-3-3-3330000000003i3−3i30000000000000000002-2-1-100001100000000000i3−i30000
χ606666-3-6-6-3-3-3330000000003i3−3i3000000000000000000-22110000-1-100000000000−i3i30000
χ6188-8-8800-88-800-4-444-4-4440002-2-2200000000000000000000000000000000000000000
χ628-88-88008-8-800-4-4-4444-4400022-2-200000000000000000000000000000000000000000
χ631212-12-12-6006-6600000000000000000000000000000000000000023−2300000000000000000
χ641212-12-12-6006-66000000000000000000000000000000000000000−232300000000000000000
χ6512-1212-12-600-666000000000000000000000000000000000−2i32i300000000000000000000000
χ6612-1212-12-600-6660000000000000000000000000000000002i3−2i300000000000000000000000
χ6712-12-1212-612-1266-6-6600000000000000000000000000000000000000000000000000000000
χ6812-12-1212-6-121266-66-600000000000000000000000000000000000000000000000000000000

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