Finite Group Databasebeta

← Group #13138985

Character table — Group #13138985

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636727272727272727272727272
order12223446668812122424242433666666121212123666121212121212242424242424242424242424242424244488121212122424242422246666661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-11111-1-1-1-1
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-11-1-1-1-11111
χ71111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-11-1-111-1-111
χ81111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-111-1-111-1-1
χ92222222222222222222-1-1-12-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000220000-1-1-1-100
χ102222222222222222222-1-1-12-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-20000111100
χ11222222222222222222-1222-12-1-1-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ12222222222222222222-1222-12-1-1-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ132222222222-2-222-2-2-2-22-1-1-12-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000000002-20000-1-11100
χ142222222222-2-222-2-2-2-22-1-1-12-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000-22000011-1-100
χ152222222222-2-222-2-2-2-2-1222-12-1-1-1-1-1-1-1-1-1-12-1-12-1-11111-2-2-2-21111111122-2-2-1-1-1-11111000000000000
χ162222222222-2-222-2-2-2-2-1222-12-1-1-1-1-1-1-1-1-1-12-1-12-1-11111-2-2-2-211111111-2-2221111-1-1-1-1000000000000
χ1722222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-2-2-200000000000000002-20022-2-20000000000000000
χ1822222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-2-2-20000000000000000-2200-2-2220000000000000000
χ1922222-2-222200-2-20000-1222-12-1-11111-1-1-1-1-211-21133−3−300003333−3−3−3−32-200-1-11133−3−3000000000000
χ2022222-2-222200-2-20000-1222-12-1-11111-1-1-1-1-211-21133−3−300003333−3−3−3−3-220011-1-1−3−333000000000000
χ2122222-2-222200-2-20000-1222-12-1-11111-1-1-1-1-211-211−3−3330000−3−3−3−333332-200-1-111−3−333000000000000
χ2222222-2-222200-2-20000-1222-12-1-11111-1-1-1-1-211-211−3−3330000−3−3−3−33333-220011-1-133−3−3000000000000
χ232-2-2222-2-2-222-2-2222-2-222-2-222-2-222-2-22-2-22-2-2-22222-22-222-2-222-2-222-2-2000000000000000000000000
χ242-2-2222-2-2-222-2-2222-2-22-1112-1-2-222-2-2-111-1111-1-1-12-22-2-1-111-1-111-1-111000000000000000000−i3i3−i3i300
χ252-2-2222-2-2-222-2-2222-2-22-1112-1-2-222-2-2-111-1111-1-1-12-22-2-1-111-1-111-1-111000000000000000000i3−i3i3−i300
χ262-2-2222-2-2-222-2-2222-2-2-12-2-2-1211-1-111-111-1-2112-1-1-11-1122-2-2-1-111-1-11100003−33−33−33−3000000000000
χ272-2-2222-2-2-222-2-2222-2-2-12-2-2-1211-1-111-111-1-2112-1-1-11-1122-2-2-1-111-1-1110000−33−33−33−33000000000000
χ282-2-2222-2-2-22-22-22-2-22222-2-222-2-222-2-22-2-22-2-2-2222-22-22-2-222-2-222-2-222000000000000000000000000
χ292-2-2222-2-2-22-22-22-2-2222-1112-1-2-222-2-2-111-1111-1-1-1-22-2211-1-111-1-111-1-1000000000000000000−i3i3i3−i300
χ302-2-2222-2-2-22-22-22-2-2222-1112-1-2-222-2-2-111-1111-1-1-1-22-2211-1-111-1-111-1-1000000000000000000i3−i3−i3i300
χ312-2-2222-2-2-22-22-22-2-222-12-2-2-1211-1-111-111-1-2112-1-11-11-1-2-22211-1-111-1-100003−33−3−33−33000000000000
χ322-2-2222-2-2-22-22-22-2-222-12-2-2-1211-1-111-111-1-2112-1-11-11-1-2-22211-1-111-1-10000−33−333−33−3000000000000
χ332-2-222-22-2-22002-2000022-2-222-2-2-2-2222-2-22222-2-2-20000000000000000002-200002-2-22000000000000
χ342-2-222-22-2-22002-2000022-2-222-2-2-2-2222-2-22222-2-2-2000000000000000000-220000-222-2000000000000
χ352-2-222-22-2-22002-20000-12-2-2-121111-1-1-111-12-1-1-2113−3−33000033−3−3−3−333002-2−333−3-111-1000000000000
χ362-2-222-22-2-22002-20000-12-2-2-121111-1-1-111-12-1-1-2113−3−33000033−3−3−3−33300-223−3−331-1-11000000000000
χ372-2-222-22-2-22002-20000-12-2-2-121111-1-1-111-12-1-1-211−333−30000−3−33333−3−3002-23−3−33-111-1000000000000
χ382-2-222-22-2-22002-20000-12-2-2-121111-1-1-111-12-1-1-211−333−30000−3−33333−3−300-22−333−31-1-11000000000000
χ39444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-211-211-2-2-2-2-2-2-2-211111111000000000000000000000000
χ404444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-21111-211-21122222222-1-1-1-1-1-1-1-1000000000000000000000000
χ4144444-4-444400-4-400004-2-2-24-244-4-4-4-4-2-2-2-22222220000000000000000000000000000000000000000
χ4244444-4-444400-4-40000-2-2-2-2-2-2-2-2222211112-1-12-1-12323−23−230000−3−3−3−33333000000000000000000000000
χ4344444-4-444400-4-40000-2-2-2-2-2-2-2-2222211112-1-12-1-1−23−23232300003333−3−3−3−3000000000000000000000000
χ4444-4-44004-4-400000000444-4-4-44-4000044-4-40000000000000000000000000000000000000000000000
χ4544-4-44004-4-4000000004-2-22-424-40000-2-2220000000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ4644-4-44004-4-4000000004-2-22-424-40000-2-2220000000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ4744-4-44004-4-400000000-244-42-4-2223−2323−23-2-222023−23023−230000000000000000000000000000000000000000
χ4844-4-44004-4-400000000-244-42-4-22−2323−2323-2-2220−23230−23230000000000000000000000000000000000000000
χ4944-4-44004-4-400000000-2-2-2222-2223−2323−2311-1-10−330−330000i6−i6i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000
χ5044-4-44004-4-400000000-2-2-2222-2223−2323−2311-1-10−330−330000−i6i6−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000
χ5144-4-44004-4-400000000-2-2-2222-22−2323−232311-1-103−303−30000i6−i6i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000
χ5244-4-44004-4-400000000-2-2-2222-22−2323−232311-1-103−303−30000−i6i6−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000
χ534-44-4400-44-40000000044-44-4-4-4400004-44-40000000000000000000000000000000000000000000000
χ544-44-4400-44-4000000004-22-2-42-440000-22-220000000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ554-44-4400-44-4000000004-22-2-42-440000-22-220000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ564-44-4400-44-400000000-24-442-42-223−23−2323-22-220−2323023−230000000000000000000000000000000000000000
χ574-44-4400-44-400000000-24-442-42-2−232323−23-22-22023−230−23230000000000000000000000000000000000000000
χ584-44-4400-44-400000000-2-22-2222-223−23−23231-11-103−30−330000i6−i6−i6i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000
χ594-44-4400-44-400000000-2-22-2222-223−23−23231-11-103−30−330000−i6i6i6−i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000
χ604-44-4400-44-400000000-2-22-2222-2−232323−231-11-10−3303−30000i6−i6−i6i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000
χ614-44-4400-44-400000000-2-22-2222-2−232323−231-11-10−3303−30000−i6i6i6−i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000
χ624-4-4444-4-4-444-4-4444-4-4-2-222-2-222-2-2221-1-112-1-1-211-22-22-2-22211-1-111-1-1000000000000000000000000
χ634-4-4444-4-4-44-44-44-4-444-2-222-2-222-2-2221-1-112-1-1-2112-22-222-2-2-1-111-1-111000000000000000000000000
χ644-4-444-44-4-44004-400004-2224-2-4-4-4-444-222-2-2-2-22220000000000000000000000000000000000000000
χ654-4-444-44-4-44004-40000-2-222-2-22222-2-21-1-11-2112-1-123−23−23230000−3−33333−3−3000000000000000000000000
χ664-4-444-44-4-44004-40000-2-222-2-22222-2-21-1-11-2112-1-1−232323−23000033−3−3−3−333000000000000000000000000
χ676666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000000000000022-1-10000-1-1
χ686666-366-3-3-366-3-3-3-3-3-30000000000000000000000000000000000000000000000000000-2-211000011
χ696666-366-3-3-3-6-6-3-3333300000000000000000000000000000000000000000000000000002-2-1-1000011
χ706666-366-3-3-3-6-6-3-333330000000000000000000000000000000000000000000000000000-22110000-1-1
χ716-6-66-36-633-36-63-3-3-333000000000000000000000000000000000000000000000000000000−i3i30000−i3i3
χ726-6-66-36-633-36-63-3-3-333000000000000000000000000000000000000000000000000000000i3−i30000i3−i3
χ736-6-66-36-633-3-663-333-3-3000000000000000000000000000000000000000000000000000000−i3i30000i3−i3
χ746-6-66-36-633-3-663-333-3-3000000000000000000000000000000000000000000000000000000i3−i30000−i3i3
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-600-666000036−3636−3600000000000000000000000000000000000000000000000000000000000000
χ771212-12-12-600-6660000−3636−363600000000000000000000000000000000000000000000000000000000000000
χ7812-1212-12-6006-66000036−36−363600000000000000000000000000000000000000000000000000000000000000
χ7912-1212-12-6006-660000−363636−3600000000000000000000000000000000000000000000000000000000000000
χ8012-12-1212-6-121266-600-66000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.