Finite Group Databasebeta

← Group #13138977

Character table — Group #13138977

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636727272727272727272727272
order1222344666881212242424243366666612121212366612121212121224242424242424242424242424242424246688121224242424244466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-11-111-1-111-1-1
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11-11-1-111-1-111
χ71111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1111-1-1-1-111
χ81111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-1-11111-1-1
χ92222222222222222222-12-1-12-12-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ102222222222222222222-12-1-12-12-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ11222222222222222222-12-122-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1
χ12222222222222222222-12-122-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-200001111
χ132222222222-2-222-2-2-2-22-12-1-12-12-1-1-1-1-1-1-1-12-1-12-1-11111-2-2-2-21111111122-1-1-2-2-1-11111000000000000
χ142222222222-2-222-2-2-2-22-12-1-12-12-1-1-1-1-1-1-1-12-1-12-1-11111-2-2-2-211111111-2-2112211-1-1-1-1000000000000
χ152222222222-2-222-2-2-2-2-12-122-12-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000002-20000-1-111
χ162222222222-2-222-2-2-2-2-12-122-12-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000-22000011-1-1
χ1722222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-2-2-200000000000000002-22200-2-20000000000000000
χ1822222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-2-2-20000000000000000-22-2-200220000000000000000
χ1922222-2-222200-2-200002-12-1-12-121111-1-1-1-1-211-21133−3−300003333−3−3−3−32-2-1-1001133−3−3000000000000
χ2022222-2-222200-2-200002-12-1-12-121111-1-1-1-1-211-21133−3−300003333−3−3−3−3-221100-1-1−3−333000000000000
χ2122222-2-222200-2-200002-12-1-12-121111-1-1-1-1-211-211−3−3330000−3−3−3−333332-2-1-10011−3−333000000000000
χ2222222-2-222200-2-200002-12-1-12-121111-1-1-1-1-211-211−3−3330000−3−3−3−33333-221100-1-133−3−3000000000000
χ232-22-222-2-2-22002-2000022-2-2-222-222-2-22-2-22222-2-2-2000000000000000000002i−2i002i−2i2i−2i000000000000
χ242-22-222-2-2-22002-2000022-2-2-222-222-2-22-2-22222-2-2-200000000000000000000−2i2i00−2i2i−2i2i000000000000
χ252-22-222-2-2-22002-200002-1-2112-1-2-1-111-111-12-1-1-2113−33−3000033−3−333−3−300−i3i32i−2i−i3i3−ii−ii000000000000
χ262-22-222-2-2-22002-200002-1-2112-1-2-1-111-111-12-1-1-2113−33−3000033−3−333−3−300i3−i3−2i2ii3−i3i−ii−i000000000000
χ272-22-222-2-2-22002-200002-1-2112-1-2-1-111-111-12-1-1-211−33−330000−3−333−3−33300−i3i3−2i2i−i3i3i−ii−i000000000000
χ282-22-222-2-2-22002-200002-1-2112-1-2-1-111-111-12-1-1-211−33−330000−3−333−3−33300i3−i32i−2ii3−i3−ii−ii000000000000
χ292-22-22-22-2-222-2-2222-2-222-2-2-222-2-2-2222-2-22-2-2-22222-2-2222-2-222-2-2-2-222000000000000000000000000
χ302-22-22-22-2-222-2-2222-2-22-1-2112-1-211-1-1-111-1-2112-1-1-111-122-2-2-1-11111-1-100−i3i300i3−i3−i3i3i3−i3000000000000
χ312-22-22-22-2-222-2-2222-2-22-1-2112-1-211-1-1-111-1-2112-1-1-111-122-2-2-1-11111-1-100i3−i300−i3i3i3−i3−i3i3000000000000
χ322-22-22-22-2-222-2-2222-2-2-121-2-2-121-2-222-111-1111-1-1-12-2-22-1-111-1-11111-1-1000000000000000000003−33−3
χ332-22-22-22-2-222-2-2222-2-2-121-2-2-121-2-222-111-1111-1-1-12-2-22-1-111-1-11111-1-100000000000000000000−33−33
χ342-22-22-22-2-22-22-22-2-22222-2-2-222-2-2-2222-2-22-2-2-2222-222-2-2-222-2-22222-2-2000000000000000000000000
χ352-22-22-22-2-22-22-22-2-2222-1-2112-1-211-1-1-111-1-2112-1-11-1-11-2-22211-1-1-1-11100−i3i300i3−i3i3−i3−i3i3000000000000
χ362-22-22-22-2-22-22-22-2-2222-1-2112-1-211-1-1-111-1-2112-1-11-1-11-2-22211-1-1-1-11100i3−i300−i3i3−i3i3i3−i3000000000000
χ372-22-22-22-2-22-22-22-2-222-121-2-2-121-2-222-111-1111-1-1-1-222-211-1-111-1-1-1-111000000000000000000003−3−33
χ382-22-22-22-2-22-22-22-2-222-121-2-2-121-2-222-111-1111-1-1-1-222-211-1-111-1-1-1-11100000000000000000000−333−3
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
χ4144444-4-444400-4-40000-24-244-24-2-4-4-4-4-2-2-2-22222220000000000000000000000000000000000000000
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
χ4444-4-44004-4-4000000004444-4-4-4-4000044-4-40000000000000000000000000000000000000000000000
χ4544-4-44004-4-4000000004-24-22-42-423−2323−23-2-222023−23023−230000000000000000000000000000000000000000
χ4644-4-44004-4-4000000004-24-22-42-4−2323−2323-2-2220−23230−23230000000000000000000000000000000000000000
χ4744-4-44004-4-400000000-24-24-42-420000-2-2220000000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ4844-4-44004-4-400000000-24-24-42-420000-2-2220000000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ4944-4-44004-4-400000000-2-2-2-2222223−2323−2311-1-10−330−330000i6−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
χ5044-4-44004-4-400000000-2-2-2-2222223−2323−2311-1-10−330−330000−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
χ5144-4-44004-4-400000000-2-2-2-22222−2323−232311-1-103−303−30000i6−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
χ5244-4-44004-4-400000000-2-2-2-22222−2323−232311-1-103−303−30000−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
χ534-44-444-4-4-44004-40000-242-4-4-24244-4-4-222-2-2-2-22220000000000000000000000000000000000000000
χ544-44-444-4-4-44004-40000-2-2222-2-22-2-2221-1-11-2112-1-123−2323−230000−3−333−3−333000000000000000000000000
χ554-44-444-4-4-44004-40000-2-2222-2-22-2-2221-1-11-2112-1-1−2323−2323000033−3−333−3−3000000000000000000000000
χ564-44-44-44-4-444-4-4444-4-4-2-2222-2-2222-2-21-1-112-1-1-211-222-2-2-22211-1-1-1-111000000000000000000000000
χ574-44-44-44-4-44-44-44-4-444-2-2222-2-2222-2-21-1-112-1-1-2112-2-2222-2-2-1-11111-1-1000000000000000000000000
χ584-4-44400-44-40000000044-4-44-4-4400004-44-40000000000000000000000000000000000000000000000
χ594-4-44400-44-4000000004-2-42-2-42423−23−2323-22-22023−230−23230000000000000000000000000000000000000000
χ604-4-44400-44-4000000004-2-42-2-424−232323−23-22-220−2323023−230000000000000000000000000000000000000000
χ614-4-44400-44-400000000-242-442-4-20000-22-220000000000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ624-4-44400-44-400000000-242-442-4-20000-22-220000000000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ634-4-44400-44-400000000-2-222-222-223−23−23231-11-10−3303−30000i6−i6−i6i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000
χ644-4-44400-44-400000000-2-222-222-223−23−23231-11-10−3303−30000−i6i6i6−i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000
χ654-4-44400-44-400000000-2-222-222-2−232323−231-11-103−30−330000i6−i6−i6i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000
χ664-4-44400-44-400000000-2-222-222-2−232323−231-11-103−30−330000−i6i6i6−i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000
χ676666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000000000002200-1-1-1-10000
χ686666-366-3-3-366-3-3-3-3-3-300000000000000000000000000000000000000000000000000-2-20011110000
χ696666-366-3-3-3-6-6-3-33333000000000000000000000000000000000000000000000000002-200-1-1110000
χ706666-366-3-3-3-6-6-3-3333300000000000000000000000000000000000000000000000000-220011-1-10000
χ716-66-6-3-6633-36-63-3-3-333000000000000000000000000000000000000000000000000000000−i3i3−i3i30000
χ726-66-6-3-6633-36-63-3-3-333000000000000000000000000000000000000000000000000000000i3−i3i3−i30000
χ736-66-6-3-6633-3-663-333-3-3000000000000000000000000000000000000000000000000000000−i3i3i3−i30000
χ746-66-6-3-6633-3-663-333-3-3000000000000000000000000000000000000000000000000000000i3−i3−i3i30000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-600-666000036−3636−3600000000000000000000000000000000000000000000000000000000000000
χ771212-12-12-600-6660000−3636−363600000000000000000000000000000000000000000000000000000000000000
χ7812-1212-12-612-1266-600-66000000000000000000000000000000000000000000000000000000000000000000
χ7912-12-1212-6006-66000036−36−363600000000000000000000000000000000000000000000000000000000000000
χ8012-12-1212-6006-660000−363636−3600000000000000000000000000000000000000000000000000000000000000

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