Finite Group Databasebeta

← Group #13138991

Character table — Group #13138991

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636727272727272727272727272
order1222344666881212242424243366666612121212366612121212121224242424242424242424242424242424246688121224242424244466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1
χ51111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-111111-1-1-1-1
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-1-1-1-11111
χ71111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-111-1-1
χ81111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-111
χ92222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000002020-1-10000-1-1
χ102222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-20-2011000011
χ11222222222222222222-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ12222222222222222222-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ132222222222-2-222-2-2-2-22-122-1-12-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000020-20-1-1000011
χ142222222222-2-222-2-2-2-22-122-1-12-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000-2020110000-1-1
χ152222222222-2-222-2-2-2-2-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-11111-2-2-2-21111111122-1-1-2-2-1-11111000000000000
χ162222222222-2-222-2-2-2-2-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-11111-2-2-2-211111111-2-2112211-1-1-1-1000000000000
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
χ1922222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-21133−3−300003333−3−3−3−32-2-1-1001133−3−3000000000000
χ2022222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-21133−3−300003333−3−3−3−3-221100-1-1−3−333000000000000
χ2122222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-211−3−3330000−3−3−3−333332-2-1-10011−3−333000000000000
χ2222222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-211−3−3330000−3−3−3−33333-221100-1-133−3−3000000000000
χ232-22-222-2-2-222i−2i2-22i2i−2i−2i22-2-2-222-222-2-22-2-22222-2-2-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ242-22-222-2-2-222i−2i2-22i2i−2i−2i2-1-2-21-12122-2-2-111-1-1-1-11112i−2i2i−2i−i−iii−i−iii−i−iii0000000000000000−i3i300003−3
χ252-22-222-2-2-222i−2i2-22i2i−2i−2i2-1-2-21-12122-2-2-111-1-1-1-11112i−2i2i−2i−i−iii−i−iii−i−iii0000000000000000i3−i30000−33
χ262-22-222-2-2-222i−2i2-22i2i−2i−2i-1211-22-1-2-1-111-111-12-1-1-211−ii−ii2i2i−2i−2i−i−iii−i−iii00−i3i300−i3i33−33−3000000000000
χ272-22-222-2-2-222i−2i2-22i2i−2i−2i-1211-22-1-2-1-111-111-12-1-1-211−ii−ii2i2i−2i−2i−i−iii−i−iii00i3−i300i3−i3−33−33000000000000
χ282-22-222-2-2-22−2i2i2-2−2i−2i2i2i22-2-2-222-222-2-22-2-22222-2-2-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ292-22-222-2-2-22−2i2i2-2−2i−2i2i2i2-1-2-21-12122-2-2-111-1-1-1-1111−2i2i−2i2iii−i−iii−i−iii−i−i0000000000000000−i3i30000−33
χ302-22-222-2-2-22−2i2i2-2−2i−2i2i2i2-1-2-21-12122-2-2-111-1-1-1-1111−2i2i−2i2iii−i−iii−i−iii−i−i0000000000000000i3−i300003−3
χ312-22-222-2-2-22−2i2i2-2−2i−2i2i2i-1211-22-1-2-1-111-111-12-1-1-211i−ii−i−2i−2i2i2iii−i−iii−i−i00−i3i300−i3i3−33−33000000000000
χ322-22-222-2-2-22−2i2i2-2−2i−2i2i2i-1211-22-1-2-1-111-111-12-1-1-211i−ii−i−2i−2i2i2iii−i−iii−i−i00i3−i300i3−i33−33−3000000000000
χ332-22-22-22-2-2200-22000022-2-2-222-2-2-2222-2-22-2-2-2222000000000000000000002-2002-2-22000000000000
χ342-22-22-22-2-2200-22000022-2-2-222-2-2-2222-2-22-2-2-222200000000000000000000-2200-222-2000000000000
χ352-22-22-22-2-2200-220000-1211-22-1-211-1-1-111-1-2112-1-1−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i300−i3i32-2i3−i3-111-1000000000000
χ362-22-22-22-2-2200-220000-1211-22-1-211-1-1-111-1-2112-1-1−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i300i3−i3-22−i3i31-1-11000000000000
χ372-22-22-22-2-2200-220000-1211-22-1-211-1-1-111-1-2112-1-1i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i300−i3i3-22i3−i31-1-11000000000000
χ382-22-22-22-2-2200-220000-1211-22-1-211-1-1-111-1-2112-1-1i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i300i3−i32-2−i3i3-111-1000000000000
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
χ4144444-4-444400-4-400004-244-2-24-2-4-4-4-4-2-2-2-22222220000000000000000000000000000000000000000
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
χ4444-4-44004-4-400000000444-44-4-4-4000044-4-40000000000000000000000000000000000000000000000
χ4544-4-44004-4-4000000004-24-4-22-420000-2-22200000000006−66−66−66−66−66−6000000000000000000000000
χ4644-4-44004-4-4000000004-24-4-22-420000-2-2220000000000−66−66−66−66−66−66000000000000000000000000
χ4744-4-44004-4-400000000-24-224-42-423−2323−23-2-222023−23023−230000000000000000000000000000000000000000
χ4844-4-44004-4-400000000-24-224-42-4−2323−2323-2-2220−23230−23230000000000000000000000000000000000000000
χ4944-4-44004-4-400000000-2-2-22-222223−2323−2311-1-10−330−3300006−66−6−2ζ5+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
χ5044-4-44004-4-400000000-2-2-22-222223−2323−2311-1-10−330−330000−66−662ζ5−2ζ7+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
χ5144-4-44004-4-400000000-2-2-22-2222−2323−232311-1-103−303−300006−66−6ζ5−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
χ5244-4-44004-4-400000000-2-2-22-2222−2323−232311-1-103−303−30000−66−66−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
χ534-44-444-4-4-444i−4i4-44i4i−4i−4i-2-2222-2-22-2-2221-1-11-2112-1-1−2i2i−2i2i−2i−2i2i2iii−i−iii−i−i000000000000000000000000
χ544-44-444-4-4-44−4i4i4-4−4i−4i4i4i-2-2222-2-22-2-2221-1-11-2112-1-12i−2i2i−2i2i2i−2i−2i−i−iii−i−iii000000000000000000000000
χ554-44-44-44-4-4400-4400004-2-4-42-242-4-444-222-2222-2-2-20000000000000000000000000000000000000000
χ564-44-44-44-4-4400-440000-2-2222-2-2222-2-21-1-112-1-1-211−2i32i32i3−2i30000i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ574-44-44-44-4-4400-440000-2-2222-2-2222-2-21-1-112-1-1-2112i3−2i3−2i32i30000−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ584-4-44400-44-40000000044-44-4-4-4400004-44-40000000000000000000000000000000000000000000000
χ594-4-44400-44-4000000004-2-4422-4-20000-22-220000000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ604-4-44400-44-4000000004-2-4422-4-20000-22-220000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ614-4-44400-44-400000000-242-2-4-42423−23−2323-22-22023−230−23230000000000000000000000000000000000000000
χ624-4-44400-44-400000000-242-2-4-424−232323−23-22-220−2323023−230000000000000000000000000000000000000000
χ634-4-44400-44-400000000-2-22-2222-223−23−23231-11-10−3303−30000i6−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
χ644-4-44400-44-400000000-2-22-2222-223−23−23231-11-10−3303−30000−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
χ654-4-44400-44-400000000-2-22-2222-2−232323−231-11-103−30−330000i6−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
χ664-4-44400-44-400000000-2-22-2222-2−232323−231-11-103−30−330000−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
χ676666-366-3-3-366-3-3-3-3-3-300000000000000000000000000000000000000000000000000020200-1-1-1-100
χ686666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000000000000-20-200111100
χ696666-366-3-3-3-6-6-3-3333300000000000000000000000000000000000000000000000000020-20011-1-100
χ706666-366-3-3-3-6-6-3-33333000000000000000000000000000000000000000000000000000-20200-1-11100
χ716-66-6-36-633-36i−6i-33−3i−3i3i3i000000000000000000000000000000000000000000000000000000003−3−i3i300
χ726-66-6-36-633-36i−6i-33−3i−3i3i3i00000000000000000000000000000000000000000000000000000000−33i3−i300
χ736-66-6-36-633-3−6i6i-333i3i−3i−3i000000000000000000000000000000000000000000000000000000003−3i3−i300
χ746-66-6-36-633-3−6i6i-333i3i−3i−3i00000000000000000000000000000000000000000000000000000000−33−i3i300
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-600-66600003i6−3i63i6−3i600000000000000000000000000000000000000000000000000000000000000
χ771212-12-12-600-6660000−3i63i6−3i63i600000000000000000000000000000000000000000000000000000000000000
χ7812-1212-12-6-121266-6006-6000000000000000000000000000000000000000000000000000000000000000000
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.