Finite Group Databasebeta

← Group #13139002

Character table — Group #13139002

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636727272727272727272727272
order12223446668812122424242433666666121212123666121212121212242424242424242424242424242424244488121212122424242444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111
χ51111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111
χ71111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111
χ81111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-11111-1-1
χ92222222222222222222-12-1-1-122-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ102222222222222222222-12-1-1-122-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ11222222222222222222-12-1222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000002020000-1-1-1-1
χ12222222222222222222-12-1222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000-20-200001111
χ132222222222-2-222-2-2-2-22-12-1-1-122-1-1-1-1-1-1-1-12-1-12-1-11111-2-2-2-21111111122-2-2-1-1-1-11111000000000000
χ142222222222-2-222-2-2-2-22-12-1-1-122-1-1-1-1-1-1-1-12-1-12-1-11111-2-2-2-211111111-2-2221111-1-1-1-1000000000000
χ152222222222-2-222-2-2-2-2-12-1222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000020-20000-1-111
χ162222222222-2-222-2-2-2-2-12-1222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000000000-202000011-1-1
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
χ1922222-2-222200-2-200002-12-1-1-1221111-1-1-1-1-211-21133−3−300003333−3−3−3−32-200-1-11133−3−3000000000000
χ2022222-2-222200-2-200002-12-1-1-1221111-1-1-1-1-211-21133−3−300003333−3−3−3−3-220011-1-1−3−333000000000000
χ2122222-2-222200-2-200002-12-1-1-1221111-1-1-1-1-211-211−3−3330000−3−3−3−333332-200-1-111−3−333000000000000
χ2222222-2-222200-2-200002-12-1-1-1221111-1-1-1-1-211-211−3−3330000−3−3−3−33333-220011-1-133−3−3000000000000
χ232-2-2222-2-2-2200-22000022-22-2-2-2222-2-22-2-22-2-2-22220000000000000000002i−2i00002i−2i2i−2i000000000000
χ242-2-2222-2-2-2200-22000022-22-2-2-2222-2-22-2-22-2-2-2222000000000000000000−2i2i0000−2i2i−2i2i000000000000
χ252-2-2222-2-2-2200-2200002-1-2-111-22-1-111-111-1-2112-1-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3002i−2i3−33−3−ii−ii000000000000
χ262-2-2222-2-2-2200-2200002-1-2-111-22-1-111-111-1-2112-1-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i300−2i2i−33−33i−ii−i000000000000
χ272-2-2222-2-2-2200-2200002-1-2-111-22-1-111-111-1-2112-1-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3002i−2i−33−33−ii−ii000000000000
χ282-2-2222-2-2-2200-2200002-1-2-111-22-1-111-111-1-2112-1-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i300−2i2i3−33−3i−ii−i000000000000
χ292-2-222-22-2-222i−2i2-22i2i−2i−2i22-22-2-2-22-2-2222-2-22222-2-2-22i−2i−2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ302-2-222-22-2-222i−2i2-22i2i−2i−2i2-1-2-111-2211-1-1-111-12-1-1-211−iii−i2i2i−2i−2i−i−iiiii−i−i00003−3−33i3−i3−i3i3000000000000
χ312-2-222-22-2-222i−2i2-22i2i−2i−2i2-1-2-111-2211-1-1-111-12-1-1-211−iii−i2i2i−2i−2i−i−iiiii−i−i0000−333−3−i3i3i3−i3000000000000
χ322-2-222-22-2-222i−2i2-22i2i−2i−2i-1212-2-21-1-2-222-111-1-1-1-11112i−2i−2i2i−i−iii−i−iiiii−i−i000000000000000000003−3−i3i3
χ332-2-222-22-2-222i−2i2-22i2i−2i−2i-1212-2-21-1-2-222-111-1-1-1-11112i−2i−2i2i−i−iii−i−iiiii−i−i00000000000000000000−33i3−i3
χ342-2-222-22-2-22−2i2i2-2−2i−2i2i2i22-22-2-2-22-2-2222-2-22222-2-2-2−2i2i2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ352-2-222-22-2-22−2i2i2-2−2i−2i2i2i2-1-2-111-2211-1-1-111-12-1-1-211i−i−ii−2i−2i2i2iii−i−i−i−iii00003−3−33−i3i3i3−i3000000000000
χ362-2-222-22-2-22−2i2i2-2−2i−2i2i2i2-1-2-111-2211-1-1-111-12-1-1-211i−i−ii−2i−2i2i2iii−i−i−i−iii0000−333−3i3−i3−i3i3000000000000
χ372-2-222-22-2-22−2i2i2-2−2i−2i2i2i-1212-2-21-1-2-222-111-1-1-1-1111−2i2i2i−2iii−i−iii−i−i−i−iii000000000000000000003−3i3−i3
χ382-2-222-22-2-22−2i2i2-2−2i−2i2i2i-1212-2-21-1-2-222-111-1-1-1-1111−2i2i2i−2iii−i−iii−i−i−i−iii00000000000000000000−33−i3i3
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
χ4144444-4-444400-4-40000-24-2444-2-2-4-4-4-4-2-2-2-22222220000000000000000000000000000000000000000
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
χ4444-4-44004-4-40000000044-4-44-44-4000044-4-40000000000000000000000000000000000000000000000
χ4544-4-44004-4-4000000004-2-42-224-423−2323−23-2-222023−23023−230000000000000000000000000000000000000000
χ4644-4-44004-4-4000000004-2-42-224-4−2323−2323-2-2220−23230−23230000000000000000000000000000000000000000
χ4744-4-44004-4-400000000-242-44-4-220000-2-22200000000006−66−66−66−66−66−6000000000000000000000000
χ4844-4-44004-4-400000000-242-44-4-220000-2-2220000000000−66−66−66−66−66−66000000000000000000000000
χ4944-4-44004-4-400000000-2-222-22-2223−2323−2311-1-10−330−3300006−66−6−2ζ5+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
χ5044-4-44004-4-400000000-2-222-22-2223−2323−2311-1-10−330−330000−66−662ζ5−2ζ7+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
χ5144-4-44004-4-400000000-2-222-22-22−2323−232311-1-103−303−300006−66−6ζ5−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
χ5244-4-44004-4-400000000-2-222-22-22−2323−232311-1-103−303−30000−66−66−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
χ534-44-4400-44-400000000444-4-44-4-400004-44-40000000000000000000000000000000000000000000000
χ544-44-4400-44-4000000004-2422-2-4-423−23−2323-22-220−2323023−230000000000000000000000000000000000000000
χ554-44-4400-44-4000000004-2422-2-4-4−232323−23-22-22023−230−23230000000000000000000000000000000000000000
χ564-44-4400-44-400000000-24-2-4-44220000-22-220000000000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ574-44-4400-44-400000000-24-2-4-44220000-22-220000000000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ584-44-4400-44-400000000-2-2-222-22223−23−23231-11-103−30−330000i6−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
χ594-44-4400-44-400000000-2-2-222-22223−23−23231-11-103−30−330000−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
χ604-44-4400-44-400000000-2-2-222-222−232323−231-11-10−3303−30000i6−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
χ614-44-4400-44-400000000-2-2-222-222−232323−231-11-10−3303−30000−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
χ624-4-4444-4-4-4400-440000-2424-4-42-244-4-4-222-2222-2-2-20000000000000000000000000000000000000000
χ634-4-4444-4-4-4400-440000-2-22-2222-2-2-2221-1-112-1-1-211−2i32i3−2i32i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ644-4-4444-4-4-4400-440000-2-22-2222-2-2-2221-1-112-1-1-2112i3−2i32i3−2i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ654-4-444-44-4-444i−4i4-44i4i−4i−4i-2-22-2222-222-2-21-1-11-2112-1-1−2i2i2i−2i−2i−2i2i2iii−i−i−i−iii000000000000000000000000
χ664-4-444-44-4-44−4i4i4-4−4i−4i4i4i-2-22-2222-222-2-21-1-11-2112-1-12i−2i−2i2i2i2i−2i−2i−i−iiiii−i−i000000000000000000000000
χ676666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000000000002020-1-1-1-10000
χ686666-366-3-3-366-3-3-3-3-3-300000000000000000000000000000000000000000000000000-20-2011110000
χ696666-366-3-3-3-6-6-3-333330000000000000000000000000000000000000000000000000020-20-1-1110000
χ706666-366-3-3-3-6-6-3-3333300000000000000000000000000000000000000000000000000-202011-1-10000
χ716-6-66-3-6633-36i−6i-33−3i−3i3i3i0000000000000000000000000000000000000000000000000000003−3−i3i30000
χ726-6-66-3-6633-36i−6i-33−3i−3i3i3i000000000000000000000000000000000000000000000000000000−33i3−i30000
χ736-6-66-3-6633-3−6i6i-333i3i−3i−3i0000000000000000000000000000000000000000000000000000003−3i3−i30000
χ746-6-66-3-6633-3−6i6i-333i3i−3i−3i000000000000000000000000000000000000000000000000000000−33−i3i30000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-600-66600003i6−3i63i6−3i600000000000000000000000000000000000000000000000000000000000000
χ771212-12-12-600-6660000−3i63i6−3i63i600000000000000000000000000000000000000000000000000000000000000
χ7812-1212-12-6006-66000036−36−363600000000000000000000000000000000000000000000000000000000000000
χ7912-1212-12-6006-660000−363636−3600000000000000000000000000000000000000000000000000000000000000
χ8012-12-1212-612-1266-6006-6000000000000000000000000000000000000000000000000000000000000000000

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