Finite Group Databasebeta

← Group #13138952

Character table — Group #13138952

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order122234466688121224242424336666661212121236661212121212122424242424242424242424242424242444442244444488121212122424242466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ71111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111
χ81111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ91-11-11-11-11-1i−i1-1ii−i−i11-11-1-1-11-1-1111-1-11111-1-1-1ii−i−iiiiiii−i−i−i−i−i−ii−ii−i1-11-1i−ii−i1-1ii−i−i11-1-11-1i−ii−i1-1
χ101-11-11-11-11-1i−i1-1ii−i−i11-11-1-1-11-1-1111-1-11111-1-1-1ii−i−iiiiiii−i−i−i−i−i−ii−ii−i-11-11−ii−ii1-1ii−i−i11-1-1-11−ii−ii-11
χ111-11-11-11-11-1i−i1-1ii−i−i11-11-1-1-11-1-1111-1-11111-1-1-1ii−i−iiiiiii−i−i−i−i−i−i−ii−ii1-1-11i−i−ii-11−i−iii-1-1111-1i−i−ii-11
χ121-11-11-11-11-1i−i1-1ii−i−i11-11-1-1-11-1-1111-1-11111-1-1-1ii−i−iiiiiii−i−i−i−i−i−i−ii−ii-111-1−iii−i-11−i−iii-1-111-11−iii−i1-1
χ131-11-11-11-11-1−ii1-1−i−iii11-11-1-1-11-1-1111-1-11111-1-1-1−i−iii−i−i−i−i−i−iiiiiiii−ii−i1-1-11−iii−i-11ii−i−i-1-1111-1−iii−i-11
χ141-11-11-11-11-1−ii1-1−i−iii11-11-1-1-11-1-1111-1-11111-1-1-1−i−iii−i−i−i−i−i−iiiiiiii−ii−i-111-1i−i−ii-11ii−i−i-1-111-11i−i−ii1-1
χ151-11-11-11-11-1−ii1-1−i−iii11-11-1-1-11-1-1111-1-11111-1-1-1−i−iii−i−i−i−i−i−iiiiiii−ii−ii1-11-1−ii−ii1-1−i−iii11-1-11-1−ii−ii1-1
χ161-11-11-11-11-1−ii1-1−i−iii11-11-1-1-11-1-1111-1-11111-1-1-1−i−iii−i−i−i−i−i−iiiiiii−ii−ii-11-11i−ii−i1-1−i−iii11-1-1-11i−ii−i-11
χ172222222222222222222-12-1-1-122-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-122220000000022-1-1-1-1-1-1-1-100000000
χ182222222222222222222-12-1-1-122-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-200000000-2-21111111100000000
χ19222222222222222222-12-1222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000022002200000000000000-1-1-1-1
χ20222222222222222222-12-1222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-200-2-2000000000000001111
χ212222222222-2-222-2-2-2-22-12-1-1-122-1-1-1-1-1-1-1-12-1-12-1-11111-2-21111-2-21111222200000000-2-2-1-1-1-1111100000000
χ222222222222-2-222-2-2-2-22-12-1-1-122-1-1-1-1-1-1-1-12-1-12-1-11111-2-21111-2-21111-2-2-2-200000000221111-1-1-1-100000000
χ232222222222-2-222-2-2-2-2-12-1222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000002200-2-20000000000000011-1-1
χ242222222222-2-222-2-2-2-2-12-1222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000-2-2002200000000000000-1-111
χ2522222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-2-2-2000000000000000022-2-200000000002-22-2000000000000
χ2622222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-2-2-20000000000000000-2-2220000000000-22-22000000000000
χ2722222-2-222200-2-200002-12-1-1-1221111-1-1-1-1-211-2113−33−30033−3−30033−3−322-2-20000000000-11-113−33−300000000
χ2822222-2-222200-2-200002-12-1-1-1221111-1-1-1-1-211-2113−33−30033−3−30033−3−3-2-22200000000001-11-1−33−3300000000
χ2922222-2-222200-2-200002-12-1-1-1221111-1-1-1-1-211-211−33−3300−3−33300−3−33322-2-20000000000-11-11−33−3300000000
χ3022222-2-222200-2-200002-12-1-1-1221111-1-1-1-1-211-211−33−3300−3−33300−3−333-2-22200000000001-11-13−33−300000000
χ312-22-222-2-22-200-22000022-22-2-2-2222-2-22-2-22-2-2-222200000000000000002i−2i−2i2i00000000002i−2i−2i2i000000000000
χ322-22-222-2-22-200-22000022-22-2-2-2222-2-22-2-22-2-2-22220000000000000000−2i2i2i−2i0000000000−2i2i2i−2i000000000000
χ332-22-222-2-22-200-2200002-1-2-111-22-1-111-111-1-2112-1-1−i3i3i3−i300−i3−i3i3i300i3i3−i3−i32i−2i−2i2i0000000000−iii−i−333−300000000
χ342-22-222-2-22-200-2200002-1-2-111-22-1-111-111-1-2112-1-1−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3−2i2i2i−2i0000000000i−i−ii3−3−3300000000
χ352-22-222-2-22-200-2200002-1-2-111-22-1-111-111-1-2112-1-1i3−i3−i3i300i3i3−i3−i300−i3−i3i3i32i−2i−2i2i0000000000−iii−i3−3−3300000000
χ362-22-222-2-22-200-2200002-1-2-111-22-1-111-111-1-2112-1-1i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3−2i2i2i−2i0000000000i−i−ii−333−300000000
χ372-22-22-22-22-22i−2i2-22i2i−2i−2i2-1-2-111-2211-1-1-111-12-1-1-211−i−iii2i2i−i−i−i−i−2i−2iiiii2i−2i2i−2i000000002-2−i−iii-1-11100000000
χ382-22-22-22-22-22i−2i2-22i2i−2i−2i2-1-2-111-2211-1-1-111-12-1-1-211−i−iii2i2i−i−i−i−i−2i−2iiiii−2i2i−2i2i00000000-22ii−i−i11-1-100000000
χ392-22-22-22-22-22i−2i2-22i2i−2i−2i-1212-2-21-1-2-222-111-1-1-1-11112i2i−2i−2i−i−i−i−i−i−iiiiiii0000002-2002i−2i00000000000000−ii-11
χ402-22-22-22-22-22i−2i2-22i2i−2i−2i-1212-2-21-1-2-222-111-1-1-1-11112i2i−2i−2i−i−i−i−i−i−iiiiiii000000-2200−2i2i00000000000000i−i1-1
χ412-22-22-22-22-2−2i2i2-2−2i−2i2i2i2-1-2-111-2211-1-1-111-12-1-1-211ii−i−i−2i−2iiiii2i2i−i−i−i−i2i−2i2i−2i00000000-22−i−iii11-1-100000000
χ422-22-22-22-22-2−2i2i2-2−2i−2i2i2i2-1-2-111-2211-1-1-111-12-1-1-211ii−i−i−2i−2iiiii2i2i−i−i−i−i−2i2i−2i2i000000002-2ii−i−i-1-11100000000
χ432-22-22-22-22-2−2i2i2-2−2i−2i2i2i-1212-2-21-1-2-222-111-1-1-1-1111−2i−2i2i2iiiiiii−i−i−i−i−i−i0000002-200−2i2i00000000000000i−i-11
χ442-22-22-22-22-2−2i2i2-2−2i−2i2i2i-1212-2-21-1-2-222-111-1-1-1-1111−2i−2i2i2iiiiiii−i−i−i−i−i−i000000-22002i−2i00000000000000−ii1-1
χ45444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-211-211-2-2-2-2-2-21111-2-21111000000000000000000000000000000
χ464444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-21111-211-211222222-1-1-1-122-1-1-1-1000000000000000000000000000000
χ4744444-4-444400-4-40000-24-2444-2-2-4-4-4-4-2-2-2-22222220000000000000000000000000000000000000000000000
χ4844444-4-444400-4-40000-2-2-2-2-2-2-2-2222211112-1-12-1-123−2323−2300−3−33300−3−333000000000000000000000000000000
χ4944444-4-444400-4-40000-2-2-2-2-2-2-2-2222211112-1-12-1-1−2323−23230033−3−30033−3−3000000000000000000000000000000
χ5044-4-44004-4-400000000444-44-4-4-4000044-4-40000000000000000000000000000000000000000000000000000
χ5144-4-44004-4-4000000004-242-22-4-423−2323−23-2-222023−23023−230000000000000000000000000000000000000000000000
χ5244-4-44004-4-4000000004-242-22-4-4−2323−2323-2-2220−23230−23230000000000000000000000000000000000000000000000
χ5344-4-44004-4-400000000-24-2-44-4220000-2-2220000000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ5444-4-44004-4-400000000-24-2-44-4220000-2-2220000000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ5544-4-44004-4-400000000-2-2-22-222223−2323−2311-1-10−330−330000i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000000000
χ5644-4-44004-4-400000000-2-2-22-222223−2323−2311-1-10−330−330000−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000000000
χ5744-4-44004-4-400000000-2-2-22-2222−2323−232311-1-103−303−30000i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000000000
χ5844-4-44004-4-400000000-2-2-22-2222−2323−232311-1-103−303−30000−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000000000
χ594-44-444-4-44-400-440000-2424-4-42-244-4-4-222-2222-2-2-20000000000000000000000000000000000000000000000
χ604-44-444-4-44-400-440000-2-22-2222-2-2-2221-1-112-1-1-211−2i32i32i3−2i300i3i3−i3−i300−i3−i3i3i3000000000000000000000000000000
χ614-44-444-4-44-400-440000-2-22-2222-2-2-2221-1-112-1-1-2112i3−2i3−2i32i300−i3−i3i3i300i3i3−i3−i3000000000000000000000000000000
χ624-44-44-44-44-44i−4i4-44i4i−4i−4i-2-22-2222-222-2-21-1-11-2112-1-1−2i−2i2i2i−2i−2iiiii2i2i−i−i−i−i000000000000000000000000000000
χ634-44-44-44-44-4−4i4i4-4−4i−4i4i4i-2-22-2222-222-2-21-1-11-2112-1-12i2i−2i−2i2i2i−i−i−i−i−2i−2iiiii000000000000000000000000000000
χ644-4-44400-4-440000000044-4-4-444-400004-44-40000000000000000000000000000000000000000000000000000
χ654-4-44400-4-44000000004-2-422-24-423−23−2323-22-220−2323023−230000000000000000000000000000000000000000000000
χ664-4-44400-4-44000000004-2-422-24-4−232323−23-22-22023−230−23230000000000000000000000000000000000000000000000
χ674-4-44400-4-4400000000-242-4-44-220000-22-2200000000006−66−66−6−66−66−66000000000000000000000000000000
χ684-4-44400-4-4400000000-242-4-44-220000-22-220000000000−66−66−666−66−66−6000000000000000000000000000000
χ694-4-44400-4-4400000000-2-2222-2-2223−23−23231-11-103−30−3300006−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−662ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23000000000000000000000000000000
χ704-4-44400-4-4400000000-2-2222-2-2223−23−23231-11-103−30−330000−662ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ236−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23000000000000000000000000000000
χ714-4-44400-4-4400000000-2-2222-2-22−232323−231-11-10−3303−300006−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23000000000000000000000000000000
χ724-4-44400-4-4400000000-2-2222-2-22−232323−231-11-10−3303−30000−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ236−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23000000000000000000000000000000
χ736666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000220022000000000000-1-1-1-10000
χ746666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000-2-200-2-200000000000011110000
χ756666-366-3-3-3-6-6-3-333330000000000000000000000000000000000000000002200-2-2000000000000-1-1110000
χ766666-366-3-3-3-6-6-3-33333000000000000000000000000000000000000000000-2-2002200000000000011-1-10000
χ776-66-6-3-663-336i−6i-33−3i−3i3i3i0000000000000000000000000000000000000000002-2002i−2i000000000000-11−ii0000
χ786-66-6-3-663-336i−6i-33−3i−3i3i3i000000000000000000000000000000000000000000-2200−2i2i0000000000001-1i−i0000
χ796-66-6-3-663-33−6i6i-333i3i−3i−3i0000000000000000000000000000000000000000002-200−2i2i000000000000-11i−i0000
χ806-66-6-3-663-33−6i6i-333i3i−3i−3i000000000000000000000000000000000000000000-22002i−2i0000000000001-1−ii0000
χ8112121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-600-666000036−3636−3600000000000000000000000000000000000000000000000000000000000000000000
χ831212-12-12-600-6660000−3636−363600000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-612-126-66006-6000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-60066-600003i6−3i6−3i63i600000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-60066-60000−3i63i63i6−3i600000000000000000000000000000000000000000000000000000000000000000000

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