Finite Group Databasebeta

← Group #13139046

Character table — Group #13139046

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order12223446668812122424242433666666121212123666121212121212242424242424242424242424242424242244222244446688121224242424666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111
χ71111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-111
χ81111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11111-1-1
χ911-1-111-1-11-1i−i1-1ii−i−i11-1-1-111-111-1-11-1-11111-1-1-1ii−i−iiiiiii−i−i−i−i−i−i1-11-11-11-1i−ii−i1-1i−i1-1ii−i−i1-11-1i−ii−i
χ1011-1-111-1-11-1i−i1-1ii−i−i11-1-1-111-111-1-11-1-11111-1-1-1ii−i−iiiiiii−i−i−i−i−i−i1-11-1-11-11−ii−ii1-1i−i1-1ii−i−i-11-11−ii−ii
χ1111-1-111-1-11-1i−i1-1ii−i−i11-1-1-111-111-1-11-1-11111-1-1-1ii−i−iiiiiii−i−i−i−i−i−i-11-111-1-11i−i−ii-11−ii-11−i−iii1-1-11i−i−ii
χ1211-1-111-1-11-1i−i1-1ii−i−i11-1-1-111-111-1-11-1-11111-1-1-1ii−i−iiiiiii−i−i−i−i−i−i-11-11-111-1−iii−i-11−ii-11−i−iii-111-1−iii−i
χ1311-1-111-1-11-1−ii1-1−i−iii11-1-1-111-111-1-11-1-11111-1-1-1−i−iii−i−i−i−i−i−iiiiiii1-11-11-11-1−ii−ii1-1−ii1-1−i−iii1-11-1−ii−ii
χ1411-1-111-1-11-1−ii1-1−i−iii11-1-1-111-111-1-11-1-11111-1-1-1−i−iii−i−i−i−i−i−iiiiiii1-11-1-11-11i−ii−i1-1−ii1-1−i−iii-11-11i−ii−i
χ1511-1-111-1-11-1−ii1-1−i−iii11-1-1-111-111-1-11-1-11111-1-1-1−i−iii−i−i−i−i−i−iiiiiii-11-111-1-11−iii−i-11i−i-11ii−i−i1-1-11−iii−i
χ1611-1-111-1-11-1−ii1-1−i−iii11-1-1-111-111-1-11-1-11111-1-1-1−i−iii−i−i−i−i−i−iiiiiii-11-11-111-1i−i−ii-11i−i-11ii−i−i-111-1i−i−ii
χ172222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000220022000000000000-1-100-1-1
χ182222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-200-2-2000000000000110011
χ19222222222222222222-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1222200000000-1-122-1-1-1-1-1-100000000
χ20222222222222222222-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-20000000011-2-211111100000000
χ212222222222-2-222-2-2-2-22-122-1-12-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000002200-2-2000000000000-1-10011
χ222222222222-2-222-2-2-2-22-122-1-12-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000-2-200220000000000001100-1-1
χ232222222222-2-222-2-2-2-2-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-11111-2-21111-2-21111222200000000-1-1-2-2-1-1111100000000
χ242222222222-2-222-2-2-2-2-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-11111-2-21111-2-21111-2-2-2-200000000112211-1-1-1-100000000
χ2522222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-2-2-2000000000000000022-2-2000000002200-2-2000000000000
χ2622222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-2-2-20000000000000000-2-22200000000-2-20022000000000000
χ2722222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-2113−33−30033−3−30033−3−322-2-200000000-1-100113−33−300000000
χ2822222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-2113−33−30033−3−30033−3−3-2-222000000001100-1-1−33−3300000000
χ2922222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-211−33−3300−3−33300−3−33322-2-200000000-1-10011−33−3300000000
χ3022222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-211−33−3300−3−33300−3−333-2-222000000001100-1-13−33−300000000
χ3122-2-222-2-22-22i−2i2-22i2i−2i−2i2-1-2-21-12122-2-2-111-1-1-1-11112i2i−2i−2i−i−i−i−i−i−iiiiiii0000002-2002i−2i000000000000-1100−ii
χ3222-2-222-2-22-22i−2i2-22i2i−2i−2i2-1-2-21-12122-2-2-111-1-1-1-11112i2i−2i−2i−i−i−i−i−i−iiiiiii000000-2200−2i2i0000000000001-100i−i
χ3322-2-222-2-22-22i−2i2-22i2i−2i−2i-1211-22-1-2-1-111-111-12-1-1-211−i−iii2i2i−i−i−i−i−2i−2iiiii2-22-200000000-112i−2i-11−i−iii00000000
χ3422-2-222-2-22-22i−2i2-22i2i−2i−2i-1211-22-1-2-1-111-111-12-1-1-211−i−iii2i2i−i−i−i−i−2i−2iiiii-22-22000000001-1−2i2i1-1ii−i−i00000000
χ3522-2-222-2-22-2−2i2i2-2−2i−2i2i2i2-1-2-21-12122-2-2-111-1-1-1-1111−2i−2i2i2iiiiiii−i−i−i−i−i−i0000002-200−2i2i000000000000-1100i−i
χ3622-2-222-2-22-2−2i2i2-2−2i−2i2i2i2-1-2-21-12122-2-2-111-1-1-1-1111−2i−2i2i2iiiiiii−i−i−i−i−i−i000000-22002i−2i0000000000001-100−ii
χ3722-2-222-2-22-2−2i2i2-2−2i−2i2i2i-1211-22-1-2-1-111-111-12-1-1-211ii−i−i−2i−2iiiii2i2i−i−i−i−i2-22-200000000-11−2i2i-11ii−i−i00000000
χ3822-2-222-2-22-2−2i2i2-2−2i−2i2i2i-1211-22-1-2-1-111-111-12-1-1-211ii−i−i−2i−2iiiii2i2i−i−i−i−i-22-22000000001-12i−2i1-1−i−iii00000000
χ3922-2-22-22-22-200-22000022-2-2-222-2-2-2222-2-22-2-2-222200000000000000002-2-22000000002-200-22000000000000
χ4022-2-22-22-22-200-22000022-2-2-222-2-2-2222-2-22-2-2-22220000000000000000-222-200000000-22002-2000000000000
χ4122-2-22-22-22-200-220000-1211-22-1-211-1-1-111-1-2112-1-1−i3i3i3−i300−i3−i3i3i300i3i3−i3−i32-2-2200000000-11001-1−i3i3i3−i300000000
χ4222-2-22-22-22-200-220000-1211-22-1-211-1-1-111-1-2112-1-1−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3-222-2000000001-100-11i3−i3−i3i300000000
χ4322-2-22-22-22-200-220000-1211-22-1-211-1-1-111-1-2112-1-1i3−i3−i3i300i3i3−i3−i300−i3−i3i3i32-2-2200000000-11001-1i3−i3−i3i300000000
χ4422-2-22-22-22-200-220000-1211-22-1-211-1-1-111-1-2112-1-1i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3-222-2000000001-100-11−i3i3i3−i300000000
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
χ4744444-4-444400-4-400004-244-2-24-2-4-4-4-4-2-2-2-22222220000000000000000000000000000000000000000000000
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
χ5044-4-444-4-44-44i−4i4-44i4i−4i−4i-2-2222-2-22-2-2221-1-11-2112-1-1−2i−2i2i2i−2i−2iiiii2i2i−i−i−i−i000000000000000000000000000000
χ5144-4-444-4-44-4−4i4i4-4−4i−4i4i4i-2-2222-2-22-2-2221-1-11-2112-1-12i2i−2i−2i2i2i−i−i−i−i−2i−2iiiii000000000000000000000000000000
χ5244-4-44-44-44-400-4400004-2-4-42-242-4-444-222-2222-2-2-20000000000000000000000000000000000000000000000
χ5344-4-44-44-44-400-440000-2-2222-2-2222-2-21-1-112-1-1-211−2i32i32i3−2i300i3i3−i3−i300−i3−i3i3i3000000000000000000000000000000
χ5444-4-44-44-44-400-440000-2-2222-2-2222-2-21-1-112-1-1-2112i3−2i3−2i32i300−i3−i3i3i300i3i3−i3−i3000000000000000000000000000000
χ554-44-44004-4-400000000444-4-4-4-44000044-4-40000000000000000000000000000000000000000000000000000
χ564-44-44004-4-4000000004-24-422-4-20000-2-2220000000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ574-44-44004-4-4000000004-24-422-4-20000-2-2220000000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ584-44-44004-4-400000000-24-22-4-42423−2323−23-2-222023−23023−230000000000000000000000000000000000000000000000
χ594-44-44004-4-400000000-24-22-4-424−2323−2323-2-2220−23230−23230000000000000000000000000000000000000000000000
χ604-44-44004-4-400000000-2-2-22222-223−2323−2311-1-10−330−330000i6−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
χ614-44-44004-4-400000000-2-2-22222-223−2323−2311-1-10−330−330000−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
χ624-44-44004-4-400000000-2-2-22222-2−2323−232311-1-103−303−30000i6−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
χ634-44-44004-4-400000000-2-2-22222-2−2323−232311-1-103−303−30000−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
χ644-4-44400-4-440000000044-444-4-4-400004-44-40000000000000000000000000000000000000000000000000000
χ654-4-44400-4-44000000004-2-44-22-420000-22-2200000000006−66−66−6−66−66−66000000000000000000000000000000
χ664-4-44400-4-44000000004-2-44-22-420000-22-220000000000−66−66−666−66−66−6000000000000000000000000000000
χ674-4-44400-4-4400000000-242-24-42-423−23−2323-22-22023−230−23230000000000000000000000000000000000000000000000
χ684-4-44400-4-4400000000-242-24-42-4−232323−23-22-220−2323023−230000000000000000000000000000000000000000000000
χ694-4-44400-4-4400000000-2-22-2-222223−23−23231-11-10−3303−300006−6ζ5−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
χ704-4-44400-4-4400000000-2-22-2-222223−23−23231-11-10−3303−30000−66−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
χ714-4-44400-4-4400000000-2-22-2-2222−232323−231-11-103−30−3300006−6−2ζ5+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
χ724-4-44400-4-4400000000-2-22-2-2222−232323−231-11-103−30−330000−662ζ5−2ζ7+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
χ736666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000220022000000000000-1-100-1-100
χ746666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000-2-200-2-200000000000011001100
χ756666-366-3-3-3-6-6-3-333330000000000000000000000000000000000000000002200-2-2000000000000-1-1001100
χ766666-366-3-3-3-6-6-3-33333000000000000000000000000000000000000000000-2-200220000000000001100-1-100
χ7766-6-6-36-63-336i−6i-33−3i−3i3i3i0000000000000000000000000000000000000000002-2002i−2i000000000000-1100−ii00
χ7866-6-6-36-63-336i−6i-33−3i−3i3i3i000000000000000000000000000000000000000000-2200−2i2i0000000000001-100i−i00
χ7966-6-6-36-63-33−6i6i-333i3i−3i−3i0000000000000000000000000000000000000000002-200−2i2i000000000000-1100i−i00
χ8066-6-6-36-63-33−6i6i-333i3i−3i−3i000000000000000000000000000000000000000000-22002i−2i0000000000001-100−ii00
χ8112121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6-12126-66006-6000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-600-666000036−3636−3600000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-600-6660000−3636−363600000000000000000000000000000000000000000000000000000000000000000000
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.