Finite Group Databasebeta

← Group #13138863

Character table — Group #13138863

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order12442346661212121288242424243366121212123666661212121212122424242424242424242424242424242488882244448888121212122424242466121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-111-1-1-1-1-1-111111-11-111-1-1
χ611111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-111-1-1-1-11111-11-11-1-111
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1111111-1-1-1-11-11-1-1-111
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-11111-1-1-1-1-11-1111-1-1
χ911-1-1-1111-1-111-1-11-111-1-11111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1ii−i−i11-1-1i−ii−ii−iii−i−iii−i−i11-1-1i−ii−i
χ1011-1-1-1111-1-111-1-11-111-1-11111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1ii−i−i-1-111i−i−ii−iiii−i−iii−i−i-1-111−ii−ii
χ1111-1-1-1111-1-111-1-11-111-1-11111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1−i−iii11-1-1−ii−ii−ii−i−iii−i−iii11-1-1−ii−ii
χ1211-1-1-1111-1-111-1-11-111-1-11111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1−i−iii-1-111−iii−ii−i−i−iii−i−iii-1-111i−ii−i
χ1311-1-1-1111-1-111-1-1-11-1-1111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111ii−i−i1-1-11−iii−i−ii−i−iiiii−i−i1-1-11i−i−ii
χ1411-1-1-1111-1-111-1-1-11-1-1111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111ii−i−i-111-1−ii−iii−i−i−iiiii−i−i-111-1−iii−i
χ1511-1-1-1111-1-111-1-1-11-1-1111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111−i−iii1-1-11i−i−iii−iii−i−i−i−iii1-1-11−iii−i
χ1611-1-1-1111-1-111-1-1-11-1-1111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111−i−iii-111-1i−ii−i−iiii−i−i−i−iii-111-1i−i−ii
χ17222222222222222222222-12-1-1-122-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000222200000000000000-1-1-1-10000
χ18222222222222222222222-12-1-1-122-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-20000000000000011110000
χ1922222222222222222222-12-1222-1-1-1-12-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000002222000000000000-1-1-1-1
χ2022222222222222222222-12-1222-1-1-1-12-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000000000-2-2-2-20000000000001111
χ2122222222222222-2-2-2-2-2-22-12-1-1-122-12-1-1-1-1-1-12-1-1-1-2-2111111-2-211111100002-22-200000000000000-11-110000
χ2222222222222222-2-2-2-2-2-22-12-1-1-122-12-1-1-1-1-1-12-1-1-1-2-2111111-2-21111110000-22-22000000000000001-11-10000
χ2322222222222222-2-2-2-2-2-2-12-1222-1-1-1-12-1-1-1-1-1-12-1-111-2-2111111-2-21111000000000022-2-2000000000000-1-111
χ2422222222222222-2-2-2-2-2-2-12-1222-1-1-1-12-1-1-1-1-1-12-1-111-2-2111111-2-211110000000000-2-22200000000000011-1-1
χ252222-22-22-2-2-2-222000000222222222-2-2-2-2222-2-2-2-200000000000000002-22-2000000000000002-22-200000000
χ262222-22-22-2-2-2-222000000222222222-2-2-2-2222-2-2-2-20000000000000000-22-2200000000000000-22-2200000000
χ2722-2-222-2222-2-2-2-20000002222-2-2-2-2222222-2-2-2-2-2-200000000000000002i−2i−2i2i000000000000002i−2i−2i2i00000000
χ2822-2-222-2222-2-2-2-20000002222-2-2-2-2222222-2-2-2-2-2-20000000000000000−2i2i2i−2i00000000000000−2i2i2i−2i00000000
χ2922-2-2-2222-2-222-2-22-222-2-22-12-111-2-2-1-2111-1112-1-1-122-1-1-1-1-1-1-2-2111111000022-2-200000000000000-1-1110000
χ3022-2-2-2222-2-222-2-22-222-2-22-12-111-2-2-1-2111-1112-1-1-122-1-1-1-1-1-1-2-21111110000-2-2220000000000000011-1-10000
χ3122-2-2-2222-2-222-2-22-222-2-2-12-12-2-211-11-211-111-12-1-1-1-122-1-1-1-111-2-2111100000000002i−2i2i−2i000000000000−ii−ii
χ3222-2-2-2222-2-222-2-22-222-2-2-12-12-2-211-11-211-111-12-1-1-1-122-1-1-1-111-2-211110000000000−2i2i−2i2i000000000000i−ii−i
χ3322-2-2-2222-2-222-2-2-22-2-2222-12-111-2-2-1-2111-1112-1-1-1-2-211111122-1-1-1-1-1-100002-2-2200000000000000-111-10000
χ3422-2-2-2222-2-222-2-2-22-2-2222-12-111-2-2-1-2111-1112-1-1-1-2-211111122-1-1-1-1-1-10000-222-2000000000000001-1-110000
χ3522-2-2-2222-2-222-2-2-22-2-222-12-12-2-211-11-211-111-12-1-111-2-21111-1-122-1-1-1-100000000002i−2i−2i2i000000000000−iii−i
χ3622-2-2-2222-2-222-2-2-22-2-222-12-12-2-211-11-211-111-12-1-111-2-21111-1-122-1-1-1-10000000000−2i2i2i−2i000000000000i−i−ii
χ3744444444444444444444-2-2-2-2-2-2-2-21-2-211111-2-211-2-2-2-21111-2-2-2-21111000000000000000000000000000000
χ3844444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-21-2-211111-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000000
χ394444-44-44-4-4-4-4440000004-24-2-2-244-2-4222-2-2-2-42220000000000000000000000000000000000000000000000
χ404444-44-44-4-4-4-444000000-24-2444-2-2-22-422-2-2-22-4220000000000000000000000000000000000000000000000
χ414444-44-44-4-4-4-444000000-2-2-2-2-2-2-2-2122-1-111122-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000
χ424444-44-44-4-4-4-444000000-2-2-2-2-2-2-2-2122-1-111122-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000
χ4344-4-444-4444-4-4-4-40000004-24-222-4-4-24-2-2-2-222-42220000000000000000000000000000000000000000000000
χ4444-4-444-4444-4-4-4-4000000-24-24-4-422-2-24-2-2-2222-4220000000000000000000000000000000000000000000000
χ4544-4-444-4444-4-4-4-4000000-2-2-2-222221-2-2111-1-122-1-100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000
χ4644-4-444-4444-4-4-4-4000000-2-2-2-222221-2-2111-1-122-1-10000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000
χ4744-4-4-4444-4-444-4-44-444-4-4-2-2-2-22222122-1-11-1-1-2-211-2-2-2-211112222-1-1-1-1000000000000000000000000000000
χ4844-4-4-4444-4-444-4-4-44-4-444-2-2-2-22222122-1-11-1-1-2-2112222-1-1-1-1-2-2-2-21111000000000000000000000000000000
χ494-44i−4i040-400004i−4i00000044-4-44i−4i4i−4i40000-44i−4i00000000000000000000000000000000000000000000000000
χ504-44i−4i040-400004i−4i0000004-2-42−2i2i4i−4i-200002−2i2i000000i6−i6i6−i6i6−i6006−66−66−6000000000000000000000000000000
χ514-44i−4i040-400004i−4i0000004-2-42−2i2i4i−4i-200002−2i2i000000−i6i6−i6i6−i6i600−66−66−66000000000000000000000000000000
χ524-44i−4i040-400004i−4i000000-242-44i−4i−2i2i-200002−2i2i00006−6006−6−66i6−i600−i6i6i6−i6000000000000000000000000000000
χ534-44i−4i040-400004i−4i000000-242-44i−4i−2i2i-200002−2i2i0000−6600−666−6−i6i600i6−i6−i6i6000000000000000000000000000000
χ544-44i−4i040-400004i−4i000000-2-222−2i2i−2i2i1003-3-1i−i003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ554-44i−4i040-400004i−4i000000-2-222−2i2i−2i2i1003-3-1i−i003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ564-44i−4i040-400004i−4i000000-2-222−2i2i−2i2i100-33-1i−i00−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ574-44i−4i040-400004i−4i000000-2-222−2i2i−2i2i100-33-1i−i00−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ584-4−4i4i040-40000−4i4i00000044-4-4−4i4i−4i4i40000-4−4i4i00000000000000000000000000000000000000000000000000
χ594-4−4i4i040-40000−4i4i0000004-2-422i−2i−4i4i-2000022i−2i000000i6−i6i6−i6i6−i600−66−66−66000000000000000000000000000000
χ604-4−4i4i040-40000−4i4i0000004-2-422i−2i−4i4i-2000022i−2i000000−i6i6−i6i6−i6i6006−66−66−6000000000000000000000000000000
χ614-4−4i4i040-40000−4i4i000000-242-4−4i4i2i−2i-2000022i−2i00006−6006−6−66−i6i600i6−i6−i6i6000000000000000000000000000000
χ624-4−4i4i040-40000−4i4i000000-242-4−4i4i2i−2i-2000022i−2i0000−6600−666−6i6−i600−i6i6i6−i6000000000000000000000000000000
χ634-4−4i4i040-40000−4i4i000000-2-2222i−2i2i−2i1003-3-1−ii00−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ644-4−4i4i040-40000−4i4i000000-2-2222i−2i2i−2i1003-3-1−ii00−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ654-4−4i4i040-40000−4i4i000000-2-2222i−2i2i−2i100-33-1−ii003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ664-4−4i4i040-40000−4i4i000000-2-2222i−2i2i−2i100-33-1−ii003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ6766666-36-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000022220000220000-1-1-1-1-1-1-1-100000000
χ6866666-36-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-2-2-20000-2-200001111111100000000
χ6966666-36-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000022220000-2-200001111-1-1-1-100000000
χ7066666-36-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-2-2-20000220000-1-1-1-1111100000000
χ716666-6-3-6-33333-3-30033−3333−330000000000000000000000000000000000002-22-200000000003−33−3-11-1100000000
χ726666-6-3-6-33333-3-30033−3333−33000000000000000000000000000000000000-22-220000000000−33−331-11-100000000
χ736666-6-3-6-33333-3-300−3333−33330000000000000000000000000000000000002-22-20000000000−33−33-11-1100000000
χ746666-6-3-6-33333-3-300−3333−3333000000000000000000000000000000000000-22-2200000000003−33−31-11-100000000
χ7566-6-66-3-6-3-3-333330033−33−33330000000000000000000000000000000000002i−2i−2i2i0000000000i3−i3−i3i3−iii−i00000000
χ7666-6-66-3-6-3-3-333330033−33−3333000000000000000000000000000000000000−2i2i2i−2i0000000000−i3i3i3−i3i−i−ii00000000
χ7766-6-66-3-6-3-3-3333300−333333−330000000000000000000000000000000000002i−2i−2i2i0000000000−i3i3i3−i3−iii−i00000000
χ7866-6-66-3-6-3-3-3333300−333333−33000000000000000000000000000000000000−2i2i2i−2i0000000000i3−i3−i3i3i−i−ii00000000
χ7966-6-6-6-36-333-3-3336-6-3-3330000000000000000000000000000000000002i2i−2i−2i00002i−2i0000−i−iii−i−iii00000000
χ8066-6-6-6-36-333-3-3336-6-3-333000000000000000000000000000000000000−2i−2i2i2i0000−2i2i0000ii−i−iii−i−i00000000
χ8166-6-6-6-36-333-3-333-6633-3-30000000000000000000000000000000000002i2i−2i−2i0000−2i2i0000ii−i−i−i−iii00000000
χ8266-6-6-6-36-333-3-333-6633-3-3000000000000000000000000000000000000−2i−2i2i2i00002i−2i0000−i−iiiii−i−i00000000
χ8312-1212i−12i0-606−6i36i363−63−6i6i000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212i−12i0-6066i3−6i3−6363−6i6i000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12−12i12i0-606−6i36i3−63636i−6i000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12−12i12i0-6066i3−6i363−636i−6i000000000000000000000000000000000000000000000000000000000000000000000000

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