Finite Group Databasebeta

← Group #13149814

Character table — Group #13149814

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1244234666121212128824242424336612121212366666121212121212242424242424242424242424242424242244222244446688121224242424666612121212
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
χ511111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-11-11-111-1-111-1-1-1-11-11-11-11-1
χ611111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-11-1111-1-111-1-1-1-1-11-11-11-11
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11-1-111-1-111111-1-111-1-11
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-11111-111-1-111-1
χ911-1-1-111-1-11-1-1111-111-1-11111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-11-11-1111-1-1-1-111-11-11-111-1-1111-1-1-1-11
χ1011-1-1-111-1-11-1-1111-111-1-11111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-11-11-1-1-1-11111-11-11-11-111-1-1-1-1-11111-1
χ1111-1-1-111-1-11-1-1111-111-1-11111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-11-1111-11-1-11-1-11-11-11-1-11111-11-1-11-1
χ1211-1-1-111-1-11-1-1111-111-1-11111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-11-111-11-11-11-11-1-111-1-11-111-11
χ1311-1-1-111-1-11-1-111-11-1-1111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111111-11-11-111-11-1-11-1-111-1-1-1111-111-11-1-1
χ1411-1-1-111-1-11-1-111-11-1-1111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111111-11-1-11-1-11-1111-1-111-1-1-111-11-1-11-111
χ1511-1-1-111-1-11-1-111-11-1-1111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-11-111-1-1-1-1111-111-1-1111-1-11-1-1-1-1111
χ1611-1-1-111-1-11-1-111-11-1-1111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-11-11-11111-1-1-1-111-1-1111-1-1-11111-1-1-1
χ17222222222222222222222-12-122-1-1-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000220022000000000000-1-100-1-1
χ18222222222222222222222-12-122-1-1-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000-2-200-2-2000000000000110011
χ1922222222222222222222-12-12-1-122-1-12-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000220022000000000000-1-100-1-100
χ2022222222222222222222-12-12-1-122-1-12-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-200-2-200000000000011001100
χ2122222222222222-2-2-2-2-2-22-12-122-1-1-12-1-1-1-1-1-12-1-1-1-2-2111111-2-21111110000002-2002-2000000000000-1100-11
χ2222222222222222-2-2-2-2-2-22-12-122-1-1-12-1-1-1-1-1-12-1-1-1-2-2111111-2-2111111000000-2200-220000000000001-1001-1
χ2322222222222222-2-2-2-2-2-2-12-12-1-122-1-12-1-1-1-1-1-12-1-111-2-2111111-2-2111100002-2002-2000000000000-1100-1100
χ2422222222222222-2-2-2-2-2-2-12-12-1-122-1-12-1-1-1-1-1-12-1-111-2-2111111-2-211110000-2200-220000000000001-1001-100
χ252222-22-2-2-2222-2-2000000222222222-2-2-2-2222-2-2-2-200000000000000002-2-22000000002-200-22000000000000
χ262222-22-2-2-2222-2-2000000222222222-2-2-2-2222-2-2-2-20000000000000000-222-200000000-22002-2000000000000
χ2722-2-222-2222-2-2-2-20000002222-2-2-2-2222222-2-2-2-2-2-2000000000000000022-2-2000000002200-2-2000000000000
χ2822-2-222-2222-2-2-2-20000002222-2-2-2-2222222-2-2-2-2-2-20000000000000000-2-22200000000-2-20022000000000000
χ2922-2-2-222-2-22-2-2222-222-2-22-12-1-2-211-1-2111-1112-1-1-122-1-1-1-1-1-1-2-21111110000002-200-22000000000000-11001-1
χ3022-2-2-222-2-22-2-2222-222-2-22-12-1-2-211-1-2111-1112-1-1-122-1-1-1-1-1-1-2-2111111000000-22002-20000000000001-100-11
χ3122-2-2-222-2-22-2-2222-222-2-2-12-1211-2-2-11-211-111-12-1-1-1-122-1-1-1-111-2-2111100002200-2-2000000000000-1-1001100
χ3222-2-2-222-2-22-2-2222-222-2-2-12-1211-2-2-11-211-111-12-1-1-1-122-1-1-1-111-2-211110000-2-200220000000000001100-1-100
χ3322-2-2-222-2-22-2-222-22-2-2222-12-1-2-211-1-2111-1112-1-1-1-2-211111122-1-1-1-1-1-10000002200-2-2000000000000-1-10011
χ3422-2-2-222-2-22-2-222-22-2-2222-12-1-2-211-1-2111-1112-1-1-1-2-211111122-1-1-1-1-1-1000000-2-200220000000000001100-1-1
χ3522-2-2-222-2-22-2-222-22-2-222-12-1211-2-2-11-211-111-12-1-111-2-21111-1-122-1-1-1-100002-200-22000000000000-11001-100
χ3622-2-2-222-2-22-2-222-22-2-222-12-1211-2-2-11-211-111-12-1-111-2-21111-1-122-1-1-1-10000-22002-20000000000001-100-1100
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
χ394444-44-4-4-4444-4-40000004-24-244-2-2-2-4222-2-2-2-42220000000000000000000000000000000000000000000000
χ404444-44-4-4-4444-4-4000000-24-24-2-244-22-422-2-2-22-4220000000000000000000000000000000000000000000000
χ414444-44-4-4-4444-4-4000000-2-2-2-2-2-2-2-2122-1-111122-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000
χ424444-44-4-4-4444-4-4000000-2-2-2-2-2-2-2-2122-1-111122-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000
χ4344-4-444-4444-4-4-4-40000004-24-2-4-422-24-2-2-2-222-42220000000000000000000000000000000000000000000000
χ4444-4-444-4444-4-4-4-4000000-24-2422-4-4-2-24-2-2-2222-4220000000000000000000000000000000000000000000000
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
χ4744-4-4-444-4-44-4-4444-444-4-4-2-2-2-22222122-1-11-1-1-2-211-2-2-2-211112222-1-1-1-1000000000000000000000000000000
χ4844-4-4-444-4-44-4-444-44-4-444-2-2-2-22222122-1-11-1-1-2-2112222-1-1-1-1-2-2-2-21111000000000000000000000000000000
χ494-44i−4i04000-44i−4i0000000044-4-44i−4i4i−4i40000-44i−4i00000000000000000000000000000000000000000000000000
χ504-44i−4i04000-44i−4i000000004-2-424i−4i−2i2i-200002−2i2i0000006−66−66−600i6−i6i6−i6i6−i6000000000000000000000000000000
χ514-44i−4i04000-44i−4i000000004-2-424i−4i−2i2i-200002−2i2i000000−66−66−6600−i6i6−i6i6−i6i6000000000000000000000000000000
χ524-44i−4i04000-44i−4i00000000-242-4−2i2i4i−4i-200002−2i2i0000i6−i600i6−i6−i6i66−600−666−6000000000000000000000000000000
χ534-44i−4i04000-44i−4i00000000-242-4−2i2i4i−4i-200002−2i2i0000−i6i600−i6i6i6−i6−66006−6−66000000000000000000000000000000
χ544-44i−4i04000-44i−4i00000000-2-222−2i2i−2i2i1003-3-1i−i003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ554-44i−4i04000-44i−4i00000000-2-222−2i2i−2i2i1003-3-1i−i003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ564-44i−4i04000-44i−4i00000000-2-222−2i2i−2i2i100-33-1i−i00−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ574-44i−4i04000-44i−4i00000000-2-222−2i2i−2i2i100-33-1i−i00−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ584-4−4i4i04000-4−4i4i0000000044-4-4−4i4i−4i4i40000-4−4i4i00000000000000000000000000000000000000000000000000
χ594-4−4i4i04000-4−4i4i000000004-2-42−4i4i2i−2i-2000022i−2i0000006−66−66−600−i6i6−i6i6−i6i6000000000000000000000000000000
χ604-4−4i4i04000-4−4i4i000000004-2-42−4i4i2i−2i-2000022i−2i000000−66−66−6600i6−i6i6−i6i6−i6000000000000000000000000000000
χ614-4−4i4i04000-4−4i4i00000000-242-42i−2i−4i4i-2000022i−2i0000i6−i600i6−i6−i6i6−66006−6−66000000000000000000000000000000
χ624-4−4i4i04000-4−4i4i00000000-242-42i−2i−4i4i-2000022i−2i0000−i6i600−i6i6i6−i66−600−666−6000000000000000000000000000000
χ634-4−4i4i04000-4−4i4i00000000-2-2222i−2i2i−2i1003-3-1−ii00−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ644-4−4i4i04000-4−4i4i00000000-2-2222i−2i2i−2i1003-3-1−ii00−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ654-4−4i4i04000-4−4i4i00000000-2-2222i−2i2i−2i100-33-1−ii003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ664-4−4i4i04000-4−4i4i00000000-2-2222i−2i2i−2i100-33-1−ii003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ6766666-36-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000222200000000-1-122-1-1-1-1-1-100000000
χ6866666-36-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-2-2-20000000011-2-211111100000000
χ6966666-36-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000222200000000-1-1-2-2-1-1111100000000
χ7066666-36-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-2-2-200000000112211-1-1-1-100000000
χ716666-6-3-633-3-3-3330033−3333−330000000000000000000000000000000000002-2-2200000000-11001-13−33−300000000
χ726666-6-3-633-3-3-3330033−3333−33000000000000000000000000000000000000-222-2000000001-100-11−33−3300000000
χ736666-6-3-633-3-3-33300−3333−33330000000000000000000000000000000000002-2-2200000000-11001-1−33−3300000000
χ746666-6-3-633-3-3-33300−3333−3333000000000000000000000000000000000000-222-2000000001-100-113−33−300000000
χ7566-6-66-3-6-3-3-333330033−33−333300000000000000000000000000000000000022-2-200000000-1-100113−3−3300000000
χ7666-6-66-3-6-3-3-333330033−33−3333000000000000000000000000000000000000-2-222000000001100-1-1−333−300000000
χ7766-6-66-3-6-3-3-3333300−333333−3300000000000000000000000000000000000022-2-200000000-1-10011−333−300000000
χ7866-6-66-3-6-3-3-3333300−333333−33000000000000000000000000000000000000-2-222000000001100-1-13−3−3300000000
χ7966-6-6-6-3633-333-3-36-6-3-3330000000000000000000000000000000000002-22-200000000-112-2-11-1-11100000000
χ8066-6-6-6-3633-333-3-36-6-3-333000000000000000000000000000000000000-22-22000000001-1-221-111-1-100000000
χ8166-6-6-6-3633-333-3-3-6633-3-30000000000000000000000000000000000002-22-200000000-11-22-1111-1-100000000
χ8266-6-6-6-3633-333-3-3-6633-3-3000000000000000000000000000000000000-22-22000000001-12-21-1-1-11100000000
χ8312-1212i−12i0-60−6i36i36−6i6i63−63000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212i−12i0-606i3−6i36−6i6i−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12−12i12i0-60−6i36i366i−6i−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12−12i12i0-606i3−6i366i−6i63−63000000000000000000000000000000000000000000000000000000000000000000000000

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