Finite Group Databasebeta

← Group #13146556

Character table — Group #13146556

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222441212121212121212121212121818181818181818242436363636363636363636363636363636363636363636363636363636363672727272
order124423461212612336666121212121212224466121261222446888888881224242424242424242424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111-11-1111-1-111-1-1111111-1-11-11-1-1-1-1-1-1-11-11-11ii−i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i1-11-1
χ61111-11-1111-1-111-1-1111111-1-11-11-1-1-1-1-1-1-11-11-11−i−iii−i−iii1−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ71111-11-1111-1-111-1-1111111-1-11-11-1-1-1-1-1-1-1-11-111ii−i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii-11-11
χ81111-11-1111-1-111-1-1111111-1-11-11-1-1-1-1-1-1-1-11-111−i−iiiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i-11-11
χ911-1-111-11-1-11-1111111-1-1-1-1-1-111-1-111-1-11-11-1-111i−ii−ii−ii−i-1ii−i−iii−i−iii−i−iii−i−i1-1-11
χ1011-1-111-11-1-11-1111111-1-1-1-1-1-111-1-111-1-11-11-1-111−ii−ii−ii−ii-1−i−iii−i−iii−i−iii−i−iii1-1-11
χ1111-1-111-11-1-11-1111111-1-1-1-1-1-111-1-111-1-11-1-111-11i−ii−i−ii−ii-1ii−i−iii−i−i−i−iii−i−iii-111-1
χ1211-1-111-11-1-11-1111111-1-1-1-1-1-111-1-111-1-11-1-111-11−ii−iii−ii−i-1−i−iii−i−iiiii−i−iii−i−i-111-1
χ1311-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-11-1-111-1111-1-111-1-111-1-11-111-1-1-1-11111-1-1-1-11111-1-1
χ1411-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-11-1-111-1111-1-11-111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1
χ1511-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-11-1-111-11-1-11111-1-11-111-1-111-1-1-1-111-1-11111-1-1-1-111
χ1611-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-11-1-111-11-1-1111-111-11-1-11-1-1-11111-1-111-1-1-1-111-1-111
χ17222222222222222222222222-2-2-2-2-2-2-2-2220000-200000000-200000000000000000000
χ182222-22-2222-2-222-2-2222222-2-2-22-222222-2-20000-200000000-200000000000000000000
χ1922-2-222-22-2-22-2222222-2-2-2-2-2-2-2-222-2-2222-20000-200000000200000000000000000000
χ2022-2-2-2222-2-2-2222-2-222-2-2-2-222-222-222-2-2-220000-200000000200000000000000000000
χ214444444444441-2111-211-2-21100000000-2-200000222200000-1-1-1-1-1-1-1-1000000000000
χ224444444444441-2111-211-2-21100000000-2-200000-2-2-2-20000011111111000000000000
χ23444444444444-21-2-2-21-2-211-2-20000000011222200000000000000000000000000-1-1-1-1
χ24444444444444-21-2-2-21-2-211-2-20000000011-2-2-2-2000000000000000000000000001111
χ254444-44-4444-4-41-2-1-11-211-2-2-1-10000000022000002i2i−2i−2i00000−i−i−i−iiiii000000000000
χ264444-44-4444-4-41-2-1-11-211-2-2-1-1000000002200000−2i−2i2i2i00000iiii−i−i−i−i000000000000
χ274444-44-4444-4-4-2122-21-2-2112200000000-1-12-22-200000000000000000000000000-11-11
χ284444-44-4444-4-4-2122-21-2-2112200000000-1-1-22-22000000000000000000000000001-11-1
χ2944-4-444-44-4-44-41-2111-2-1-122-1-100000000-22000002i−2i2i−2i00000−i−iii−i−iii000000000000
χ3044-4-444-44-4-44-41-2111-2-1-122-1-100000000-2200000−2i2i−2i2i00000ii−i−iii−i−i000000000000
χ3144-4-444-44-4-44-4-21-2-2-2122-1-122000000001-12-2-2200000000000000000000000000-111-1
χ3244-4-444-44-4-44-4-21-2-2-2122-1-122000000001-1-222-2000000000000000000000000001-1-11
χ3344-4-4-4444-4-4-441-2-1-11-2-1-12211000000002-2000002-2-2200000-1-11111-1-1000000000000
χ3444-4-4-4444-4-4-441-2-1-11-2-1-12211000000002-200000-222-20000011-1-1-1-111000000000000
χ3544-4-4-4444-4-4-44-2122-2122-1-1-2-200000000-1122-2-200000000000000000000000000-1-111
χ3644-4-4-4444-4-4-44-2122-2122-1-1-2-200000000-11-2-2220000000000000000000000000011-1-1
χ374-44i−4i040-44i−4i001-23-3-12i−i2i−2i3i−3i000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ384-44i−4i040-44i−4i001-23-3-12i−i2i−2i3i−3i000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ394-44i−4i040-44i−4i001-2-33-12i−i2i−2i−3i3i000000000000000000000000−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ404-44i−4i040-44i−4i001-2-33-12i−i2i−2i−3i3i000000000000000000000000ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ414-44i−4i040-44i−4i004400-4-44i−4i−4i4i0000000000000000000000000000000000000000000000
χ424-4−4i4i040-4−4i4i001-23-3-12−ii−2i2i−3i3i000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ434-4−4i4i040-4−4i4i001-23-3-12−ii−2i2i−3i3i000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ444-4−4i4i040-4−4i4i001-2-33-12−ii−2i2i3i−3i000000000000000000000000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ454-4−4i4i040-4−4i4i001-2-33-12−ii−2i2i3i−3i000000000000000000000000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ464-4−4i4i040-4−4i4i004400-4-4−4i4i4i−4i0000000000000000000000000000000000000000000000
χ4766666-36-3-3-3-3-30000000000002222-1-1-1-1000000-100000000-1000000003−33−33−33−30000
χ4866666-36-3-3-3-3-30000000000002222-1-1-1-1000000-100000000-100000000−33−33−33−330000
χ4966666-36-3-3-3-3-3000000000000-2-2-2-21111000000100002222100000000-1-1-1-1-1-1-1-10000
χ5066666-36-3-3-3-3-3000000000000-2-2-2-2111100000010000-2-2-2-2100000000111111110000
χ516666-6-3-6-3-3-3330000000000002-22-21111000000-100000000-100000000−i3i3−i3i3i3−i3i3−i30000
χ526666-6-3-6-3-3-3330000000000002-22-21111000000-100000000-100000000i3−i3i3−i3−i3i3−i3i30000
χ536666-6-3-6-3-3-333000000000000-22-22-1-1-1-1000000100002i2i−2i−2i100000000−i−i−i−iiiii0000
χ546666-6-3-6-3-3-333000000000000-22-22-1-1-1-100000010000−2i−2i2i2i100000000iiii−i−i−i−i0000
χ5566-6-66-3-6-333-3300000000000022-2-2-1-111000000-100000000100000000−i3i3i3−i3−i3i3i3−i30000
χ5666-6-66-3-6-333-3300000000000022-2-2-1-111000000-100000000100000000i3−i3−i3i3i3−i3−i3i30000
χ5766-6-66-3-6-333-33000000000000-2-22211-1-1000000100002i−2i2i−2i-100000000−i−iii−i−iii0000
χ5866-6-66-3-6-333-33000000000000-2-22211-1-100000010000−2i2i−2i2i-100000000ii−i−iii−i−i0000
χ5966-6-6-6-36-3333-30000000000002-2-2211-1-1000000-1000000001000000003−3−33−333−30000
χ6066-6-6-6-36-3333-30000000000002-2-2211-1-1000000-100000000100000000−333−33−3−330000
χ6166-6-6-6-36-3333-3000000000000-222-2-1-111000000100002-2-22-100000000-1-11111-1-10000
χ6266-6-6-6-36-3333-3000000000000-222-2-1-11100000010000-222-2-10000000011-1-1-1-1110000
χ638-88i−8i080-88i−8i00-42004-2−4i4i−2i2i0000000000000000000000000000000000000000000000
χ648-8−8i8i080-8−8i8i00-42004-24i−4i2i−2i0000000000000000000000000000000000000000000000
χ6512-1212i−12i0-606−6i6i000000000000000000−2i32i323−23000000000000000000000000000000000000
χ6612-1212i−12i0-606−6i6i0000000000000000002i3−2i3−2323000000000000000000000000000000000000
χ6712-12−12i12i0-6066i−6i000000000000000000−2i32i3−2323000000000000000000000000000000000000
χ6812-12−12i12i0-6066i−6i0000000000000000002i3−2i323−23000000000000000000000000000000000000

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