Finite Group Databasebeta

← Group #10593329

Character table — Group #10593329

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111144444444121212121212121212121212181818181818111144444444121212121212121212121212181818181818
order124433661212121288882424242424242424248888224466661212121288882424242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-11111-1-1-1-111-1-1-1-111111111111111-1-11111-1-1-1-111-1-1-1-1
χ3111111111111-1-111-1-1-1-1111111-1-1-1-1111111111111-1-111-1-1-1-1111111-1-1-1-1
χ4111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511-1-11111-1-1-1-1i−ii−iii−i−iii−i−i-1111-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i-1111-1-1
χ611-1-11111-1-1-1-1i−i−iiii−i−i−i−iii-11-1-11111-1-11111-1-1-1-1i−i−iiii−i−i−i−iii-11-1-111
χ711-1-11111-1-1-1-1−iii−i−i−iiiii−i−i-11-1-11111-1-11111-1-1-1-1−iii−i−i−iiiii−i−i-11-1-111
χ811-1-11111-1-1-1-1−ii−ii−i−iii−i−iii-1111-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii-1111-1-1
χ9222222222222000000000000-2-20000222222222222000000000000-2-20000
χ1022-2-22222-2-2-2-20000000000002-2000022-2-22222-2-2-2-20000000000002-20000
χ112-22i−2i22-2-22i2i−2i−2i000000000000002−2−i2i22-22i−2i22-2-22i2i−2i−2i000000000000002−2−i2i2
χ122-22i−2i22-2-22i2i−2i−2i00000000000000−22i2−i22-22i−2i22-2-22i2i−2i−2i00000000000000−22i2−i2
χ132-2−2i2i22-2-2−2i−2i2i2i000000000000002−2i2−i22-2−2i2i22-2-2−2i−2i2i2i000000000000002−2i2−i2
χ142-2−2i2i22-2-2−2i−2i2i2i00000000000000−22−i2i22-2−2i2i22-2-2−2i−2i2i2i00000000000000−22−i2i2
χ1544441-21-21-21-200220000-1-1-1-100000044441-21-21-21-200220000-1-1-1-1000000
χ1644441-21-21-21-200-2-20000111100000044441-21-21-21-200-2-200001111000000
χ174444-21-21-21-212200-1-1-1-100000000004444-21-21-21-212200-1-1-1-10000000000
χ184444-21-21-21-21-2-200111100000000004444-21-21-21-21-2-20011110000000000
χ1944-4-41-21-2-12-12002i−2i0000−i−iii00000044-4-41-21-2-12-12002i−2i0000−i−iii000000
χ2044-4-41-21-2-12-1200−2i2i0000ii−i−i00000044-4-41-21-2-12-1200−2i2i0000ii−i−i000000
χ2144-4-4-21-212-12-12i−2i00−i−iii000000000044-4-4-21-212-12-12i−2i00−i−iii0000000000
χ2244-4-4-21-212-12-1−2i2i00ii−i−i000000000044-4-4-21-212-12-1−2i2i00ii−i−i0000000000
χ234-44i−4i1-2-12i−2i−i2i00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000004-44i−4i1-2-12i−2i−i2i00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ244-44i−4i1-2-12i−2i−i2i00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000004-44i−4i1-2-12i−2i−i2i00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ254-44i−4i-212-1−2ii2i−i0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000004-44i−4i-212-1−2ii2i−i0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ264-44i−4i-212-1−2ii2i−i0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000004-44i−4i-212-1−2ii2i−i0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ274-4−4i4i1-2-12−i2ii−2i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000004-4−4i4i1-2-12−i2ii−2i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ284-4−4i4i1-2-12−i2ii−2i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000004-4−4i4i1-2-12−i2ii−2i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ294-4−4i4i-212-12i−i−2ii0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000004-4−4i4i-212-12i−i−2ii0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ304-4−4i4i-212-12i−i−2ii0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000004-4−4i4i-212-12i−i−2ii0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3211111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111
χ33111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111
χ34111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ3511-1-11111-1-1-1-1i−ii−iii−i−iii−i−i-1111-1-1-1-111-1-1-1-11111−ii−ii−i−iii−i−iii1-1-1-111
χ3611-1-11111-1-1-1-1i−i−iiii−i−i−i−iii-11-1-111-1-111-1-1-1-11111−iii−i−i−iiiii−i−i1-111-1-1
χ3711-1-11111-1-1-1-1−iii−i−i−iiiii−i−i-11-1-111-1-111-1-1-1-11111i−i−iiii−i−i−i−iii1-111-1-1
χ3811-1-11111-1-1-1-1−ii−ii−i−iii−i−iii-1111-1-1-1-111-1-1-1-11111i−ii−iii−i−iii−i−i1-1-1-111
χ39222222222222000000000000-2-20000-2-2-2-2-2-2-2-2-2-2-2-2000000000000220000
χ4022-2-22222-2-2-2-20000000000002-20000-2-222-2-2-2-22222000000000000-220000
χ412-22i−2i22-2-22i2i−2i−2i000000000000002−2−i2i2-22−2i2i-2-222−2i−2i2i2i00000000000000−22i2−i2
χ422-22i−2i22-2-22i2i−2i−2i00000000000000−22i2−i2-22−2i2i-2-222−2i−2i2i2i000000000000002−2−i2i2
χ432-2−2i2i22-2-2−2i−2i2i2i000000000000002−2i2−i2-222i−2i-2-2222i2i−2i−2i00000000000000−22−i2i2
χ442-2−2i2i22-2-2−2i−2i2i2i00000000000000−22−i2i2-222i−2i-2-2222i2i−2i−2i000000000000002−2i2−i2
χ4544441-21-21-21-200220000-1-1-1-1000000-4-4-4-4-12-12-12-1200-2-200001111000000
χ4644441-21-21-21-200-2-200001111000000-4-4-4-4-12-12-12-1200220000-1-1-1-1000000
χ474444-21-21-21-212200-1-1-1-10000000000-4-4-4-42-12-12-12-1-2-20011110000000000
χ484444-21-21-21-21-2-20011110000000000-4-4-4-42-12-12-12-12200-1-1-1-10000000000
χ4944-4-41-21-2-12-12002i−2i0000−i−iii000000-4-444-12-121-21-200−2i2i0000ii−i−i000000
χ5044-4-41-21-2-12-1200−2i2i0000ii−i−i000000-4-444-12-121-21-2002i−2i0000−i−iii000000
χ5144-4-4-21-212-12-12i−2i00−i−iii0000000000-4-4442-12-1-21-21−2i2i00ii−i−i0000000000
χ5244-4-4-21-212-12-1−2i2i00ii−i−i0000000000-4-4442-12-1-21-212i−2i00−i−iii0000000000
χ534-44i−4i1-2-12i−2i−i2i00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000-44−4i4i-121-2−i2ii−2i00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ544-44i−4i1-2-12i−2i−i2i00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000-44−4i4i-121-2−i2ii−2i00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ554-44i−4i-212-1−2ii2i−i0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000-44−4i4i2-1-212i−i−2ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ564-44i−4i-212-1−2ii2i−i0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000-44−4i4i2-1-212i−i−2ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ574-4−4i4i1-2-12−i2ii−2i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000-444i−4i-121-2i−2i−i2i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ584-4−4i4i1-2-12−i2ii−2i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000-444i−4i-121-2i−2i−i2i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ594-4−4i4i-212-12i−i−2ii0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000-444i−4i2-1-21−2ii2i−i0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ604-4−4i4i-212-12i−i−2ii0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000-444i−4i2-1-21−2ii2i−i0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000

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