Finite Group Databasebeta

← Group #98608

Character table — Group #98608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444422444444444422444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1iiii−i−i−i−i-11111-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1−i−i−i−iiiii-11111-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111iiii−i−i−i−i1-1-1-11-1−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111−i−i−i−iiiii1-1-1-11-1ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-11-1-1-11−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-11-1-1-11ii−i−iii−i−i−i−iii
χ1511111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1iiii−i−i−i−i1-111-11ii−i−i−i−iii−i−iii
χ1611111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1−i−i−i−iiiii1-111-11−i−iiiii−i−iii−i−i
χ1722222222222222-2-222-2-2-2-2-2-20000000022-2-200000000002-200000000000000
χ1822222222222222-2-222-2-2-2-2-2-200000000-2-2220000000000-2200000000000000
χ19222222222222-2-222-2-2-2-2-2-222222200000000000000000000-2-2000000000000
χ20222222222222-2-222-2-2-2-2-2-222-2-2-2-20000000000000000000022000000000000
χ21222222222222-2-2-2-2-2-22222-2-200002222000000000000-2-20000000000000000
χ22222222222222-2-2-2-2-2-22222-2-20000-2-2-2-2000000000000220000000000000000
χ2322222222-2-2-2-22222-2-2-2-222-2-222-2-200000000000000000000-22000000000000
χ2422222222-2-2-2-22222-2-2-2-222-2-2-2-222000000000000000000002-2000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-222000022-2-20000000000002-20000000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2220000-2-222000000000000-220000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-222220000000022-2-20000000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2222200000000-2-22200000000002-200000000000000
χ29222-2-2-2-222i−2i2i−2i002-20000002i−2i2-22i−2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000001+i−1−i1−i−1+i0000
χ30222-2-2-2-222i−2i2i−2i002-20000002i−2i2-22i−2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−1−i1+i−1+i1−i0000
χ31222-2-2-2-222i−2i2i−2i002-20000002i−2i-22−2i2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−1−i1+i−1+i1−i0000
χ32222-2-2-2-222i−2i2i−2i002-20000002i−2i-22−2i2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000001+i−1−i1−i−1+i0000
χ33222-2-2-2-22−2i2i−2i2i002-2000000−2i2i2-2−2i2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000001−i−1+i1+i−1−i0000
χ34222-2-2-2-22−2i2i−2i2i002-2000000−2i2i2-2−2i2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−1+i1−i−1−i1+i0000
χ35222-2-2-2-22−2i2i−2i2i002-2000000−2i2i-222i−2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−1+i1−i−1−i1+i0000
χ36222-2-2-2-22−2i2i−2i2i002-2000000−2i2i-222i−2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000001−i−1+i1+i−1−i0000
χ3722-2-22-22-22i−2i−2i2i0000002-22i−2i0000002-22i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000001+i−1−i1−i−1+i
χ3822-2-22-22-22i−2i−2i2i0000002-22i−2i0000002-22i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000−1−i1+i−1+i1−i
χ3922-2-22-22-22i−2i−2i2i0000002-22i−2i000000-22−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000−1−i1+i−1+i1−i
χ4022-2-22-22-22i−2i−2i2i0000002-22i−2i000000-22−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000001+i−1−i1−i−1+i
χ4122-2-22-22-2−2i2i2i−2i0000002-2−2i2i0000002-2−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000001−i−1+i1+i−1−i
χ4222-2-22-22-2−2i2i2i−2i0000002-2−2i2i0000002-2−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000−1+i1−i−1−i1+i
χ4322-2-22-22-2−2i2i2i−2i0000002-2−2i2i000000-222i−2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000−1+i1−i−1−i1+i
χ4422-2-22-22-2−2i2i2i−2i0000002-2−2i2i000000-222i−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000001−i−1+i1+i−1−i
χ45444-4-4-4-444i−4i4i−4i00-44000000−4i4i00000000000000000000000000000000000000
χ46444-4-4-4-44−4i4i−4i4i00-440000004i−4i00000000000000000000000000000000000000
χ4744-44-44-4-444-4-40000000000000000000000002-2-222-2-22000000000000000000
χ4844-44-44-4-444-4-4000000000000000000000000-222-2-222-2000000000000000000
χ4944-44-44-4-4-4-4440000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ5044-44-44-4-4-4-444000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ5144-4-44-44-44i−4i−4i4i000000-44−4i4i0000000000000000000000000000000000000000
χ5244-4-44-44-4−4i4i4i−4i000000-444i−4i0000000000000000000000000000000000000000
χ534-44-4-444-4000000004-400000000000000004i−4i00000000000000000000000000
χ544-44-4-444-4000000004-40000000000000000−4i4i00000000000000000000000000
χ554-44-4-444-400000000-44000000000000004i−4i0000000000000000000000000000
χ564-44-4-444-400000000-4400000000000000−4i4i0000000000000000000000000000
χ574-4-4-444-4400004-40000000000000000000000000000000000002i−2i2i−2i00000000
χ584-4-4-444-4400004-4000000000000000000000000000000000000−2i2i−2i2i00000000
χ594-4-4-444-440000-440000000000000000000000000000000000002-2-2200000000
χ604-4-4-444-440000-44000000000000000000000000000000000000-222-200000000
χ618-8888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-8-88-8-888000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).