Finite Group Databasebeta

← Group #168850

Character table — Group #168850

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444442444444444444888888882244448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-111-1-1111111111-1-1-11-11111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1111111
χ511111111111111111111111-1-11111-1-1-1-1-1-111111111-11-1-1-11-1-1-1-1-1-1-1-111
χ611111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111111-1-1
χ711111111111111111111111-1-1-1-1-1-111-1-11111111111-1-111-1-1-1-1-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ911111111-1-1-1-1-1-1-1-1111111-11111-1-111-1-1-1-11111-1-1-1-1-1-11-11111-1-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1111111-11111-1-111-1-1-1-1-1-1-1-11111-1-11-111-1-111-1-111-11
χ1111111111-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-1111111-1-1-1-1-11-111-111-1-1-1-111-11
χ1211111111-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-111-1-1-1-11111-11-111-1-1-11111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-111111111-1-1-1-11-1-11-11-1-111-1-1111-1
χ1411111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-111111-1-11-1111-1-111-1-1-11
χ1511111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111-1-11111-1-1-1-1111-1-1-1-1-11111-1-1-11
χ1611111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-11111111-1-1-111-1-1-1-1111-1
χ1722222222222222-2-2-2-2-2-222-222000000220000000000-2000-200000000000
χ1822222222222222-2-2-2-2-2-222-2-2-2000000-2-200000000002000200000000000
χ19222222222222-2-22222-2-2-2-2-20000002200220000000000-2-2000000000000
χ20222222222222-2-22222-2-2-2-2-2000000-2-200-2-2000000000022000000000000
χ21222222222222-2-2-2-2-2-222-2-22002222000000000000000-2000-20000000000
χ22222222222222-2-2-2-2-2-222-2-2200-2-2-2-2000000000000000200020000000000
χ2322222222-2-2-2-22222-2-222-2-2-20022-2-20000000000000002000-20000000000
χ2422222222-2-2-2-22222-2-222-2-2-200-2-222000000000000000-200020000000000
χ2522222222-2-2-2-222-2-222-2-2-2-220000002200-2-20000000000-22000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-22000000-2-2002200000000002-2000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-222222000000-2-200000000002000-200000000000
χ2822222222-2-2-2-2-2-222-2-2-2-2222-2-2000000220000000000-2000200000000000
χ29222-2-2-2-222i2i−2i−2i2i−2i0000002-202-20000002i−2i0022−2−2i2i2−i2−i20000002−2i2−i2000000
χ30222-2-2-2-222i2i−2i−2i2i−2i0000002-202-20000002i−2i00−2−222−i2−i2i2i2000000−22−i2i2000000
χ31222-2-2-2-222i2i−2i−2i2i−2i0000002-20-22000000−2i2i0022−2−2i2i2−i2−i2000000−22−i2i2000000
χ32222-2-2-2-222i2i−2i−2i2i−2i0000002-20-22000000−2i2i00−2−222−i2−i2i2i20000002−2i2−i2000000
χ33222-2-2-2-22−2i−2i2i2i−2i2i0000002-202-2000000−2i2i0022−2−2−i2−i2i2i20000002−2−i2i2000000
χ34222-2-2-2-22−2i−2i2i2i−2i2i0000002-202-2000000−2i2i00−2−222i2i2−i2−i2000000−22i2−i2000000
χ35222-2-2-2-22−2i−2i2i2i−2i2i0000002-20-220000002i−2i0022−2−2−i2−i2i2i2000000−22i2−i2000000
χ36222-2-2-2-22−2i−2i2i2i−2i2i0000002-20-220000002i−2i00−2−222i2i2−i2−i20000002−2−i2i2000000
χ372-222-22-2-22i−2i2i−2i002i−2i2-2000000000002-2002i−2ii2−i2i2−i22−22−20000000000i2−i22−200
χ382-222-22-2-22i−2i2i−2i002i−2i2-2000000000002-2002i−2i−i2i2−i2i2−22−220000000000−i2i2−2200
χ392-222-22-2-22i−2i2i−2i002i−2i2-200000000000-2200−2i2ii2−i2i2−i22−22−20000000000−i2i2−2200
χ402-222-22-2-22i−2i2i−2i002i−2i2-200000000000-2200−2i2i−i2i2−i2i2−22−220000000000i2−i22−200
χ412-222-22-2-2−2i2i−2i2i00−2i2i2-2000000000002-200−2i2ii2−i2i2−i2−22−220000000000i2−i2−2200
χ422-222-22-2-2−2i2i−2i2i00−2i2i2-2000000000002-200−2i2i−i2i2−i2i22−22−20000000000−i2i22−200
χ432-222-22-2-2−2i2i−2i2i00−2i2i2-200000000000-22002i−2ii2−i2i2−i2−22−220000000000−i2i22−200
χ442-222-22-2-2−2i2i−2i2i00−2i2i2-200000000000-22002i−2i−i2i2−i2i22−22−20000000000i2−i2−2200
χ45444-4-4-4-444i4i−4i−4i−4i4i000000-440000000000000000000000000000000000000
χ46444-4-4-4-44−4i−4i4i4i4i−4i000000-440000000000000000000000000000000000000
χ4744-4-4-444-400000000004-400000004i−4i000000000000000000000000000000
χ4844-4-4-444-400000000004-40000000−4i4i000000000000000000000000000000
χ4944-4-4-444-40000000000-44000004i−4i00000000000000000000000000000000
χ5044-4-4-444-40000000000-4400000−4i4i00000000000000000000000000000000
χ514-444-44-4-44i−4i4i−4i00−4i4i-4400000000000000000000000000000000000000000
χ524-444-44-4-4−4i4i−4i4i004i−4i-4400000000000000000000000000000000000000000
χ534-44-44-44-44-4-44000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ544-44-44-44-44-4-4400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ554-44-44-44-4-444-4000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ564-44-44-44-4-444-400000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5788-888-8-8-8000000000000000000000000000000000000000000000000000
χ588-8-88-8-888000000000000000000000000000000000000000000000000000
χ598-8-8-888-88000000000000000000000000000000000000000000000000000

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