Finite Group Databasebeta

← Group #168792

Character table — Group #168792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444444444444444444888888882244448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-11-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-11-111111111-1-1
χ51111111111111111111111-1-111111-1-1-1-1-1-111111111-11-1-1-111111-1-1-1-1-1-1
χ61111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1111111
χ71111111111111111111111-1-11-1-1-1-11111-1-111111111-1-111-1-1-1-1-1-11111-1-1
χ81111111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ911111111-1-1-1-1-1-11-1-11111111-111-1-111-1-1-1-11111-1-1-1-1-111-11-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-11-1-11111111-111-1-111-1-1-1-1-1-1-1-11111-111-11-1-1-111-1-111-11
χ1111111111-1-1-1-1-1-11-1-11111111-1-1-111-1-111-1-11111-1-1-1-1-1-1-1111-1-111-1-1111-1
χ1211111111-1-1-1-1-1-11-1-11111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-111111-1-111-1-1-11
χ1311111111-1-1-1-1-1-11-1-111111-1-1-111-1-1-1-111111111-1-1-1-111-11-1-111-1-1-1-111-11
χ1411111111-1-1-1-1-1-11-1-111111-1-1-111-1-1-1-11111-1-1-1-1111111-11-1-1-1-11111-1-11-1
χ1511111111-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-1111111-1-1-1-11-11-1-11-1-11111-1-1-11
χ1611111111-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-111-1-1-1-111111-11-1-1111-1-1-1-1111-1
χ1722222222222222-2-2-22-2-2-2200-22222000000000000000-2000-20000000000
χ1822222222222222-2-2-22-2-2-2200-2-2-2-2-2000000000000000200020000000000
χ19222222222222-2-22-2-2-2-2-22-2222000000002200000000-2000-200000000000
χ20222222222222-2-22-2-2-2-2-22-2-2-2200000000-2-2000000002000200000000000
χ21222222222222-2-2-222-222-2-200-200002222000000000000-2-2000000000000
χ22222222222222-2-2-222-222-2-200-20000-2-2-2-200000000000022000000000000
χ2322222222-2-2-2-222222-2-2-22-222-200000000-2-2000000002000-200000000000
χ2422222222-2-2-2-222222-2-2-22-2-2-2-2000000002200000000-2000200000000000
χ2522222222-2-2-2-222-2-2-2-222-2-2002000022-2-2000000000000-22000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-20020000-2-2220000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-2222-2-2-2200222-2-2000000000000000-200020000000000
χ2822222222-2-2-2-2-2-2-2222-2-2-22002-2-2220000000000000002000-20000000000
χ2922-2-2-2-22222-2-22-20002000-20002i−2i2i−2i00000022−2−222−2−2000000i2−i2i2−i2000000
χ3022-2-2-2-22222-2-22-20002000-20002i−2i2i−2i000000−2−222−2−222000000−i2i2−i2i2000000
χ3122-2-2-2-22222-2-22-20002000-2000−2i2i−2i2i00000022−2−222−2−2000000−i2i2−i2i2000000
χ3222-2-2-2-22222-2-22-20002000-2000−2i2i−2i2i000000−2−222−2−222000000i2−i2i2−i2000000
χ3322-2-2-2-222-2-222-220002000-20002i−2i−2i2i00000022−2−2−2−222000000i2−i2−i2i2000000
χ3422-2-2-2-222-2-222-220002000-20002i−2i−2i2i000000−2−22222−2−2000000−i2i2i2−i2000000
χ3522-2-2-2-222-2-222-220002000-2000−2i2i2i−2i00000022−2−2−2−222000000−i2i2i2−i2000000
χ3622-2-2-2-222-2-222-220002000-2000−2i2i2i−2i000000−2−22222−2−2000000i2−i2−i2i2000000
χ372-222-2-22-22i−2i2i−2i0002i−2i02-20000000002i−2i2-200i2−i2i2−i22−22−200000000002−2i2−i200
χ382-222-2-22-22i−2i2i−2i0002i−2i02-20000000002i−2i2-200−i2i2−i2i2−22−220000000000−22−i2i200
χ392-222-2-22-22i−2i2i−2i0002i−2i02-2000000000−2i2i-2200i2−i2i2−i22−22−20000000000−22−i2i200
χ402-222-2-22-22i−2i2i−2i0002i−2i02-2000000000−2i2i-2200−i2i2−i2i2−22−2200000000002−2i2−i200
χ412-222-2-22-2−2i2i−2i2i000−2i2i02-20000000002i−2i-2200i2−i2i2−i2−22−2200000000002−2−i2i200
χ422-222-2-22-2−2i2i−2i2i000−2i2i02-20000000002i−2i-2200−i2i2−i2i22−22−20000000000−22i2−i200
χ432-222-2-22-2−2i2i−2i2i000−2i2i02-2000000000−2i2i2-200i2−i2i2−i2−22−220000000000−22i2−i200
χ442-222-2-22-2−2i2i−2i2i000−2i2i02-2000000000−2i2i2-200−i2i2−i2i22−22−200000000002−2−i2i200
χ45444-44-4-4-4000000400000-404-400000000000000000000000000000000000
χ46444-44-4-4-4000000400000-40-4400000000000000000000000000000000000
χ47444-44-4-4-4000000-40000040000000000004i−4i000000000000000000000000
χ48444-44-4-4-4000000-4000004000000000000−4i4i000000000000000000000000
χ4944-4-4-4-44444-4-4-44000-400040000000000000000000000000000000000000
χ5044-4-4-4-444-4-4444-4000-400040000000000000000000000000000000000000
χ514-444-4-44-44i−4i4i−4i000−4i4i0-44000000000000000000000000000000000000000
χ524-444-4-44-4−4i4i−4i4i0004i−4i0-44000000000000000000000000000000000000000
χ534-4-4-4444-44i−4i−4i4i000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ544-4-4-4444-44i−4i−4i4i00000000000000000000000−2i2i2i−2i-222-20000000000000000
χ554-4-4-4444-4−4i4i4i−4i000000000000000000000002i−2i−2i2i-222-20000000000000000
χ564-4-4-4444-4−4i4i4i−4i00000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ5788-88-88-8-8000000000000000000000000000000000000000000000000000
χ588-88-8-88-88000000000000000000000000000000000000000000000000000
χ598-8-888-8-88000000000000000000000000000000000000000000000000000

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