Finite Group Databasebeta

← Group #168784

Character table — Group #168784

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444444444444888888884444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-11-1-1111111111-1-11-1-11111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111-1-1111-1-111111111-11-1-11-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-11-1-11-111111111-1-1
χ71111111111111111111111-1-1-1-1-1-111-1-111111111111-1-11-1-11-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111
χ911111111-1-1-1-11-1-1-1-11111111-1-11111-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-11-1
χ1011111111-1-1-1-11-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1111-1-111-1-111-11
χ1111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-111-1111111-1-1-1-1-1111-1-111-1-1-1-111-11
χ1211111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-111-111-1-1-1-11111-1111-1-1-1-11111-1-11-1
χ1311111111-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1111111-1-1-1-11-11-11-1-1-111-1-1111-1
χ1411111111-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-111-1-1-1-111111-11-11-111-1-111-1-1-11
χ1511111111-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-11111-1-1-1-111-1-1-11-1-11111-1-1-11
χ1611111111-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-1111-1
χ17222222222222222-2-2-2-2-2-222222000000-20000000000-200-2000000000000
χ18222222222222222-2-2-2-2-2-22-2-2-2-2000000-200000000002002000000000000
χ19222222222222-2-2-22222-2-2-20000002200-2220000000000-200-20000000000
χ20222222222222-2-2-22222-2-2-2000000-2-200-2-2-2000000000020020000000000
χ21222222222222-2-2-2-2-2-2-222-20000220022200000000000-200-200000000000
χ22222222222222-2-2-2-2-2-2-222-20000-2-200-2-2200000000000200200000000000
χ2322222222-2-2-2-22-2-222-2-2-2-2222-2-200000020000000000200-2000000000000
χ2422222222-2-2-2-22-2-222-2-2-2-22-2-22200000020000000000-2002000000000000
χ2522222222-2-2-2-2-22222-2-222-200002200-2-2-200000000000200-200000000000
χ2622222222-2-2-2-2-22222-2-222-20000-2-20022-200000000000-200200000000000
χ2722222222-2-2-2-2-222-2-222-2-2-200000022002-2-20000000000200-20000000000
χ2822222222-2-2-2-2-222-2-222-2-2-2000000-2-2002220000000000-20020000000000
χ292222-2-2-2-222-2-222-2000000-22-22-200000000022−2−222−2−20000002−22−2000000
χ302222-2-2-2-222-2-222-2000000-22-22-2000000000−2−222−2−222000000−22−22000000
χ312222-2-2-2-222-2-222-2000000-2-22-2200000000022−2−222−2−2000000−22−22000000
χ322222-2-2-2-222-2-222-2000000-2-22-22000000000−2−222−2−2220000002−22−2000000
χ332222-2-2-2-2-2-2222-22000000-22-2-2200000000022−2−2−2−2220000002−2−22000000
χ342222-2-2-2-2-2-2222-22000000-22-2-22000000000−2−22222−2−2000000−222−2000000
χ352222-2-2-2-2-2-2222-22000000-2-222-200000000022−2−2−2−222000000−222−2000000
χ362222-2-2-2-2-2-2222-22000000-2-222-2000000000−2−22222−2−20000002−2−22000000
χ372-22-22-2-222i−2i2i−2i0002i−2i2-20000000002i−2i0002-2i2−i2i2−i22−22−200000000002−2i2−i200
χ382-22-22-2-222i−2i2i−2i0002i−2i2-20000000002i−2i0002-2−i2i2−i2i2−22−220000000000−22−i2i200
χ392-22-22-2-222i−2i2i−2i0002i−2i2-2000000000−2i2i000-22i2−i2i2−i22−22−20000000000−22−i2i200
χ402-22-22-2-222i−2i2i−2i0002i−2i2-2000000000−2i2i000-22−i2i2−i2i2−22−2200000000002−2i2−i200
χ412-22-22-2-22−2i2i−2i2i000−2i2i2-20000000002i−2i000-22i2−i2i2−i2−22−2200000000002−2−i2i200
χ422-22-22-2-22−2i2i−2i2i000−2i2i2-20000000002i−2i000-22−i2i2−i2i22−22−20000000000−22i2−i200
χ432-22-22-2-22−2i2i−2i2i000−2i2i2-2000000000−2i2i0002-2i2−i2i2−i2−22−220000000000−22i2−i200
χ442-22-22-2-22−2i2i−2i2i000−2i2i2-2000000000−2i2i0002-2−i2i2−i2i22−22−200000000002−2−i2i200
χ454444-4-4-4-444-4-4-4-4400000040000000000000000000000000000000000000
χ464444-4-4-4-4-4-444-44-400000040000000000000000000000000000000000000
χ4744-4-4-44-44000000000004-40000000004i−4i000000000000000000000000000
χ4844-4-4-44-44000000000004-4000000000−4i4i000000000000000000000000000
χ4944-4-4-44-4400000000000-44000004i−4i0000000000000000000000000000000
χ5044-4-4-44-4400000000000-4400000−4i4i0000000000000000000000000000000
χ514-44-44-4-444i−4i4i−4i000−4i4i-440000000000000000000000000000000000000000
χ524-44-44-4-44−4i4i−4i4i0004i−4i-440000000000000000000000000000000000000000
χ534-44-4-444-44i−4i−4i4i000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ544-44-4-444-44i−4i−4i4i00000000000000000000000−2i2i2i−2i-222-20000000000000000
χ554-44-4-444-4−4i4i4i−4i000000000000000000000002i−2i−2i2i-222-20000000000000000
χ564-44-4-444-4−4i4i4i−4i00000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ5788-8-88-88-8000000000000000000000000000000000000000000000000000
χ588-8-8888-8-8000000000000000000000000000000000000000000000000000
χ598-8-88-8-888000000000000000000000000000000000000000000000000000

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