Finite Group Databasebeta

← Group #167174

Character table — Group #167174

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-111111111
χ51111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ61111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-11-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-1-11-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-1-11-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-11-1-1111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11-1111-1-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11-1111-111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-11-1111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11-11-11-1-11111-1-1
χ172222222222222222-2-22-2-2-2-22-2002222000000000000000000000000-2-200000000
χ182222222222222222-2-22-2-2-2-22-200-2-2-2-20000000000000000000000002200000000
χ19222222222222-2-2-2-222-2-2-222-2-2220000220000000000000000-20000-20000000000
χ20222222222222-2-2-2-222-2-2-222-2-2-2-20000-2-200000000000000002000020000000000
χ21222222222222-2-2-2-2-2-2-222-2-2-2200000000000000000000000002-2-2200000000000
χ22222222222222-2-2-2-2-2-2-222-2-2-220000000000000000000000000-222-200000000000
χ2322222222-2-2-2-2222222-222-2-2-2-2000000000000000000000000022-2-200000000000
χ2422222222-2-2-2-2222222-222-2-2-2-20000000000000000000000000-2-22200000000000
χ2522222222-2-2-2-22222-2-2-2-2-222-22220000-2-20000000000000000-2000020000000000
χ2622222222-2-2-2-22222-2-2-2-2-222-22-2-2000022000000000000000020000-20000000000
χ2722222222-2-2-2-2-2-2-2-2222-2-2-2-2220022-2-2000000000000000000000000-2200000000
χ2822222222-2-2-2-2-2-2-2-2222-2-2-2-22200-2-2220000000000000000000000002-200000000
χ2922-2-22-22-22i2i−2i−2i00002i−2i0002-2002i−2i00002-2i2i2−i2−i222−2−222−2−2i2i2−i2−i20000000000000000
χ3022-2-22-22-22i2i−2i−2i00002i−2i0002-2002i−2i00002-2−i2−i2i2i2−2−222−2−222−i2−i2i2i20000000000000000
χ3122-2-22-22-22i2i−2i−2i00002i−2i0002-200−2i2i0000-22i2i2−i2−i222−2−2−2−222−i2−i2i2i20000000000000000
χ3222-2-22-22-22i2i−2i−2i00002i−2i0002-200−2i2i0000-22−i2−i2i2i2−2−22222−2−2i2i2−i2−i20000000000000000
χ3322-2-22-22-2−2i−2i2i2i0000−2i2i0002-2002i−2i0000-22i2i2−i2−i2−2−22222−2−2−i2−i2i2i20000000000000000
χ3422-2-22-22-2−2i−2i2i2i0000−2i2i0002-2002i−2i0000-22−i2−i2i2i222−2−2−2−222i2i2−i2−i20000000000000000
χ3522-2-22-22-2−2i−2i2i2i0000−2i2i0002-200−2i2i00002-2i2i2−i2−i2−2−222−2−222i2i2−i2−i20000000000000000
χ3622-2-22-22-2−2i−2i2i2i0000−2i2i0002-200−2i2i00002-2−i2−i2i2i222−2−222−2−2−i2−i2i2i20000000000000000
χ372-22-2-2-2222-22-222-2-20020000-20002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i2000000000000000000002−22−2
χ382-22-2-2-2222-22-222-2-20020000-20002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i200000000000000000000−22−22
χ392-22-2-2-2222-22-222-2-20020000-2000−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i200000000000000000000−22−22
χ402-22-2-2-2222-22-222-2-20020000-2000−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i2000000000000000000002−22−2
χ412-22-2-2-222-22-22-2-2220020000-20002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i2000000000000000000002−2−22
χ422-22-2-2-222-22-22-2-2220020000-20002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i200000000000000000000−222−2
χ432-22-2-2-222-22-22-2-2220020000-2000−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i200000000000000000000−222−2
χ442-22-2-2-222-22-22-2-2220020000-2000−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i2000000000000000000002−2−22
χ454444-4-4-4-4000000000004-40000000000000000000022−2222−2200000000000000000000
χ464444-4-4-4-4000000000004-400000000000000000000−2222−222200000000000000000000
χ474444-4-4-4-400000000000-4400000000000000000000000022−2222−220000000000000000
χ484444-4-4-4-400000000000-44000000000000000000000000−2222−22220000000000000000
χ4944-4-44-44-44i4i−4i−4i0000−4i4i000-44000000000000000000000000000000000000000000
χ5044-4-44-44-4−4i−4i4i4i00004i−4i000-44000000000000000000000000000000000000000000
χ5144-4-4-44-4400004i−4i4i−4i00000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ5244-4-4-44-4400004i−4i4i−4i0000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ5344-4-4-44-440000−4i4i−4i4i00000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ5444-4-4-44-440000−4i4i−4i4i0000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ554-44-4-4-4444-44-4-4-44400-40000400000000000000000000000000000000000000000
χ564-44-4-4-444-44-4444-4-400-40000400000000000000000000000000000000000000000
χ574-4-444-4-4400004i−4i−4i4i000000000000000000000000000000000000000002i−2i2-20000
χ584-4-444-4-4400004i−4i−4i4i00000000000000000000000000000000000000000−2i2i-220000
χ594-4-444-4-440000−4i4i4i−4i000000000000000000000000000000000000000002i−2i-220000
χ604-4-444-4-440000−4i4i4i−4i00000000000000000000000000000000000000000−2i2i2-20000
χ614-4-44-444-44i−4i−4i4i0000000000000000000002-2-22−2i2i2i−2i000000000000000000000000
χ624-4-44-444-44i−4i−4i4i000000000000000000000-222-22i−2i−2i2i000000000000000000000000
χ634-4-44-444-4−4i4i4i−4i0000000000000000000002-2-222i−2i−2i2i000000000000000000000000
χ644-4-44-444-4−4i4i4i−4i000000000000000000000-222-2−2i2i2i−2i000000000000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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