Finite Group Databasebeta

← Group #314721

Character table — Group #314721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444224444448888888888888888244444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111111-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-111-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-111
χ911111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-111111-1-1-1-1-1-1-111-1-111-1-111
χ1011111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-1-1-1-11111-1-1-1-111-1-11111
χ1111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-111111-1-1-1-111-1-111-1-111-1-1
χ1211111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1111111111-1-111-1-1-1-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1111-1-1-1-1-1111111-1-1-1-111-1-1
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-111-111-1-111-1-11111-1-1-1-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-1-11-1-111-1-1-1-11111-1-111
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1-111111-1-1-1-111-1-1-1-11111
χ172222222222222-2-2-2-2222-2-2-2-222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ182222222222222-2-2-2-2222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ19222222222222-22222-2-2-2-2-2-2-2-2-222000000000000000022-20000-20000000000000000
χ20222222222222-22222-2-2-2-2-2-2-2-2-2220000000000000000-2-22000020000000000000000
χ21222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000002i−2i000000002i−2i
χ22222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000−2i2i00000000−2i2i
χ2322222222-2-2-2-22-2-2-2-222222-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ2422222222-2-2-2-22-2-2-2-222222-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-222-2-222-2-200000000000000002-2-2000020000000000000000
χ2622222222-2-2-2-2-22222-2-2-222-2-222-2-20000000000000000-2220000-20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000002i−2i00000000−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000000000−2i2i000000002i−2i
χ2922-2-2-222-22i2i−2i−2i20000-2-2200002i−2i0000002i2i−2i−2i22-2-20000000000000000002−2i2−i22−2i2−i200
χ3022-2-2-222-22i2i−2i−2i20000-2-2200002i−2i0000002i2i−2i−2i22-2-2000000000000000000−22−i2i2−22−i2i200
χ3122-2-2-222-22i2i−2i−2i20000-2-2200002i−2i000000−2i−2i2i2i-2-2220000000000000000002−2i2−i2−22−i2i200
χ3222-2-2-222-22i2i−2i−2i20000-2-2200002i−2i000000−2i−2i2i2i-2-222000000000000000000−22−i2i22−2i2−i200
χ3322-2-2-222-2−2i−2i2i2i20000-2-220000−2i2i0000002i2i−2i−2i-2-2220000000000000000002−2−i2i2−22i2−i200
χ3422-2-2-222-2−2i−2i2i2i20000-2-220000−2i2i0000002i2i−2i−2i-2-222000000000000000000−22i2−i22−2−i2i200
χ3522-2-2-222-2−2i−2i2i2i20000-2-220000−2i2i000000−2i−2i2i2i22-2-20000000000000000002−2−i2i22−2−i2i200
χ3622-2-2-222-2−2i−2i2i2i20000-2-220000−2i2i000000−2i−2i2i2i22-2-2000000000000000000−22i2−i2−22i2−i200
χ372-222-22-2-20000-222-2-22-22002-2000022-2-200002-22-20000000000002i−2i2i−2i000000000000
χ382-222-22-2-20000-222-2-22-22002-2000022-2-200002-22-2000000000000−2i2i−2i2i000000000000
χ392-222-22-2-20000-222-2-22-22002-20000-2-2220000-22-220000000000002i−2i−2i2i000000000000
χ402-222-22-2-20000-222-2-22-22002-20000-2-2220000-22-22000000000000−2i2i2i−2i000000000000
χ412-222-22-2-20000-2-2-2222-2200-22000022-2-20000-22-2200000002i−2i2i−2i00000000000000000
χ422-222-22-2-20000-2-2-2222-2200-22000022-2-20000-22-220000000−2i2i−2i2i00000000000000000
χ432-222-22-2-20000-2-2-2222-2200-220000-2-22200002-22-200000002i−2i−2i2i00000000000000000
χ442-222-22-2-20000-2-2-2222-2200-220000-2-22200002-22-20000000−2i2i2i−2i00000000000000000
χ45444-44-4-4-44-44-4000000000000000022−2222−22000000002222−22−22000000000000000000000000
χ46444-44-4-4-44-44-40000000000000000−2222−222200000000−22−222222000000000000000000000000
χ47444-44-4-4-4-44-44000000000000000022−2222−2200000000−22−222222000000000000000000000000
χ48444-44-4-4-4-44-440000000000000000−2222−2222000000002222−22−22000000000000000000000000
χ4944-44-4-4-444i−4i−4i4i04-44-40000000004i−4i0000000000000000000000000000000000000000
χ5044-44-4-4-444i−4i−4i4i0-44-44000000000−4i4i0000000000000000000000000000000000000000
χ5144-44-4-4-44−4i4i4i−4i04-44-4000000000−4i4i0000000000000000000000000000000000000000
χ5244-44-4-4-44−4i4i4i−4i0-44-440000000004i−4i0000000000000000000000000000000000000000
χ5344-4-4-444-44i4i−4i−4i-4000044-40000−4i4i000000000000000000000000000000000000000000
χ5444-4-4-444-4−4i−4i4i4i-4000044-400004i−4i000000000000000000000000000000000000000000
χ554-444-44-4-40000444-4-4-44-400-4400000000000000000000000000000000000000000000
χ564-444-44-4-400004-4-444-44-4004-400000000000000000000000000000000000000000000
χ574-44-4-4-4440000000000004-400000022−22−222222−2222−2200000000000000000000000000000000
χ584-44-4-4-4440000000000004-4000000−222222−22−2222−222200000000000000000000000000000000
χ594-44-4-4-444000000000000-4400000022−22−2222−2222−222200000000000000000000000000000000
χ604-44-4-4-444000000000000-44000000−222222−2222−2222−2200000000000000000000000000000000
χ614-4-444-44-4000004-4-440000000000000002i2−2i2−2i22i200002i2−2i22i2−2i2000000000000000000000000
χ624-4-444-44-4000004-4-44000000000000000−2i22i22i2−2i20000−2i22i2−2i22i2000000000000000000000000
χ634-4-444-44-400000-444-40000000000000002i2−2i2−2i22i20000−2i22i2−2i22i2000000000000000000000000
χ644-4-444-44-400000-444-4000000000000000−2i22i22i2−2i200002i2−2i22i2−2i2000000000000000000000000
χ654-4-4-444-440000400004-4-4000000000000000000004i−4i−4i4i000000000000000000000000
χ664-4-4-444-440000400004-4-400000000000000000000−4i4i4i−4i000000000000000000000000
χ674-4-4-444-440000-40000-44400000000000000004-4-440000000000000000000000000000
χ684-4-4-444-440000-40000-4440000000000000000-444-40000000000000000000000000000

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