Finite Group Databasebeta

← Group #317658

Character table — Group #317658

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111
χ911111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111-1-1-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-11-1-1-11-1-111-1-111-1-111
χ1111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1111-1-1-111-1-11111-1-1
χ1211111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1111-1-111-1-1-1-111
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11-1111-111-1-1-1-111-1-111
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1111-11-1-11111-1-111-1-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1-1-11-1-1-11111-1-1-1-111
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-11-1-1-1111-1-1-1-11111-1-1
χ17222222222222222-2-2-2-22-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-22222-2-2-2-2-222-2-200000000000000000000002-200-22000000000000
χ20222222222222-2-2-22222-2-2-2-2-222-2-20000000000000000000000-22002-2000000000000
χ21222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000000000002i−2i2i−2i
χ22222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-2-2-2222-2-2-2-22-2-22222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-2-2-222-2-22200000000000000000000002200-2-2000000000000
χ2622222222-2-2-2-2-2-2-22222-2-2-222-2-2220000000000000000000000-2-20022000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000000000000000000000000−2i2i2i−2i
χ2922-222-2-2-200002-2-222-2-222-20000002i2i−2i−2i2i2i−2i−2i00000000002-200002i−2i00000000000000
χ3022-222-2-2-200002-2-222-2-222-20000002i2i−2i−2i2i2i−2i−2i0000000000-220000−2i2i00000000000000
χ3122-222-2-2-200002-2-222-2-222-2000000−2i−2i2i2i−2i−2i2i2i00000000002-20000−2i2i00000000000000
χ3222-222-2-2-200002-2-222-2-222-2000000−2i−2i2i2i−2i−2i2i2i0000000000-2200002i−2i00000000000000
χ3322-222-2-2-200002-2-2-2-2222-220000002i2i−2i−2i−2i−2i2i2i000000002i−2i002-2000000000000000000
χ3422-222-2-2-200002-2-2-2-2222-220000002i2i−2i−2i−2i−2i2i2i00000000−2i2i00-22000000000000000000
χ3522-222-2-2-200002-2-2-2-2222-22000000−2i−2i2i2i2i2i−2i−2i000000002i−2i00-22000000000000000000
χ3622-222-2-2-200002-2-2-2-2222-22000000−2i−2i2i2i2i2i−2i−2i00000000−2i2i002-2000000000000000000
χ372-2-22-22-2222-2-222-20000-20000002-200002i−2i2i−2i00002i2i−2i−2i000000000000i2−i2i2−i22−22−20000
χ382-2-22-22-2222-2-222-20000-20000002-200002i−2i2i−2i00002i2i−2i−2i000000000000−i2i2−i2i2−22−220000
χ392-2-22-22-2222-2-222-20000-20000002-20000−2i2i−2i2i0000−2i−2i2i2i000000000000i2−i2i2−i2−22−220000
χ402-2-22-22-2222-2-222-20000-20000002-20000−2i2i−2i2i0000−2i−2i2i2i000000000000−i2i2−i2i22−22−20000
χ412-2-22-22-22-2-22222-20000-2000000-2200002i−2i2i−2i0000−2i−2i2i2i000000000000i2−i2−i2i22−2−220000
χ422-2-22-22-22-2-22222-20000-2000000-2200002i−2i2i−2i0000−2i−2i2i2i000000000000−i2i2i2−i2−222−20000
χ432-2-22-22-22-2-22222-20000-2000000-220000−2i2i−2i2i00002i2i−2i−2i000000000000i2−i2−i2i2−222−20000
χ442-2-22-22-22-2-22222-20000-2000000-220000−2i2i−2i2i00002i2i−2i−2i000000000000−i2i2i2−i22−2−220000
χ45444-4-44-4-4000000000000004-4000022−2222−220000000022−2222−22000000000000000000000000
χ46444-4-44-4-4000000000000004-40000−2222−222200000000−2222−2222000000000000000000000000
χ47444-4-44-4-400000000000000-44000022−2222−2200000000−2222−2222000000000000000000000000
χ48444-4-44-4-400000000000000-440000−2222−22220000000022−2222−22000000000000000000000000
χ4944-444-4-4-40000-44444-4-4-4-440000000000000000000000000000000000000000000000
χ5044-444-4-4-40000-444-4-444-44-40000000000000000000000000000000000000000000000
χ5144-4-4-4-4444i−4i4i−4i00000000000000002i2−2i2−2i22i200002222−22−220000000000000000000000000000
χ5244-4-4-4-4444i−4i4i−4i0000000000000000−2i22i22i2−2i20000−22−2222220000000000000000000000000000
χ5344-4-4-4-444−4i4i−4i4i00000000000000002i2−2i2−2i22i20000−22−2222220000000000000000000000000000
χ5444-4-4-4-444−4i4i−4i4i0000000000000000−2i22i22i2−2i200002222−22−220000000000000000000000000000
χ554-444-4-44-400004-440000-40000000000004-4-4400000000000000000000000000000000
χ564-444-4-44-400004-440000-4000000000000-444-400000000000000000000000000000000
χ574-444-4-44-40000-44-40000400000000000000004i−4i4i−4i0000000000000000000000000000
χ584-444-4-44-40000-44-4000040000000000000000−4i4i−4i4i0000000000000000000000000000
χ594-44-44-4-444i−4i−4i4i0004-44-4000004i−4i000000000000000000000000000000000000000000
χ604-44-44-4-444i−4i−4i4i000-44-4400000−4i4i000000000000000000000000000000000000000000
χ614-44-44-4-44−4i4i4i−4i0004-44-400000−4i4i000000000000000000000000000000000000000000
χ624-44-44-4-44−4i4i4i−4i000-44-44000004i−4i000000000000000000000000000000000000000000
χ634-4-44-44-4444-4-4-4-4400004000000-440000000000000000000000000000000000000000
χ644-4-44-44-44-4-444-4-44000040000004-40000000000000000000000000000000000000000
χ654-4-4-4444-400000004-4-44000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000
χ664-4-4-4444-400000004-4-4400000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000
χ674-4-4-4444-40000000-444-4000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000
χ684-4-4-4444-40000000-444-400000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000

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