Finite Group Databasebeta

← Group #508992

Character table — Group #508992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244444444444444444444444488888888888888883232323232323232
order122222224444888888882244444444448888888888881616161616161616161616161616161624444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1111-1
χ911111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1111-1-1-1
χ1011111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1111
χ1111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-111-11
χ1211111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-11-1
χ1311111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-111
χ1411111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1111-1-1
χ1511111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11-111-1
χ1611111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-11-1-11
χ17222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-222222222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222222222-2-2-2-2000000000000000000000000
χ2122222222-2-2-2-200000000222222-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−200000000
χ2222222222-2-2-2-200000000222222-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−22200000000
χ2322222222-2-2-2-20000000022-2-2-2-22222-2-200000000000022−2−222−2−2−2−222−2−22200000000
χ2422222222-2-2-2-20000000022-2-2-2-22222-2-2000000000000−2−222−2−22222−2−222−2−200000000
χ2522222222-2-2-2-200000000-2-222-2-2-2-2222200000000000022−2−2−2−22222−2−2−2−22200000000
χ2622222222-2-2-2-200000000-2-222-2-2-2-22222000000000000−2−22222−2−2−2−22222−2−200000000
χ2722222222-2-2-2-200000000-2-2-2-22222-2-22200000000000022−2−2−2−222−2−22222−2−200000000
χ2822222222-2-2-2-200000000-2-2-2-22222-2-222000000000000−2−22222−2−222−2−2−2−22200000000
χ2922-22-2-2-222-22-200000000002i−2i002i−2i00002i2i−2i−2i000022-2-22−22−2i2−i2i2−i2i2−i2i2−i22−22−200000000
χ3022-22-2-2-222-22-200000000002i−2i002i−2i00002i2i−2i−2i000022-2-2−22−22−i2i2−i2i2−i2i2−i2i2−22−2200000000
χ3122-22-2-2-222-22-200000000002i−2i002i−2i0000−2i−2i2i2i0000-2-2222−22−2−i2i2−i2i2i2−i2i2−i2−22−2200000000
χ3222-22-2-2-222-22-200000000002i−2i002i−2i0000−2i−2i2i2i0000-2-222−22−22i2−i2i2−i2−i2i2−i2i22−22−200000000
χ3322-22-2-2-222-22-20000000000−2i2i00−2i2i00002i2i−2i−2i0000-2-2222−22−2i2−i2i2−i2−i2i2−i2i2−22−2200000000
χ3422-22-2-2-222-22-20000000000−2i2i00−2i2i00002i2i−2i−2i0000-2-222−22−22−i2i2−i2i2i2−i2i2−i22−22−200000000
χ3522-22-2-2-222-22-20000000000−2i2i00−2i2i0000−2i−2i2i2i000022-2-22−22−2−i2i2−i2i2−i2i2−i2i22−22−200000000
χ3622-22-2-2-222-22-20000000000−2i2i00−2i2i0000−2i−2i2i2i000022-2-2−22−22i2−i2i2−i2i2−i2i2−i2−22−2200000000
χ3722-22-2-2-22-22-222222-2-2-2-2002i−2i00−2i2i000000002i2i−2i−2i000000002i−2i−2i2i00002-2-2200000000
χ3822-22-2-2-22-22-222222-2-2-2-2002i−2i00−2i2i000000002i2i−2i−2i00000000−2i2i2i−2i0000-222-200000000
χ3922-22-2-2-22-22-222222-2-2-2-200−2i2i002i−2i00000000−2i−2i2i2i000000002i−2i−2i2i0000-222-200000000
χ4022-22-2-2-22-22-222222-2-2-2-200−2i2i002i−2i00000000−2i−2i2i2i00000000−2i2i2i−2i00002-2-2200000000
χ4122-22-2-2-22-22-22-2-2-2-22222002i−2i00−2i2i00000000−2i−2i2i2i00002-2-2200002i−2i−2i2i000000000000
χ4222-22-2-2-22-22-22-2-2-2-22222002i−2i00−2i2i00000000−2i−2i2i2i0000-222-20000−2i2i2i−2i000000000000
χ4322-22-2-2-22-22-22-2-2-2-2222200−2i2i002i−2i000000002i2i−2i−2i00002-2-220000−2i2i2i−2i000000000000
χ4422-22-2-2-22-22-22-2-2-2-2222200−2i2i002i−2i000000002i2i−2i−2i0000-222-200002i−2i−2i2i000000000000
χ45444-44-4-4-400002222−22−222222−22−224-4000000000022−2222−2200000000000000000000000000000000
χ46444-44-4-4-400002222−22−222222−22−22-440000000000−2222−222200000000000000000000000000000000
χ47444-44-4-4-40000−22−222222−22−2222224-40000000000−2222−222200000000000000000000000000000000
χ48444-44-4-4-40000−22−222222−22−222222-44000000000022−2222−2200000000000000000000000000000000
χ4944-4-4-444-400002222−22−22−22−22222200000000004i−4i2i2−2i2−2i22i200000000000000000000000000000000
χ5044-4-4-444-400002222−22−22−22−2222220000000000−4i4i−2i22i22i2−2i200000000000000000000000000000000
χ5144-4-4-444-40000−22−2222222222−22−2200000000004i−4i−2i22i22i2−2i200000000000000000000000000000000
χ5244-4-4-444-40000−22−2222222222−22−220000000000−4i4i2i2−2i2−2i22i200000000000000000000000000000000
χ534-444-4-44-4000022−2222−2222−2222−22000000004i−4i00000000002i2−2i22i2−2i2000000000000000000000000
χ544-444-4-44-4000022−2222−2222−2222−2200000000−4i4i0000000000−2i22i2−2i22i2000000000000000000000000
χ554-444-4-44-40000−2222−2222−2222−2222000000004i−4i0000000000−2i22i2−2i22i2000000000000000000000000
χ564-444-4-44-40000−2222−2222−2222−222200000000−4i4i00000000002i2−2i22i2−2i2000000000000000000000000
χ574-44-4-44-4444-4-40000000000000000000000004i−4i4i−4i0000000000000000000000000000
χ584-44-4-44-4444-4-4000000000000000000000000−4i4i−4i4i0000000000000000000000000000
χ594-44-4-44-44-4-4444-4-444-4-44000000000000000000000000000000000000000000000000
χ604-44-4-44-44-4-444-444-4-444-4000000000000000000000000000000000000000000000000
χ614-4-4444-4-4000022−2222−22−2222−222200004i−4i000000000000002i2−2i2−2i22i2000000000000000000000000
χ624-4-4444-4-4000022−2222−22−2222−22220000−4i4i00000000000000−2i22i22i2−2i2000000000000000000000000
χ634-4-4444-4-40000−2222−222222−2222−2200004i−4i00000000000000−2i22i22i2−2i2000000000000000000000000
χ644-4-4444-4-40000−2222−222222−2222−220000−4i4i000000000000002i2−2i2−2i22i2000000000000000000000000
χ654-4-4-44-4444-4-444-4-44-444-4000000000000000000000000000000000000000000000000
χ664-4-4-44-4444-4-44-444-44-4-44000000000000000000000000000000000000000000000000
χ674-4-4-44-444-444-40000000000000000000000004-4-440000000000000000000000000000
χ684-4-4-44-444-444-4000000000000000000000000-444-40000000000000000000000000000

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