Finite Group Databasebeta

← Group #239913

Character table — Group #239913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222244488888888888888881616161616161111222222224448888888888888888161616161616
order12222244444444444448888888888884488882222224444444444444888888888888448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1
χ41111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ6111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1
χ8111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ922222222-2-222-2-2-222-2-200000000000000000022222222-2-222-2-2-222-2-2000000000000000000
χ1022222222-2-222-2-2-2-2-22200000000000000000022222222-2-222-2-2-2-2-222000000000000000000
χ11222222-2-222-2-22-2-2000000000000000000002i−2i222222-2-222-2-22-2-2000000000000000000002i−2i
χ12222222-2-222-2-22-2-200000000000000000000−2i2i222222-2-222-2-22-2-200000000000000000000−2i2i
χ13222222-2-2-2-2-2-2-2220000000000000000002i−2i00222222-2-2-2-2-2-2-2220000000000000000002i−2i00
χ14222222-2-2-2-2-2-2-222000000000000000000−2i2i00222222-2-2-2-2-2-2-222000000000000000000−2i2i00
χ152222-2-22-2222-2-2-22000022-2-2000000000000002222-2-22-2222-2-2-22000022-2-200000000000000
χ162222-2-22-2222-2-2-220000-2-222000000000000002222-2-22-2222-2-2-220000-2-22200000000000000
χ172222-2-22-2-2-22-222-20000000000002i2i−2i−2i0000002222-2-22-2-2-22-222-20000000000002i2i−2i−2i000000
χ182222-2-22-2-2-22-222-2000000000000−2i−2i2i2i0000002222-2-22-2-2-22-222-2000000000000−2i−2i2i2i000000
χ192222-2-2-2222-22-22-20000000022-2-200000000002222-2-2-2222-22-22-20000000022-2-20000000000
χ202222-2-2-2222-22-22-200000000-2-22200000000002222-2-2-2222-22-22-200000000-2-2220000000000
χ212222-2-2-22-2-2-222-2200000000000000002-200002222-2-2-22-2-2-222-2200000000000000002-20000
χ222222-2-2-22-2-2-222-220000000000000000-2200002222-2-2-22-2-2-222-220000000000000000-220000
χ232-22-22-22200-2-20002-2002−22−200002−22−20000002-22-22-22200-2-20002-2002−22−200002−22−2000000
χ242-22-22-22200-2-20002-200−22−220000−22−220000002-22-22-22200-2-20002-200−22−220000−22−22000000
χ252-22-22-22200-2-2000-22002−22−20000−22−220000002-22-22-22200-2-2000-22002−22−20000−22−22000000
χ262-22-22-22200-2-2000-2200−22−2200002−22−20000002-22-22-22200-2-2000-2200−22−2200002−22−2000000
χ272-22-2-222-200-22000002i−2i2−2−220000i2−i2−i2i20000002-22-2-222-200-22000002i−2i2−2−220000i2−i2−i2i2000000
χ282-22-2-222-200-22000002i−2i−222−20000−i2i2i2−i20000002-22-2-222-200-22000002i−2i−222−20000−i2i2i2−i2000000
χ292-22-2-222-200-2200000−2i2i2−2−220000−i2i2i2−i20000002-22-2-222-200-2200000−2i2i2−2−220000−i2i2i2−i2000000
χ302-22-2-222-200-2200000−2i2i−222−20000i2−i2−i2i20000002-22-2-222-200-2200000−2i2i−222−20000i2−i2−i2i2000000
χ3144-4-400004-400000000000000022−22000000000044-4-400004-400000000000000022−220000000000
χ3244-4-400004-4000000000000000−2222000000000044-4-400004-4000000000000000−22220000000000
χ3344-4-40000-44000000000000022−2200000000000044-4-40000-44000000000000022−22000000000000
χ3444-4-40000-440000000000000−222200000000000044-4-40000-440000000000000−2222000000000000
χ354-44-44-4-4-4004400000000000000000000000004-44-44-4-4-400440000000000000000000000000
χ364-44-4-44-44004-400000000000000000000000004-44-4-44-44004-40000000000000000000000000
χ378-8-880000000000000000000000000000000008-8-88000000000000000000000000000000000
χ381111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3911111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ401111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ42111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ43111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111
χ44111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111
χ45111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ4622222222-2-222-2-2-222-2-2000000000000000000-2-2-2-2-2-2-2-222-2-2222-2-222000000000000000000
χ4722222222-2-222-2-2-2-2-222000000000000000000-2-2-2-2-2-2-2-222-2-222222-2-2000000000000000000
χ48222222-2-222-2-22-2-2000000000000000000002i−2i-2-2-2-2-2-222-2-222-22200000000000000000000−2i2i
χ49222222-2-222-2-22-2-200000000000000000000−2i2i-2-2-2-2-2-222-2-222-222000000000000000000002i−2i
χ50222222-2-2-2-2-2-2-2220000000000000000002i−2i00-2-2-2-2-2-22222222-2-2000000000000000000−2i2i00
χ51222222-2-2-2-2-2-2-222000000000000000000−2i2i00-2-2-2-2-2-22222222-2-20000000000000000002i−2i00
χ522222-2-22-2222-2-2-22000022-2-200000000000000-2-2-2-222-22-2-2-2222-20000-2-22200000000000000
χ532222-2-22-2222-2-2-220000-2-22200000000000000-2-2-2-222-22-2-2-2222-2000022-2-200000000000000
χ542222-2-22-2-2-22-222-20000000000002i2i−2i−2i000000-2-2-2-222-2222-22-2-22000000000000−2i−2i2i2i000000
χ552222-2-22-2-2-22-222-2000000000000−2i−2i2i2i000000-2-2-2-222-2222-22-2-220000000000002i2i−2i−2i000000
χ562222-2-2-2222-22-22-20000000022-2-20000000000-2-2-2-2222-2-2-22-22-2200000000-2-2220000000000
χ572222-2-2-2222-22-22-200000000-2-2220000000000-2-2-2-2222-2-2-22-22-220000000022-2-20000000000
χ582222-2-2-22-2-2-222-2200000000000000002-20000-2-2-2-2222-2222-2-22-20000000000000000-220000
χ592222-2-2-22-2-2-222-220000000000000000-220000-2-2-2-2222-2222-2-22-200000000000000002-20000
χ602-22-22-22200-2-20002-2002−22−200002−22−2000000-22-22-22-2-20022000-2200−22−220000−22−22000000
χ612-22-22-22200-2-20002-200−22−220000−22−22000000-22-22-22-2-20022000-22002−22−200002−22−2000000
χ622-22-22-22200-2-2000-22002−22−20000−22−22000000-22-22-22-2-200220002-200−22−2200002−22−2000000
χ632-22-22-22200-2-2000-2200−22−2200002−22−2000000-22-22-22-2-200220002-2002−22−20000−22−22000000
χ642-22-2-222-200-22000002i−2i2−2−220000i2−i2−i2i2000000-22-222-2-22002-200000−2i2i−222−20000−i2i2i2−i2000000
χ652-22-2-222-200-22000002i−2i−222−20000−i2i2i2−i2000000-22-222-2-22002-200000−2i2i2−2−220000i2−i2−i2i2000000
χ662-22-2-222-200-2200000−2i2i2−2−220000−i2i2i2−i2000000-22-222-2-22002-2000002i−2i−222−20000i2−i2−i2i2000000
χ672-22-2-222-200-2200000−2i2i−222−20000i2−i2−i2i2000000-22-222-2-22002-2000002i−2i2−2−220000−i2i2i2−i2000000
χ6844-4-400004-400000000000000022−220000000000-4-4440000-44000000000000000−22220000000000
χ6944-4-400004-4000000000000000−22220000000000-4-4440000-4400000000000000022−220000000000
χ7044-4-40000-44000000000000022−22000000000000-4-44400004-40000000000000−2222000000000000
χ7144-4-40000-440000000000000−2222000000000000-4-44400004-4000000000000022−22000000000000
χ724-44-44-4-4-400440000000000000000000000000-44-44-444400-4-40000000000000000000000000
χ734-44-4-44-44004-40000000000000000000000000-44-444-44-400-440000000000000000000000000
χ748-8-88000000000000000000000000000000000-888-8000000000000000000000000000000000

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