Finite Group Databasebeta

← Group #325573

Character table — Group #325573

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444444444444488888888444444888888888888444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ1011111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11
χ1111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11
χ1211111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-11
χ172222222222222222-2-2-22222-200000000-2-2-2-2-2-200000000000022-2-222-2-20000000000000000000000000000
χ182222222222222222-2-2-22222-200000000-2-2-2-2-2-2000000000000-2-222-2-2220000000000000000000000000000
χ19222222222222-2-2-2-2222-2-2-2-222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ20222222222222-2-2-2-2222-2-2-2-22-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-22222000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000
χ2322222222-2-2-2-22222222-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ2422222222-2-2-2-22222222-2-2-2-22-2-2-2-2-2-2-2-2-2-222-2-222222222-2-2-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-2220000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-222000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-2-22222-2000000002222-2-200000000000022-2-2-2-2220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-22222-2000000002222-2-2000000000000-2-22222-2-20000000000000000000000000000
χ292222-2-2-2-222-2-2000022-20000-22222-2-2-2-22-20000000022-2-200000000000022−2−222−2−222−2−222−2−2000000000000
χ302222-2-2-2-222-2-2000022-20000-22222-2-2-2-22-20000000022-2-2000000000000−2−222−2−222−2−222−2−222000000000000
χ312222-2-2-2-222-2-2000022-20000-2-2-2-2-222222-200000000-2-22200000000000022−2−222−2−2−2−222−2−222000000000000
χ322222-2-2-2-222-2-2000022-20000-2-2-2-2-222222-200000000-2-222000000000000−2−222−2−22222−2−222−2−2000000000000
χ332222-2-2-2-2-2-222000022-20000-22222-2-2-2-2-2200000000-2-22200000000000022−2−2−2−22222−2−2−2−222000000000000
χ342222-2-2-2-2-2-222000022-20000-22222-2-2-2-2-2200000000-2-222000000000000−2−22222−2−2−2−22222−2−2000000000000
χ352222-2-2-2-2-2-222000022-20000-2-2-2-2-22222-220000000022-2-200000000000022−2−2−2−222−2−22222−2−2000000000000
χ362222-2-2-2-2-2-222000022-20000-2-2-2-2-22222-220000000022-2-2000000000000−2−22222−2−222−2−2−2−222000000000000
χ3722-2-222-2-2000022-2-22-2-20000222-2-222-2-2002-2000000000022-2-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3822-2-222-2-2000022-2-22-2-20000222-2-222-2-2002-2000000000022-2-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3922-2-222-2-2000022-2-22-2-200002-2-222-2-222002-20000000000-2-22200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4022-2-222-2-2000022-2-22-2-200002-2-222-2-222002-20000000000-2-22200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4122-2-222-2-20000-2-2222-2-20000222-2-222-2-200-220000000000-2-22200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4222-2-222-2-20000-2-2222-2-20000222-2-222-2-200-220000000000-2-22200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4322-2-222-2-20000-2-2222-2-200002-2-222-2-22200-22000000000022-2-200000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4422-2-222-2-20000-2-2222-2-200002-2-222-2-22200-22000000000022-2-200000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4522-2-2-2-222000000002-2222-2-2-222-2-2-2-22200002-222-2-2000000000000000000002i−2i−2i2i00002i−2i−2i2i000000000000
χ4622-2-2-2-222000000002-2222-2-2-222-2-2-2-22200002-222-2-200000000000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ4722-2-2-2-222000000002-2222-2-2-2-2-22222-2-200002-2-2-222000000000000000000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ4822-2-2-2-222000000002-2222-2-2-2-2-22222-2-200002-2-2-22200000000000000000000−2i2i2i−2i00002i−2i−2i2i000000000000
χ4922-2-2-2-222000000002-22-2-222-222-2-2-2-2220000-22-2-22200000000000000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ5022-2-2-2-222000000002-22-2-222-222-2-2-2-2220000-22-2-2220000000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ5122-2-2-2-222000000002-22-2-222-2-2-22222-2-20000-2222-2-200000000000000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ5222-2-2-2-222000000002-22-2-222-2-2-22222-2-20000-2222-2-20000000000000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ532-22-22-22-22i−2i2i−2i2i−2i2i−2i0002-22-20i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i22−22−22−22−2002i−2i002-200000000000000002−22−2i2−i2i2−i20000
χ542-22-22-22-22i−2i2i−2i2i−2i2i−2i0002-22-20i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i22−22−22−22−200−2i2i00-220000000000000000−22−22−i2i2−i2i20000
χ552-22-22-22-22i−2i2i−2i2i−2i2i−2i0002-22-20−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2−22−22−22−22002i−2i002-20000000000000000−22−22−i2i2−i2i20000
χ562-22-22-22-22i−2i2i−2i2i−2i2i−2i0002-22-20−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2−22−22−22−2200−2i2i00-2200000000000000002−22−2i2−i2i2−i20000
χ572-22-22-22-22i−2i2i−2i−2i2i−2i2i000-22-220i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i22−22−2−22−222-2002i−2i000000000000000000i2−i2−i2i2−222−20000
χ582-22-22-22-22i−2i2i−2i−2i2i−2i2i000-22-220i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i22−22−2−22−22-2200−2i2i000000000000000000−i2i2i2−i22−2−220000
χ592-22-22-22-22i−2i2i−2i−2i2i−2i2i000-22-220−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i2−22−222−22−22-2002i−2i000000000000000000−i2i2i2−i22−2−220000
χ602-22-22-22-22i−2i2i−2i−2i2i−2i2i000-22-220−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i2−22−222−22−2-2200−2i2i000000000000000000i2−i2−i2i2−222−20000
χ612-22-22-22-2−2i2i−2i2i2i−2i2i−2i000-22-220i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i2−22−222−22−22-200−2i2i000000000000000000i2−i2−i2i22−2−220000
χ622-22-22-22-2−2i2i−2i2i2i−2i2i−2i000-22-220i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i2−22−222−22−2-22002i−2i000000000000000000−i2i2i2−i2−222−20000
χ632-22-22-22-2−2i2i−2i2i2i−2i2i−2i000-22-220−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i22−22−2−22−222-200−2i2i000000000000000000−i2i2i2−i2−222−20000
χ642-22-22-22-2−2i2i−2i2i2i−2i2i−2i000-22-220−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i22−22−2−22−22-22002i−2i000000000000000000i2−i2−i2i22−2−220000
χ652-22-22-22-2−2i2i−2i2i−2i2i−2i2i0002-22-20i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2−22−22−22−22002i−2i00-2200000000000000002−22−2−i2i2−i2i20000
χ662-22-22-22-2−2i2i−2i2i−2i2i−2i2i0002-22-20i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2−22−22−22−2200−2i2i002-20000000000000000−22−22i2−i2i2−i20000
χ672-22-22-22-2−2i2i−2i2i−2i2i−2i2i0002-22-20−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i22−22−22−22−2002i−2i00-220000000000000000−22−22i2−i2i2−i20000
χ682-22-22-22-2−2i2i−2i2i−2i2i−2i2i0002-22-20−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i22−22−22−22−200−2i2i002-200000000000000002−22−2−i2i2−i2i20000
χ694444-4-4-4-444-4-40000-4-440000400000000-440000000000000000000000000000000000000000000000000000
χ704444-4-4-4-4-4-4440000-4-4400004000000004-40000000000000000000000000000000000000000000000000000
χ7144-4-444-4-4000044-4-4-4440000-40000000000-4400000000000000000000000000000000000000000000000000
χ7244-4-444-4-40000-4-444-4440000-400000000004-400000000000000000000000000000000000000000000000000
χ7344-4-4-4-44400000000-44-444-4-44000000000000-44000000000000000000000000000000000000000000000000
χ7444-4-4-4-44400000000-44-4-4-44440000000000004-4000000000000000000000000000000000000000000000000
χ754-44-4-44-444i−4i−4i4i0000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000022−22−22220000000000000000000000000000000000000000
χ764-44-4-44-444i−4i−4i4i000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000−222222−220000000000000000000000000000000000000000
χ774-44-4-44-44−4i4i4i−4i0000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000−222222−220000000000000000000000000000000000000000
χ784-44-4-44-44−4i4i4i−4i000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000022−22−22220000000000000000000000000000000000000000
χ794-4-444-4-4400004i−4i−4i4i000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000022−22−2222000000000000000000000000000000000000
χ804-4-444-4-4400004i−4i−4i4i00000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000−222222−22000000000000000000000000000000000000
χ814-4-444-4-440000−4i4i4i−4i000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000−222222−22000000000000000000000000000000000000
χ824-4-444-4-440000−4i4i4i−4i00000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000022−22−2222000000000000000000000000000000000000
χ834-4-44-444-4000000000004-4-4402i2−2i2−2i22i2−2i22i22i2−2i20000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ844-4-44-444-4000000000004-4-440−2i22i22i2−2i22i2−2i2−2i22i2000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ854-4-44-444-400000000000-444-402i2−2i2−2i22i2−2i22i22i2−2i2000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ864-4-44-444-400000000000-444-40−2i22i22i2−2i22i2−2i2−2i22i20000002i2−2i2−2i22i200000000000000000000000000000000000000000000

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