Finite Group Databasebeta

← Group #239409

Character table — Group #239409

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222444444442222444444444444224444444444444444444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ17222222222222222222222222-2-2-2-2-2-2-2-2222200000000-2-2-2-200000000000000000000000000000000
χ18222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-22-222-2-22-200000000000000000000000000000000000000002-22-20000
χ202222222222222222-2-2-2-2-2-2-2-22-222-2-22-20000000000000000000000000000000000000000-22-220000
χ212222222222222222-2-2-2-2-2-2-2-2-22-2-222-22000000000000000000000000000000000000000000002-22-2
χ222222222222222222-2-2-2-2-2-2-2-2-22-2-222-2200000000000000000000000000000000000000000000-22-22
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-222-2-200000000-2-22200000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2220000000022-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2222-200000000000000000000000000000000000000002-2-220000
χ2622222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2222-20000000000000000000000000000000000000000-222-20000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2222-2-2-22000000000000000000000000000000000000000000002-2-22
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2222-2-2-2200000000000000000000000000000000000000000000-222-2
χ292222-2-2-2-22222-2-2-2-22-2-2222-2-2000000000000000000002i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000
χ302222-2-2-2-22222-2-2-2-22-2-2222-2-2000000000000000000002i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000
χ312222-2-2-2-22222-2-2-2-22-2-2222-2-200000000000000000000−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000
χ322222-2-2-2-22222-2-2-2-22-2-2222-2-200000000000000000000−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000
χ332222-2-2-2-2-2-2-2-222222-2-22-2-222000000000000000000002i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000
χ342222-2-2-2-2-2-2-2-222222-2-22-2-222000000000000000000002i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000
χ352222-2-2-2-2-2-2-2-222222-2-22-2-22200000000000000000000−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000
χ362222-2-2-2-2-2-2-2-222222-2-22-2-22200000000000000000000−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000
χ3722-2-222-2-222-2-222-2-2-22-222-22-2000000002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ3822-2-222-2-222-2-222-2-2-22-222-22-2000000002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ3922-2-222-2-222-2-222-2-2-22-222-22-200000000-22-2200000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ4022-2-222-2-222-2-222-2-2-22-222-22-200000000-22-2200000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ4122-2-222-2-2-2-222-2-222-22-22-22-22000000002-2-2200000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ4222-2-222-2-2-2-222-2-222-22-22-22-22000000002-2-2200000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ4322-2-222-2-2-2-222-2-222-22-22-22-2200000000-222-200000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ4422-2-222-2-2-2-222-2-222-22-22-22-2200000000-222-200000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ4522-2-2-2-22222-2-2-2-22222-2-2-222-22-22-22-2-2200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ4622-2-2-2-22222-2-2-2-22222-2-2-222-22-22-22-2-220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ4722-2-2-2-22222-2-2-2-22222-2-2-222-2-22-22-222-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ4822-2-2-2-22222-2-2-2-22222-2-2-222-2-22-22-222-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ4922-2-2-2-22222-2-2-2-222-2-2222-2-22222-2-22-2-2000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ5022-2-2-2-22222-2-2-2-222-2-2222-2-22222-2-22-2-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ5122-2-2-2-22222-2-2-2-222-2-2222-2-22-2-2-222-2220000000000000000000000002-2-222-2-220000000000000000
χ5222-2-2-2-22222-2-2-2-222-2-2222-2-22-2-2-222-222000000000000000000000000-222-2-222-20000000000000000
χ5322-2-2-2-222-2-22222-2-222-2-22-2-222-2-22-22-2200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ5422-2-2-2-222-2-22222-2-222-2-22-2-222-2-22-22-220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ5522-2-2-2-222-2-22222-2-222-2-22-2-22-222-22-22-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ5622-2-2-2-222-2-22222-2-222-2-22-2-22-222-22-22-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ5722-2-2-2-222-2-22222-2-2-2-222-222-222-222-2-2-2000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ5822-2-2-2-222-2-22222-2-2-2-222-222-222-222-2-2-200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ5922-2-2-2-222-2-22222-2-2-2-222-222-2-2-22-2-22220000000000000000000000002-2-22-222-20000000000000000
χ6022-2-2-2-222-2-22222-2-2-2-222-222-2-2-22-2-2222000000000000000000000000-222-22-2-220000000000000000
χ614444-4-4-4-44444-4-4-4-4-444-4-4-44400000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-4-4-44444-444-444-4-400000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-444-4-444-4-44-44-4-44-4400000000000000000000000000000000000000000000000000000000
χ6444-4-444-4-4-4-444-4-4444-44-44-44-400000000000000000000000000000000000000000000000000000000
χ654-44-44-44-44i−4i4i−4i4i−4i4i−4i000000000000000000002-22-22i−2i2i−2i000000000000000000000000000000000000
χ664-44-44-44-44i−4i4i−4i4i−4i4i−4i00000000000000000000-22-22−2i2i−2i2i000000000000000000000000000000000000
χ674-44-44-44-4−4i4i−4i4i−4i4i−4i4i000000000000000000002-22-2−2i2i−2i2i000000000000000000000000000000000000
χ684-44-44-44-4−4i4i−4i4i−4i4i−4i4i00000000000000000000-22-222i−2i2i−2i000000000000000000000000000000000000
χ694-44-4-44-444i−4i4i−4i−4i4i−4i4i000000000000000000000000000000002i−2i2i−2i2-22-2000000000000000000000000
χ704-44-4-44-444i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000−2i2i−2i2i-22-22000000000000000000000000
χ714-44-4-44-44−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000002i−2i2i−2i-22-22000000000000000000000000
χ724-44-4-44-44−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000−2i2i−2i2i2-22-2000000000000000000000000
χ734-4-444-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000002-2-22−2i2i2i−2i000000000000000000000000
χ744-4-444-4-444i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000-222-22i−2i−2i2i000000000000000000000000
χ754-4-444-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000002-2-222i−2i−2i2i000000000000000000000000
χ764-4-444-4-44−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000-222-2−2i2i2i−2i000000000000000000000000
χ774-4-44-444-44i−4i−4i4i−4i4i4i−4i000000000000000000002i−2i−2i2i-222-2000000000000000000000000000000000000
χ784-4-44-444-44i−4i−4i4i−4i4i4i−4i00000000000000000000−2i2i2i−2i2-2-22000000000000000000000000000000000000
χ794-4-44-444-4−4i4i4i−4i4i−4i−4i4i000000000000000000002i−2i−2i2i2-2-22000000000000000000000000000000000000
χ804-4-44-444-4−4i4i4i−4i4i−4i−4i4i00000000000000000000−2i2i2i−2i-222-2000000000000000000000000000000000000

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