Finite Group Databasebeta

← Group #239261

Character table — Group #239261

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222222444444444444448888888888888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222-2-2-2-22-2-2-2-222-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ20222222222-2-2-2-22-2-2-2-222-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ2122222222-222-2-2-222-2-2-2-22-222-2-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222222-222-2-2-222-2-2-2-22-222-2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-222-2-2-222-2-2-2-2-22-2-222-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2422222222-222-2-2-222-2-2-2-2-22-2-222-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2522222222-2-2-222-2-2-222-2-22-2-2-2222-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-2-222-2-2-222-2-22-2-2-2222-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2722222222-2-2-222-2-2-222-2-2-2222-2-2-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-222-2-2-222-2-2-2222-2-2-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ292222-2-2-2-2222222-2-2-2-2-2-2222-22-2-2-20000000000000000000000000000000000002i−2i2i−2i
χ302222-2-2-2-2222222-2-2-2-2-2-2222-22-2-2-2000000000000000000000000000000000000−2i2i−2i2i
χ312222-2-2-2-2222222-2-2-2-2-2-2-2-2-22-2222000000000000000000000000000000002-22-20000
χ322222-2-2-2-2222222-2-2-2-2-2-2-2-2-22-222200000000000000000000000000000000-22-220000
χ332222-2-2-2-22-2-2-2-222222-2-222-22-22-2-20000000000000000000000000000000000002i−2i−2i2i
χ342222-2-2-2-22-2-2-2-222222-2-222-22-22-2-2000000000000000000000000000000000000−2i2i2i−2i
χ352222-2-2-2-22-2-2-2-222222-2-2-2-22-22-222000000000000000000000000000000002-2-220000
χ362222-2-2-2-22-2-2-2-222222-2-2-2-22-22-22200000000000000000000000000000000-222-20000
χ372222-2-2-2-2-222-2-2-2-2-222222-22-2-22-220000000000000000000000002-22-2000000000000
χ382222-2-2-2-2-222-2-2-2-2-222222-22-2-22-22000000000000000000000000-22-22000000000000
χ392222-2-2-2-2-222-2-2-2-2-22222-22-222-22-200000000000000000000000000002-22-200000000
χ402222-2-2-2-2-222-2-2-2-2-22222-22-222-22-20000000000000000000000000000-22-2200000000
χ412222-2-2-2-2-2-2-222-222-2-2222-2-222-2-220000000000000000000000002-2-22000000000000
χ422222-2-2-2-2-2-2-222-222-2-2222-2-222-2-22000000000000000000000000-222-2000000000000
χ432222-2-2-2-2-2-2-222-222-2-222-222-2-222-200000000000000000000000000002-2-2200000000
χ442222-2-2-2-2-2-2-222-222-2-222-222-2-222-20000000000000000000000000000-222-200000000
χ4522-2-222-2-222-22-2-22-22-22-2000000002-22-200002−22−22−22−22−22−22−22−20000000000000000
χ4622-2-222-2-222-22-2-22-22-22-2000000002-22-20000−22−22−22−22−22−22−22−220000000000000000
χ4722-2-222-2-222-22-2-22-22-22-200000000-22-2200002−22−22−22−2−22−22−22−220000000000000000
χ4822-2-222-2-222-22-2-22-22-22-200000000-22-220000−22−22−22−222−22−22−22−20000000000000000
χ4922-2-222-2-22-22-22-2-22-222-2000000002-2-2200002−22−2−22−222−22−2−22−220000000000000000
χ5022-2-222-2-22-22-22-2-22-222-2000000002-2-220000−22−222−22−2−22−222−22−20000000000000000
χ5122-2-222-2-22-22-22-2-22-222-200000000-222-200002−22−2−22−22−22−222−22−20000000000000000
χ5222-2-222-2-22-22-22-2-22-222-200000000-222-20000−22−222−22−22−22−2−22−220000000000000000
χ5322-2-222-2-2-22-2-2222-2-22-220000000000002-22-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ5422-2-222-2-2-22-2-2222-2-22-220000000000002-22-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ5522-2-222-2-2-22-2-2222-2-22-22000000000000-22-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ5622-2-222-2-2-22-2-2222-2-22-22000000000000-22-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ5722-2-222-2-2-2-222-22-222-2-220000000000002-2-22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ5822-2-222-2-2-2-222-22-222-2-220000000000002-2-22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ5922-2-222-2-2-2-222-22-222-2-22000000000000-222-2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ6022-2-222-2-2-2-222-22-222-2-22000000000000-222-2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ6144-4-4-4-44444-44-4-4-44-44-44000000000000000000000000000000000000000000000000
χ6244-4-4-4-4444-44-44-44-44-4-44000000000000000000000000000000000000000000000000
χ6344-4-4-4-444-44-4-444-444-44-4000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-4-444-444-4-444-4000000000000000000000000000000000000000000000000
χ658-88-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000
χ668-88-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ678-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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