Finite Group Databasebeta

← Group #243321

Character table — Group #243321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444444444444444888888888888888822444444888888882222444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222-2-2-2-222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-22222-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ20222222222222-2-2-2-22222-2-22222-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2422222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222000000000000000022-2-2-2-222000000000000000000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2220000000000000000-2-22222-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ29222-22-2-2-22i2i−2i−2i00002i2i−2i−2i0022-2-200000022−2−2i2i2−i2−i222−2−2i2i2−i2−i2002i−2i002-2i2−i2i2−i22−22−20000000000000000
χ30222-22-2-2-22i2i−2i−2i00002i2i−2i−2i0022-2-200000022−2−2i2i2−i2−i222−2−2i2i2−i2−i200−2i2i00-22−i2i2−i2i2−22−220000000000000000
χ31222-22-2-2-22i2i−2i−2i00002i2i−2i−2i0022-2-2000000−2−222−i2−i2i2i2−2−222−i2−i2i2i2002i−2i002-2−i2i2−i2i2−22−220000000000000000
χ32222-22-2-2-22i2i−2i−2i00002i2i−2i−2i0022-2-2000000−2−222−i2−i2i2i2−2−222−i2−i2i2i200−2i2i00-22i2−i2i2−i22−22−20000000000000000
χ33222-22-2-2-22i2i−2i−2i0000−2i−2i2i2i00-2-22200000022−2−2i2i2−i2−i2−2−222−i2−i2i2i22-2002i−2i002−2−22−i2i2i2−i20000000000000000
χ34222-22-2-2-22i2i−2i−2i0000−2i−2i2i2i00-2-22200000022−2−2i2i2−i2−i2−2−222−i2−i2i2i2-2200−2i2i00−222−2i2−i2−i2i20000000000000000
χ35222-22-2-2-22i2i−2i−2i0000−2i−2i2i2i00-2-222000000−2−222−i2−i2i2i222−2−2i2i2−i2−i22-2002i−2i00−222−2i2−i2−i2i20000000000000000
χ36222-22-2-2-22i2i−2i−2i0000−2i−2i2i2i00-2-222000000−2−222−i2−i2i2i222−2−2i2i2−i2−i2-2200−2i2i002−2−22−i2i2i2−i20000000000000000
χ37222-22-2-2-2−2i−2i2i2i00002i2i−2i−2i00-2-22200000022−2−2−i2−i2i2i2−2−222i2i2−i2−i22-200−2i2i002−2−22i2−i2−i2i20000000000000000
χ38222-22-2-2-2−2i−2i2i2i00002i2i−2i−2i00-2-22200000022−2−2−i2−i2i2i2−2−222i2i2−i2−i2-22002i−2i00−222−2−i2i2i2−i20000000000000000
χ39222-22-2-2-2−2i−2i2i2i00002i2i−2i−2i00-2-222000000−2−222i2i2−i2−i222−2−2−i2−i2i2i22-200−2i2i00−222−2−i2i2i2−i20000000000000000
χ40222-22-2-2-2−2i−2i2i2i00002i2i−2i−2i00-2-222000000−2−222i2i2−i2−i222−2−2−i2−i2i2i2-22002i−2i002−2−22i2−i2−i2i20000000000000000
χ41222-22-2-2-2−2i−2i2i2i0000−2i−2i2i2i0022-2-200000022−2−2−i2−i2i2i222−2−2−i2−i2i2i2002i−2i00-22i2−i2i2−i2−22−220000000000000000
χ42222-22-2-2-2−2i−2i2i2i0000−2i−2i2i2i0022-2-200000022−2−2−i2−i2i2i222−2−2−i2−i2i2i200−2i2i002-2−i2i2−i2i22−22−20000000000000000
χ43222-22-2-2-2−2i−2i2i2i0000−2i−2i2i2i0022-2-2000000−2−222i2i2−i2−i2−2−222i2i2−i2−i2002i−2i00-22−i2i2−i2i22−22−20000000000000000
χ44222-22-2-2-2−2i−2i2i2i0000−2i−2i2i2i0022-2-2000000−2−222i2i2−i2−i2−2−222i2i2−i2−i200−2i2i002-2i2−i2i2−i2−22−220000000000000000
χ4522-22-22-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i2-22-22-22-22-22i−2i00000000000000000000000000000000002-2002i−2i00000000
χ4622-22-22-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i2-22-22-22-22-22i−2i0000000000000000000000000000000000-2200−2i2i00000000
χ4722-22-22-2-22i−2i2i−2i2i2i−2i−2i−2i2i−2i2i2-2-22-222-2-22−2i2i000000000000000000000000000000002-2002i−2i0000000000
χ4822-22-22-2-22i−2i2i−2i2i2i−2i−2i−2i2i−2i2i2-2-22-222-2-22−2i2i00000000000000000000000000000000-2200−2i2i0000000000
χ4922-22-22-2-22i−2i2i−2i−2i−2i2i2i2i−2i2i−2i-222-22-2-22-22−2i2i000000000000000000000000000000000000000000002-22i−2i
χ5022-22-22-2-22i−2i2i−2i−2i−2i2i2i2i−2i2i−2i-222-22-2-22-22−2i2i00000000000000000000000000000000000000000000-22−2i2i
χ5122-22-22-2-22i−2i2i−2i−2i−2i2i2i−2i2i−2i2i-22-22-22-222-22i−2i00000000000000000000000000000000000000002-22i−2i0000
χ5222-22-22-2-22i−2i2i−2i−2i−2i2i2i−2i2i−2i2i-22-22-22-222-22i−2i0000000000000000000000000000000000000000-22−2i2i0000
χ5322-22-22-2-2−2i2i−2i2i2i2i−2i−2i2i−2i2i−2i-22-22-22-222-2−2i2i00000000000000000000000000000000000000002-2−2i2i0000
χ5422-22-22-2-2−2i2i−2i2i2i2i−2i−2i2i−2i2i−2i-22-22-22-222-2−2i2i0000000000000000000000000000000000000000-222i−2i0000
χ5522-22-22-2-2−2i2i−2i2i2i2i−2i−2i−2i2i−2i2i-222-22-2-22-222i−2i000000000000000000000000000000000000000000002-2−2i2i
χ5622-22-22-2-2−2i2i−2i2i2i2i−2i−2i−2i2i−2i2i-222-22-2-22-222i−2i00000000000000000000000000000000000000000000-222i−2i
χ5722-22-22-2-2−2i2i−2i2i−2i−2i2i2i2i−2i2i−2i2-2-22-222-2-222i−2i000000000000000000000000000000002-200−2i2i0000000000
χ5822-22-22-2-2−2i2i−2i2i−2i−2i2i2i2i−2i2i−2i2-2-22-222-2-222i−2i00000000000000000000000000000000-22002i−2i0000000000
χ5922-22-22-2-2−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i2-22-22-22-22-2−2i2i00000000000000000000000000000000002-200−2i2i00000000
χ6022-22-22-2-2−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i2-22-22-22-22-2−2i2i0000000000000000000000000000000000-22002i−2i00000000
χ6144-4-4-4-4444-4-4400004-4-44004-4-44000000000000000000000000000000000000000000000000000000
χ6244-4-4-4-4444-4-440000-444-400-444-4000000000000000000000000000000000000000000000000000000
χ6344-4-4-4-444-444-400004-4-4400-444-4000000000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-444-40000-444-4004-4-44000000000000000000000000000000000000000000000000000000
χ654-444-4-44-400004i−4i4i−4i000000000000000022−2222−222i2−2i22i2−2i20000000000000000000000000000000000000000
χ664-444-4-44-400004i−4i4i−4i0000000000000000−2222−2222−2i22i2−2i22i20000000000000000000000000000000000000000
χ674-444-4-44-40000−4i4i−4i4i000000000000000022−2222−22−2i22i2−2i22i20000000000000000000000000000000000000000
χ684-444-4-44-40000−4i4i−4i4i0000000000000000−2222−22222i2−2i22i2−2i20000000000000000000000000000000000000000
χ694-44-4-44-440000000000004-40000-4400004-4-4400000000000000000000000000000000000000000000
χ704-44-4-44-440000000000004-40000-440000-444-400000000000000000000000000000000000000000000
χ714-44-4-44-44000000000000-4400004-4000000004-4-440000000000000000000000000000000000000000
χ724-44-4-44-44000000000000-4400004-400000000-444-40000000000000000000000000000000000000000
χ734-4-444-4-4400004-4-4400000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ744-4-444-4-4400004-4-44000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ754-4-444-4-440000-444-400000000000000000000000022−2222−22−2222−222200000000000000000000000000000000
χ764-4-444-4-440000-444-4000000000000000000000000−2222−222222−2222−2200000000000000000000000000000000
χ774-4-4-4444-4000000000000440000-4-400000000000000004i−4i−4i4i00000000000000000000000000000000
χ784-4-4-4444-4000000000000440000-4-40000000000000000−4i4i4i−4i00000000000000000000000000000000
χ794-4-4-4444-4000000000000-4-40000440000000000004-4-44000000000000000000000000000000000000
χ804-4-4-4444-4000000000000-4-4000044000000000000-444-4000000000000000000000000000000000000

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