Finite Group Databasebeta

← Group #242106

Character table — Group #242106

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444444444444444888888888888888822444444888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-111-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11-1-111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-1-11-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-11111111-1-1-1-1
χ91111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111-1-1-111-1-1-1111-1-1
χ101111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1111-1-1111-1-1-111
χ111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-11111-1-1-1-1-111
χ121111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1
χ131111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111111-1-1-1-1-1-1111-1-111
χ141111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1111111-1-1-111-1-1
χ151111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-11-1-1111-111-1-1
χ161111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1111-111-1-1-11-1-111
χ1722222222222222-2-22222-2-2-2-222-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222-2-22222-2-2-2-222-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-2222222-2-222-2-2000000000000000022-2-2-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2222222-2-222-2-20000000000000000-2-22222-2-2000000000000000000000000
χ2122222222-2-2222222-2-2-2-22222-2-222-2-2-2-20000000000000000000000000000000000200200-200-20000
χ2222222222-2-2222222-2-2-2-22222-2-222-2-2-2-20000000000000000000000000000000000-200-20020020000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002-202-200000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-220-2200000000000
χ2522222222-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-20000000000000000000000000000000000200-200200-20000
χ2622222222-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-20000000000000000000000000000000000-200200-20020000
χ2722222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222000000000000000000000000000000002-20-2200000000000
χ2822222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-22200000000000000000000000000000000-2202-200000000000
χ29222-22-2-2-2-2-222-2-20022-2-2000022000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200002i−2i2i−2i22−2−222−2−20000000000000000
χ30222-22-2-2-2-2-222-2-20022-2-2000022000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000−2i2i−2i2i−2−222−2−2220000000000000000
χ31222-22-2-2-2-2-222-2-20022-2-2000022000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200002i−2i2i−2i−2−222−2−2220000000000000000
χ32222-22-2-2-2-2-222-2-20022-2-2000022000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000−2i2i−2i2i22−2−222−2−20000000000000000
χ33222-22-2-2-2-2-2-2-22200-2-222000022000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200002i−2i−2i2i22−2−2−2−2220000000000000000
χ34222-22-2-2-2-2-2-2-22200-2-222000022000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000−2i2i2i−2i−2−22222−2−20000000000000000
χ35222-22-2-2-2-2-2-2-22200-2-222000022000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200002i−2i−2i2i−2−22222−2−20000000000000000
χ36222-22-2-2-2-2-2-2-22200-2-222000022000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000−2i2i2i−2i22−2−2−2−2220000000000000000
χ3722-22-2-2-222-22i−2i2i−2i002i−2i2i−2i00002-2000000i2i2−i2−i2i2i2−i2−i222−2−222−2−22-22i−2i0000i2−i2i2−i22−22−20000000000000000
χ3822-22-2-2-222-22i−2i2i−2i002i−2i2i−2i00002-2000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2-22−2i2i0000−i2i2−i2i2−22−220000000000000000
χ3922-22-2-2-222-22i−2i2i−2i002i−2i2i−2i00002-2000000−i2−i2i2i2−i2−i2i2i2−2−222−2−2222-22i−2i0000−i2i2−i2i2−22−220000000000000000
χ4022-22-2-2-222-22i−2i2i−2i002i−2i2i−2i00002-2000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222-22−2i2i0000i2−i2i2−i22−22−20000000000000000
χ4122-22-2-2-222-2−2i2i−2i2i00−2i2i−2i2i00002-2000000i2i2−i2−i2i2i2−i2−i2−2−222−2−2222-2−2i2i0000i2−i2i2−i2−22−220000000000000000
χ4222-22-2-2-222-2−2i2i−2i2i00−2i2i−2i2i00002-2000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222-222i−2i0000−i2i2−i2i22−22−20000000000000000
χ4322-22-2-2-222-2−2i2i−2i2i00−2i2i−2i2i00002-2000000−i2−i2i2i2−i2−i2i2i222−2−222−2−22-2−2i2i0000−i2i2−i2i22−22−20000000000000000
χ4422-22-2-2-222-2−2i2i−2i2i00−2i2i−2i2i00002-2000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2-222i−2i0000i2−i2i2−i2−22−220000000000000000
χ4522-2-2-222-22-22i−2i−2i2i2-2−2i2i2i−2i2i2i−2i−2i-222-22i−2i2-2000000000000000000000000000000000000002-202i−2i00000
χ4622-2-2-222-22-22i−2i−2i2i2-2−2i2i2i−2i2i2i−2i−2i-222-22i−2i2-200000000000000000000000000000000000000-220−2i2i00000
χ4722-2-2-222-22-22i−2i−2i2i-22−2i2i2i−2i−2i−2i2i2i-22-22−2i2i-22000000000000000000000000000000000000000000002-22i−2i
χ4822-2-2-222-22-22i−2i−2i2i-22−2i2i2i−2i−2i−2i2i2i-22-22−2i2i-2200000000000000000000000000000000000000000000-22−2i2i
χ4922-2-2-222-22-2−2i2i2i−2i2-22i−2i−2i2i−2i−2i2i2i-222-2−2i2i2-2000000000000000000000000000000000000002-20−2i2i00000
χ5022-2-2-222-22-2−2i2i2i−2i2-22i−2i−2i2i−2i−2i2i2i-222-2−2i2i2-200000000000000000000000000000000000000-2202i−2i00000
χ5122-2-2-222-22-2−2i2i2i−2i-222i−2i−2i2i2i2i−2i−2i-22-222i−2i-22000000000000000000000000000000000000000000002-2−2i2i
χ5222-2-2-222-22-2−2i2i2i−2i-222i−2i−2i2i2i2i−2i−2i-22-222i−2i-2200000000000000000000000000000000000000000000-222i−2i
χ5322-2-2-222-2-222i−2i−2i2i2-22i−2i−2i2i2i2i−2i−2i2-22-2−2i2i-220000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ5422-2-2-222-2-222i−2i−2i2i2-22i−2i−2i2i2i2i−2i−2i2-22-2−2i2i-22000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ5522-2-2-222-2-222i−2i−2i2i-222i−2i−2i2i−2i−2i2i2i2-2-222i−2i2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ5622-2-2-222-2-222i−2i−2i2i-222i−2i−2i2i−2i−2i2i2i2-2-222i−2i2-2-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ5722-2-2-222-2-22−2i2i2i−2i2-2−2i2i2i−2i−2i−2i2i2i2-22-22i−2i-220000000000000000000000002i−2i−2i2i-222-20000000000000000
χ5822-2-2-222-2-22−2i2i2i−2i2-2−2i2i2i−2i−2i−2i2i2i2-22-22i−2i-22000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ5922-2-2-222-2-22−2i2i2i−2i-22−2i2i2i−2i2i2i−2i−2i2-2-22−2i2i2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ6022-2-2-222-2-22−2i2i2i−2i-22−2i2i2i−2i2i2i−2i−2i2-2-22−2i2i2-2-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ61444-44-4-4-44444-4-400-4-4440000-4-4000000000000000000000000000000000000000000000000000000
χ62444-44-4-4-444-4-4440044-4-40000-4-4000000000000000000000000000000000000000000000000000000
χ6344-44-4-4-44-444i−4i4i−4i00−4i4i−4i4i0000-44000000000000000000000000000000000000000000000000000000
χ6444-44-4-4-44-44−4i4i−4i4i004i−4i4i−4i0000-44000000000000000000000000000000000000000000000000000000
χ654-444-4-44-40000000000004i−4i4i−4i000000002-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ664-444-4-44-40000000000004i−4i4i−4i00000000-22-22-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ674-444-4-44-4000000000000−4i4i−4i4i000000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ684-444-4-44-4000000000000−4i4i−4i4i00000000-22-22-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ694-44-4-44-44000000440000000000-4-400002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ704-44-4-44-44000000440000000000-4-40000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ714-44-4-44-44000000-4-400000000004400000000000022−2222−22−2222−222200000000000000000000000000000000
χ724-44-4-44-44000000-4-4000000000044000000000000−2222−222222−2222−2200000000000000000000000000000000
χ734-4-4444-4-40000004-40000000000-440000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ744-4-4444-4-40000004-40000000000-44000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ754-4-4444-4-4000000-4400000000004-400002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ764-4-4444-4-4000000-4400000000004-40000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ774-4-4-44-4440000000000004-4-44000000002-2-22-222-22-2-22-222-200000000000000000000000000000000
χ784-4-4-44-4440000000000004-4-4400000000-222-22-2-22-222-22-2-2200000000000000000000000000000000
χ794-4-4-44-444000000000000-444-4000000002-2-22-222-2-222-22-2-2200000000000000000000000000000000
χ804-4-4-44-444000000000000-444-400000000-222-22-2-222-2-22-222-200000000000000000000000000000000

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