Finite Group Databasebeta

← Group #317543

Character table — Group #317543

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888884444444488888888888844444444888888882244444488888888
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
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ101111111111-1-1-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ111111111111-1-1-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-111-1-111
χ121111111111-1-1-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111
χ1722222222222222-2-2-222-200000000-2-2-2-222-2-20000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-222-200000000-2-2-2-222-2-2000000000000-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-2-2-2-222-20000000022-2-2-2-22200000000000022-2-2-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-2-222-20000000022-2-2-2-222000000000000-2-22222-2-2000000000000000000000000
χ2122222222-2-22222222-2-222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2222222222-2-22222222-2-22-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-200000000-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422222222-2-22222-2-2-2-2-2-200000000-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522222222-2-2-2-2-2-2222-2-2222222222-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-22-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-22-2-2-20022-2-22-2-20022i2i2i2i−2i−2i−2i−2i2-200000000002i2i−2i−2i0000000000000000000000000000i2−i2i2−i22−22−2
χ30222-22-2-2-20022-2-22-2-20022i2i2i2i−2i−2i−2i−2i2-200000000002i2i−2i−2i0000000000000000000000000000−i2i2−i2i2−22−22
χ31222-22-2-2-20022-2-22-2-2002−2i−2i−2i−2i2i2i2i2i2-20000000000−2i−2i2i2i0000000000000000000000000000i2−i2i2−i2−22−22
χ32222-22-2-2-20022-2-22-2-2002−2i−2i−2i−2i2i2i2i2i2-20000000000−2i−2i2i2i0000000000000000000000000000−i2i2−i2i22−22−2
χ33222-22-2-2-200-2-2222-2-20022i2i2i2i−2i−2i−2i−2i-220000000000−2i−2i2i2i0000000000000000000000000000i2−i2−i2i22−2−22
χ34222-22-2-2-200-2-2222-2-20022i2i2i2i−2i−2i−2i−2i-220000000000−2i−2i2i2i0000000000000000000000000000−i2i2i2−i2−222−2
χ35222-22-2-2-200-2-2222-2-2002−2i−2i−2i−2i2i2i2i2i-2200000000002i2i−2i−2i0000000000000000000000000000i2−i2−i2i2−222−2
χ36222-22-2-2-200-2-2222-2-2002−2i−2i−2i−2i2i2i2i2i-2200000000002i2i−2i−2i0000000000000000000000000000−i2i2i2−i22−2−22
χ3722-22-22-2-22-20000-22-22-222i2i−2i−2i2i2i−2i−2i002-200002i2i−2i−2i000000000000000000000000002i−2i2-20000000000
χ3822-22-22-2-22-20000-22-22-222i2i−2i−2i2i2i−2i−2i002-200002i2i−2i−2i00000000000000000000000000−2i2i-220000000000
χ3922-22-22-2-22-20000-22-22-22−2i−2i2i2i−2i−2i2i2i002-20000−2i−2i2i2i000000000000000000000000002i−2i-220000000000
χ4022-22-22-2-22-20000-22-22-22−2i−2i2i2i−2i−2i2i2i002-20000−2i−2i2i2i00000000000000000000000000−2i2i2-20000000000
χ4122-22-22-2-2-220000-22-2-2222i2i−2i−2i2i2i−2i−2i00-220000−2i−2i2i2i0000000000000000000000002-200002i−2i00000000
χ4222-22-22-2-2-220000-22-2-2222i2i−2i−2i2i2i−2i−2i00-220000−2i−2i2i2i000000000000000000000000-220000−2i2i00000000
χ4322-22-22-2-2-220000-22-2-222−2i−2i2i2i−2i−2i2i2i00-2200002i2i−2i−2i0000000000000000000000002-20000−2i2i00000000
χ4422-22-22-2-2-220000-22-2-222−2i−2i2i2i−2i−2i2i2i00-2200002i2i−2i−2i000000000000000000000000-2200002i−2i00000000
χ452-2-222-22-22-22-22-2000-220i2−i2i2−i2i2−i2i2−i200002-200i2−i2i2−i2i2−i2i2−i2i2i2−i2−i200002i−2i2i−2i2−22−22−22−20000000000000000
χ462-2-222-22-22-22-22-2000-220i2−i2i2−i2i2−i2i2−i200002-200i2−i2i2−i2i2−i2i2−i2i2i2−i2−i20000−2i2i−2i2i−22−22−22−220000000000000000
χ472-2-222-22-22-22-22-2000-220−i2i2−i2i2−i2i2−i2i200002-200−i2i2−i2i2−i2i2−i2i2−i2−i2i2i200002i−2i2i−2i−22−22−22−220000000000000000
χ482-2-222-22-22-22-22-2000-220−i2i2−i2i2−i2i2−i2i200002-200−i2i2−i2i2−i2i2−i2i2−i2−i2i2i20000−2i2i−2i2i2−22−22−22−20000000000000000
χ492-2-222-22-22-2-22-22000-220i2−i2i2−i2i2−i2i2−i20000-2200i2−i2i2−i2−i2i2−i2i2−i2−i2i2i200002i−2i−2i2i2−22−2−22−220000000000000000
χ502-2-222-22-22-2-22-22000-220i2−i2i2−i2i2−i2i2−i20000-2200i2−i2i2−i2−i2i2−i2i2−i2−i2i2i20000−2i2i2i−2i−22−222−22−20000000000000000
χ512-2-222-22-22-2-22-22000-220−i2i2−i2i2−i2i2−i2i20000-2200−i2i2−i2i2i2−i2i2−i2i2i2−i2−i200002i−2i−2i2i−22−222−22−20000000000000000
χ522-2-222-22-22-2-22-22000-220−i2i2−i2i2−i2i2−i2i20000-2200−i2i2−i2i2i2−i2i2−i2i2i2−i2−i20000−2i2i2i−2i2−22−2−22−220000000000000000
χ532-2-222-22-2-222-22-20002-20i2−i2i2−i2i2−i2i2−i20000-2200−i2i2−i2i2i2−i2i2−i2−i2−i2i2i22-22-20000i2−i2−i2i2i2−i2−i2i20000000000000000
χ542-2-222-22-2-222-22-20002-20i2−i2i2−i2i2−i2i2−i20000-2200−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2-22-220000−i2i2i2−i2−i2i2i2−i20000000000000000
χ552-2-222-22-2-222-22-20002-20−i2i2−i2i2−i2i2−i2i20000-2200i2−i2i2−i2−i2i2−i2i2i2i2−i2−i22-22-20000−i2i2i2−i2−i2i2i2−i20000000000000000
χ562-2-222-22-2-222-22-20002-20−i2i2−i2i2−i2i2−i2i20000-2200i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2-22-220000i2−i2−i2i2i2−i2−i2i20000000000000000
χ572-2-222-22-2-22-22-220002-20i2−i2i2−i2i2−i2i2−i200002-200−i2i2−i2i2−i2i2−i2i2i2i2−i2−i22-2-220000i2−i2−i2i2−i2i2i2−i20000000000000000
χ582-2-222-22-2-22-22-220002-20i2−i2i2−i2i2−i2i2−i200002-200−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2-222-20000−i2i2i2−i2i2−i2−i2i20000000000000000
χ592-2-222-22-2-22-22-220002-20−i2i2−i2i2−i2i2−i2i200002-200i2−i2i2−i2i2−i2i2−i2−i2−i2i2i22-2-220000−i2i2i2−i2i2−i2−i2i20000000000000000
χ602-2-222-22-2-22-22-220002-20−i2i2−i2i2−i2i2−i2i200002-200i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2-222-20000i2−i2−i2i2−i2i2i2−i20000000000000000
χ61444-44-4-4-40044-4-4-44400-400000000-4400000000000000000000000000000000000000000000000000
χ62444-44-4-4-400-4-444-44400-4000000004-400000000000000000000000000000000000000000000000000
χ6344-44-44-4-44-400004-444-4-40000000000-44000000000000000000000000000000000000000000000000
χ6444-44-44-4-4-4400004-44-44-400000000004-4000000000000000000000000000000000000000000000000
χ6544-4-4-4-44400000044-400-40000000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ6644-4-4-4-44400000044-400-4000000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ6744-4-4-4-444000000-4-4400444-4-4-4-4440000000000000000000000000000000000000000000000000000
χ6844-4-4-4-444000000-4-44004-4-44444-4-40000000000000000000000000000000000000000000000000000
χ694-444-4-4-44440000000-4-4022−22−222222−22−22220000000022−22−22220000000000000000000000000000000000000000
χ704-444-4-4-44440000000-4-40−222222−22−222222−2200000000−222222−220000000000000000000000000000000000000000
χ714-444-4-4-44-4-4000000044022−22−222222−22−222200000000−222222−220000000000000000000000000000000000000000
χ724-444-4-4-44-4-40000000440−222222−22−222222−220000000022−22−22220000000000000000000000000000000000000000
χ734-44-4-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i20000004i−4i0000000022−22−222200000000000000000000000000000000
χ744-44-4-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000−4i4i00000000−222222−2200000000000000000000000000000000
χ754-44-4-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i20000004i−4i00000000−222222−2200000000000000000000000000000000
χ764-44-4-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000−4i4i0000000022−22−222200000000000000000000000000000000
χ774-4-4-444-44004-4-4400000022−2222−22−2222−222200000000000022−22−2222000000000000000000000000000000000000
χ784-4-4-444-44004-4-44000000−2222−222222−2222−22000000000000−222222−22000000000000000000000000000000000000
χ794-4-4-444-4400-444-400000022−2222−22−2222−2222000000000000−222222−22000000000000000000000000000000000000
χ804-4-4-444-4400-444-4000000−2222−222222−2222−2200000000000022−22−2222000000000000000000000000000000000000

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