Finite Group Databasebeta

← Group #317549

Character table — Group #317549

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
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111111111-1-1-1-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ101111111111-1-1-1-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ111111111111-1-1-1-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-111-1-111
χ121111111111-1-1-1-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1722222222222222-2-2-2-2220000000022-2-2-2-2-2-200000000000022-2-2-2-222000000000000000000000000
χ1822222222222222-2-2-2-2220000000022-2-2-2-2-2-2000000000000-2-22222-2-2000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-22200000000-2-222-2-2220000000000002222-2-2-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-22200000000-2-222-2-222000000000000-2-2-2-22222000000000000000000000000
χ2122222222-2-222222222-2-222222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2222222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-200000000-2-2-2-22222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422222222-2-22222-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522222222-2-2-2-2-2-22222-2-22222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
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
χ29222-2-22-2-22-20000-2-2222-22i2i2i2i−2i−2i−2i−2i00002-2002i2i−2i−2i000000000000000000000000002-22i−2i0000000000
χ30222-2-22-2-22-20000-2-2222-22i2i2i2i−2i−2i−2i−2i00002-2002i2i−2i−2i00000000000000000000000000-22−2i2i0000000000
χ31222-2-22-2-22-20000-2-2222-2−2i−2i−2i−2i2i2i2i2i00002-200−2i−2i2i2i000000000000000000000000002-2−2i2i0000000000
χ32222-2-22-2-22-20000-2-2222-2−2i−2i−2i−2i2i2i2i2i00002-200−2i−2i2i2i00000000000000000000000000-222i−2i0000000000
χ33222-2-22-2-2-220000-2-222-222i2i2i2i−2i−2i−2i−2i0000-2200−2i−2i2i2i0000000000000000000000002-200002i−2i00000000
χ34222-2-22-2-2-220000-2-222-222i2i2i2i−2i−2i−2i−2i0000-2200−2i−2i2i2i000000000000000000000000-220000−2i2i00000000
χ35222-2-22-2-2-220000-2-222-22−2i−2i−2i−2i2i2i2i2i0000-22002i2i−2i−2i0000000000000000000000002-20000−2i2i00000000
χ36222-2-22-2-2-220000-2-222-22−2i−2i−2i−2i2i2i2i2i0000-22002i2i−2i−2i000000000000000000000000-2200002i−2i00000000
χ3722-22-2-22-2002i2i−2i−2i2-22-20022-2-222-2-2002i−2i000000002i2i−2i−2i00000000000000000000000000002−2i2−i22−2i2−i2
χ3822-22-2-22-2002i2i−2i−2i2-22-20022-2-222-2-2002i−2i000000002i2i−2i−2i0000000000000000000000000000−22−i2i2−22−i2i2
χ3922-22-2-22-2002i2i−2i−2i2-22-200-2-222-2-222002i−2i00000000−2i−2i2i2i00000000000000000000000000002−2i2−i2−22−i2i2
χ4022-22-2-22-2002i2i−2i−2i2-22-200-2-222-2-222002i−2i00000000−2i−2i2i2i0000000000000000000000000000−22−i2i22−2i2−i2
χ4122-22-2-22-200−2i−2i2i2i2-22-20022-2-222-2-200−2i2i00000000−2i−2i2i2i00000000000000000000000000002−2−i2i22−2−i2i2
χ4222-22-2-22-200−2i−2i2i2i2-22-20022-2-222-2-200−2i2i00000000−2i−2i2i2i0000000000000000000000000000−22i2−i2−22i2−i2
χ4322-22-2-22-200−2i−2i2i2i2-22-200-2-222-2-22200−2i2i000000002i2i−2i−2i00000000000000000000000000002−2−i2i2−22i2−i2
χ4422-22-2-22-200−2i−2i2i2i2-22-200-2-222-2-22200−2i2i000000002i2i−2i−2i0000000000000000000000000000−22i2−i22−2−i2i2
χ452-222-2-2-222-22-22-20000-22i2−i2i2−i2i2−i2i2−i22-2000000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2002i−2i2i−2i002−22−22−22−20000000000000000
χ462-222-2-2-222-22-22-20000-22i2−i2i2−i2i2−i2i2−i22-2000000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i200−2i2i−2i2i00−22−22−22−220000000000000000
χ472-222-2-2-222-22-22-20000-22−i2i2−i2i2−i2i2−i2i22-2000000−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2002i−2i2i−2i00−22−22−22−220000000000000000
χ482-222-2-2-222-22-22-20000-22−i2i2−i2i2−i2i2−i2i22-2000000−i2i2−i2i2−i2i2−i2i2−i2−i2i2i200−2i2i−2i2i002−22−22−22−20000000000000000
χ492-222-2-2-222-2-22-220000-22i2−i2i2−i2i2−i2i2−i2-22000000i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2002i−2i−2i2i00−22−222−22−20000000000000000
χ502-222-2-2-222-2-22-220000-22i2−i2i2−i2i2−i2i2−i2-22000000i2−i2i2−i2−i2i2−i2i2−i2−i2i2i200−2i2i2i−2i002−22−2−22−220000000000000000
χ512-222-2-2-222-2-22-220000-22−i2i2−i2i2−i2i2−i2i2-22000000−i2i2−i2i2i2−i2i2−i2i2i2−i2−i2002i−2i−2i2i002−22−2−22−220000000000000000
χ522-222-2-2-222-2-22-220000-22−i2i2−i2i2−i2i2−i2i2-22000000−i2i2−i2i2i2−i2i2−i2i2i2−i2−i200−2i2i2i−2i00−22−222−22−20000000000000000
χ532-222-2-2-22-222-22-200002-2i2−i2i2−i2i2−i2i2−i2-22000000−i2i2−i2i2i2−i2i2−i2−i2−i2i2i22-200002-2i2−i2−i2i2i2−i2−i2i20000000000000000
χ542-222-2-2-22-222-22-200002-2i2−i2i2−i2i2−i2i2−i2-22000000−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2-220000-22−i2i2i2−i2−i2i2i2−i20000000000000000
χ552-222-2-2-22-222-22-200002-2−i2i2−i2i2−i2i2−i2i2-22000000i2−i2i2−i2−i2i2−i2i2i2i2−i2−i22-200002-2−i2i2i2−i2−i2i2i2−i20000000000000000
χ562-222-2-2-22-222-22-200002-2−i2i2−i2i2−i2i2−i2i2-22000000i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2-220000-22i2−i2−i2i2i2−i2−i2i20000000000000000
χ572-222-2-2-22-22-22-2200002-2i2−i2i2−i2i2−i2i2−i22-2000000−i2i2−i2i2−i2i2−i2i2i2i2−i2−i22-20000-22i2−i2−i2i2−i2i2i2−i20000000000000000
χ582-222-2-2-22-22-22-2200002-2i2−i2i2−i2i2−i2i2−i22-2000000−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2-2200002-2−i2i2i2−i2i2−i2−i2i20000000000000000
χ592-222-2-2-22-22-22-2200002-2−i2i2−i2i2−i2i2−i2i22-2000000i2−i2i2−i2i2−i2i2−i2−i2−i2i2i22-20000-22−i2i2i2−i2i2−i2−i2i20000000000000000
χ602-222-2-2-22-22-22-2200002-2−i2i2−i2i2−i2i2−i2i22-2000000i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2-2200002-2i2−i2−i2i2−i2i2i2−i20000000000000000
χ61444-4-44-4-44-4000044-4-44-4000000000000-440000000000000000000000000000000000000000000000
χ62444-4-44-4-4-44000044-4-4-440000000000004-40000000000000000000000000000000000000000000000
χ6344-44-4-44-4004i4i−4i−4i-44-44000000000000−4i4i000000000000000000000000000000000000000000000000
χ6444-44-4-44-400−4i−4i4i4i-44-440000000000004i−4i000000000000000000000000000000000000000000000000
χ6544-4-44-4-440000004-4-44000000000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ6644-4-44-4-440000004-4-4400000000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ6744-4-44-4-44000000-444-4004i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ6844-4-44-4-44000000-444-400−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ694-44-44-44-44400000000-4-422−2222−22−2222−22220000000022−22−22220000000000000000000000000000000000000000
χ704-44-44-44-44400000000-4-4−2222−222222−2222−2200000000−222222−220000000000000000000000000000000000000000
χ714-44-44-44-4-4-4000000004422−2222−22−2222−222200000000−222222−220000000000000000000000000000000000000000
χ724-44-44-44-4-4-40000000044−2222−222222−2222−220000000022−22−22220000000000000000000000000000000000000000
χ734-4-4444-4-4004i−4i−4i4i0000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000−222222−22000000000000000000000000000000000000
χ744-4-4444-4-4004i−4i−4i4i000000−2i22i22i2−2i2−2i22i22i2−2i200000000000022−22−2222000000000000000000000000000000000000
χ754-4-4444-4-400−4i4i4i−4i0000002i2−2i2−2i22i22i2−2i2−2i22i200000000000022−22−2222000000000000000000000000000000000000
χ764-4-4444-4-400−4i4i4i−4i000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000−222222−22000000000000000000000000000000000000
χ774-4-4-4-444400000000000022−22−2222−222222−220000004-40000000022−22−222200000000000000000000000000000000
χ784-4-4-4-444400000000000022−22−2222−222222−22000000-4400000000−222222−2200000000000000000000000000000000
χ794-4-4-4-4444000000000000−222222−2222−22−22220000004-400000000−222222−2200000000000000000000000000000000
χ804-4-4-4-4444000000000000−222222−2222−22−2222000000-440000000022−22−222200000000000000000000000000000000

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