Finite Group Databasebeta

← Group #274192

Character table — Group #274192

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888882444488888888888822448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ511111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ11111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1
χ12111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-222-2-22-2-22222-2-2-2-222-2-22200000000-222-2-200000000000000000000000000
χ18222222222-2-222-2-22-2-22222-2-2-2-2-2-222-2-2000000002-2-22200000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-2-2-2222222-2-22200000000-2-2-22200000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-2-2-22222-2-222-2-200000000222-2-200000000000000000000000000
χ2122222222-222-2-222-2-2-2000000002222-2-222222222-20000-2-2-2-20000000000000000000000
χ2222222222-222-2-222-2-2-2000000002222-2-2-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ2322222222-222-2-222-2-2-200000000-2-2-2-2222222-2-2-2-220000-2-2220000000000000000000000
χ2422222222-222-2-222-2-2-200000000-2-2-2-222-2-2-2-222222000022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000000022-2-2-2-2000000002000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2220000000022-2-2-2-200000000200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-22200000000-2-2222200000000-2000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-22200000000-2-2222200000000-200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-2-22-2200-2-20020000002i2i−2i−2i2i−2i002i−2i22−2−2i2i2−i2−i20002-22−2i2−i2i2−i2i2−i22−22−200000000000000
χ30222-2-2-22-2200-2-20020000002i2i−2i−2i2i−2i002i−2i−2−222−i2−i2i2i20002-2−22−i2i2−i2i2−i2i2−22−2200000000000000
χ31222-2-2-22-2200-2-20020000002i2i−2i−2i−2i2i00−2i2i22−2−2−i2−i2i2i2000-222−2−i2i2i2−i2i2−i2−22−2200000000000000
χ32222-2-2-22-2200-2-20020000002i2i−2i−2i−2i2i00−2i2i−2−222i2i2−i2−i2000-22−22i2−i2−i2i2−i2i22−22−200000000000000
χ33222-2-2-22-2200-2-2002000000−2i−2i2i2i2i−2i002i−2i22−2−2i2i2−i2−i2000-222−2i2−i2−i2i2−i2i2−22−2200000000000000
χ34222-2-2-22-2200-2-2002000000−2i−2i2i2i2i−2i002i−2i−2−222−i2−i2i2i2000-22−22−i2i2i2−i2i2−i22−22−200000000000000
χ35222-2-2-22-2200-2-2002000000−2i−2i2i2i−2i2i00−2i2i22−2−2−i2−i2i2i20002-22−2−i2i2−i2i2−i2i22−22−200000000000000
χ36222-2-2-22-2200-2-2002000000−2i−2i2i2i−2i2i00−2i2i−2−222i2i2−i2−i20002-2−22i2−i2i2−i2i2−i2−22−2200000000000000
χ37222-2-2-22-2-2002200-20022-2-200002i−2i00−2i2i22−2−2i2i2−i2−i202i−2i00−22−i2i22−2−22−i2i2i2−i200000000000000
χ38222-2-2-22-2-2002200-20022-2-200002i−2i00−2i2i−2−222−i2−i2i2i202i−2i002−2i2−i2−222−2i2−i2−i2i200000000000000
χ39222-2-2-22-2-2002200-20022-2-20000−2i2i002i−2i22−2−2−i2−i2i2i20−2i2i00−22i2−i22−2−22i2−i2−i2i200000000000000
χ40222-2-2-22-2-2002200-20022-2-20000−2i2i002i−2i−2−222i2i2−i2−i20−2i2i002−2−i2i2−222−2−i2i2i2−i200000000000000
χ41222-2-2-22-2-2002200-200-2-22200002i−2i00−2i2i22−2−2i2i2−i2−i20−2i2i00−22−i2i2−222−2i2−i2−i2i200000000000000
χ42222-2-2-22-2-2002200-200-2-22200002i−2i00−2i2i−2−222−i2−i2i2i20−2i2i002−2i2−i22−2−22−i2i2i2−i200000000000000
χ43222-2-2-22-2-2002200-200-2-2220000−2i2i002i−2i22−2−2−i2−i2i2i202i−2i00−22i2−i2−222−2−i2i2i2−i200000000000000
χ44222-2-2-22-2-2002200-200-2-2220000−2i2i002i−2i−2−222i2i2−i2−i202i−2i002−2−i2i22−2−22i2−i2−i2i200000000000000
χ4522-22-2-2-2222-22-22-2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000002-200002i−2i0000
χ4622-22-2-2-2222-22-22-2-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000-220000−2i2i0000
χ4722-22-2-2-2222-22-22-2-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000002-20000−2i2i0000
χ4822-22-2-2-2222-22-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000-2200002i−2i0000
χ4922-22-2-2-222-222-2-22-2-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000002-2002i−2i00000000
χ5022-22-2-2-222-222-2-22-2-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000-2200−2i2i00000000
χ5122-22-2-2-222-222-2-22-2-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000002-200−2i2i00000000
χ5222-22-2-2-222-222-2-22-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000-22002i−2i00000000
χ5344-44-4-4-44-44-4-444-44-4400000000000000000000000000000000000000000000000000000
χ5444-44-4-4-44-4-44-44-4444-400000000000000000000000000000000000000000000000000000
χ5544-4-444-4-4400-4400-40000004-4-44000000000000000000000000000000000000000000000
χ5644-4-444-4-4400-4400-4000000-444-4000000000000000000000000000000000000000000000
χ5744-4-444-4-4-4004-4004004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ5844-4-444-4-4-4004-400400−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ594-44-44-4-4404400-4-40000000000000000000000000000000000000000000000002i2−2i2000000
χ604-44-44-4-4404400-4-4000000000000000000000000000000000000000000000000−2i22i2000000
χ614-44-44-4-440-4-40044000000000000000000000000000000000000000000000000000022−2200
χ624-44-44-4-440-4-400440000000000000000000000000000000000000000000000000000−222200
χ634-4-444-44-4000000000000000000004i−4i0022−2222−222i2−2i22i2−2i20000000000000000000000000000000
χ644-4-444-44-4000000000000000000004i−4i00−2222−2222−2i22i2−2i22i20000000000000000000000000000000
χ654-4-444-44-400000000000000000000−4i4i0022−2222−22−2i22i2−2i22i20000000000000000000000000000000
χ664-4-444-44-400000000000000000000−4i4i00−2222−22222i2−2i22i2−2i20000000000000000000000000000000
χ674-4-4-4-444404-400-440000000000000000000004-4-440000000000000000000000000000000
χ684-4-4-4-444404-400-44000000000000000000000-444-40000000000000000000000000000000
χ694-4-4-4-44440-44004-4000000000000000004-4-4400000000000000000000000000000000000
χ704-4-4-4-44440-44004-400000000000000000-444-400000000000000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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