Finite Group Databasebeta

← Group #293958

Character table — Group #293958

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444444444444444444444488888888888888888888888824444424
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111
χ5111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111
χ6111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11-1-1-1-1
χ7111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ8111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ91111111111-1-1-1-1111111-1-11-1-11-111-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11-1
χ101111111111-1-1-1-1111111-1-11-1-11-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-11
χ111111111111-1-1-1-1111111-1-11-1-11-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111-11
χ121111111111-1-1-1-1111111-1-11-1-11-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11111-1
χ131111111111-1-1-1-1111111-1-11-1-11-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1111-1
χ141111111111-1-1-1-1111111-1-11-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-11-111-11
χ151111111111-1-1-1-1111111-1-11-1-11-1-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-11
χ161111111111-1-1-1-1111111-1-11-1-11-1-1-111-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11-1
χ1722222222222222-2-222-2-222-2-2-2-2-22222000000000000000000000000000000000-2-200000
χ1822222222222222-2-222-2-222-2-2-2-2-2-2-2-2-20000000000000000000000000000000002200000
χ192222222222-2-2-2-2-2-222-2-2-2-2-222-2222-2-2000000000000000000000000000000000-2200000
χ202222222222-2-2-2-2-2-222-2-2-2-2-222-22-2-2220000000000000000000000000000000002-200000
χ2122222222-2-2222222-2-222-2-2-222-2-2000022220000000000000000000000000000-200-20000
χ2222222222-2-2222222-2-222-2-2-222-2-20000-2-2-2-2000000000000000000000000000020020000
χ2322222222-2-22222-2-2-2-2-2-2-2-22-2-2220000000022-2-200000000000000000000000000002-200
χ2422222222-2-22222-2-2-2-2-2-2-2-22-2-22200000000-2-2220000000000000000000000000000-2200
χ2522222222-2-2-2-2-2-222-2-22222-2-2-2-22000022-2-20000000000000000000000000000-20020000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-220000-2-2220000000000000000000000000000200-20000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000022-2-20000000000000000000000000000-2200
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000-2-22200000000000000000000000000002-200
χ29222-2-22-2-2002i2i−2i−2i2-2002-20002i−2i0000002i−2i2-200000000000022−2−2i2i2−i2−i2i2i2−i2−i222−2−200000000
χ30222-2-22-2-2002i2i−2i−2i2-2002-20002i−2i0000002i−2i2-2000000000000−2−222−i2−i2i2i2−i2−i2i2i2−2−22200000000
χ31222-2-22-2-2002i2i−2i−2i2-2002-20002i−2i000000−2i2i-2200000000000022−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000
χ32222-2-22-2-2002i2i−2i−2i2-2002-20002i−2i000000−2i2i-22000000000000−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000
χ33222-2-22-2-200−2i−2i2i2i2-2002-2000−2i2i0000002i−2i-2200000000000022−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000
χ34222-2-22-2-200−2i−2i2i2i2-2002-2000−2i2i0000002i−2i-22000000000000−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000
χ35222-2-22-2-200−2i−2i2i2i2-2002-2000−2i2i000000−2i2i2-200000000000022−2−2−i2−i2i2i2−i2−i2i2i222−2−200000000
χ36222-2-22-2-200−2i−2i2i2i2-2002-2000−2i2i000000−2i2i2-2000000000000−2−222i2i2−i2−i2i2i2−i2−i2−2−22200000000
χ3722-22-2-22-22-22i−2i2i−2i002-2002i−2i000002-22i−2i0000000022−2−2i2i2−i2−i2000000002−22−2i2−i2i2−i200000000
χ3822-22-2-22-22-22i−2i2i−2i002-2002i−2i000002-22i−2i00000000−2−222−i2−i2i2i200000000−22−22−i2i2−i2i200000000
χ3922-22-2-22-22-22i−2i2i−2i002-2002i−2i00000-22−2i2i0000000022−2−2i2i2−i2−i200000000−22−22−i2i2−i2i200000000
χ4022-22-2-22-22-22i−2i2i−2i002-2002i−2i00000-22−2i2i00000000−2−222−i2−i2i2i2000000002−22−2i2−i2i2−i200000000
χ4122-22-2-22-22-2−2i2i−2i2i002-200−2i2i000002-2−2i2i0000000022−2−2−i2−i2i2i2000000002−22−2−i2i2−i2i200000000
χ4222-22-2-22-22-2−2i2i−2i2i002-200−2i2i000002-2−2i2i00000000−2−222i2i2−i2−i200000000−22−22i2−i2i2−i200000000
χ4322-22-2-22-22-2−2i2i−2i2i002-200−2i2i00000-222i−2i0000000022−2−2−i2−i2i2i200000000−22−22i2−i2i2−i200000000
χ4422-22-2-22-22-2−2i2i−2i2i002-200−2i2i00000-222i−2i00000000−2−222i2i2−i2−i2000000002−22−2−i2i2−i2i200000000
χ452-2-22-22-222-200002-2-22-2200200-20000000002i−2i2i−2i2-22-200002i−2i2i−2i00000000000000000000
χ462-2-22-22-222-200002-2-22-2200200-20000000002i−2i2i−2i-22-220000−2i2i−2i2i00000000000000000000
χ472-2-22-22-222-200002-2-22-2200200-2000000000−2i2i−2i2i2-22-20000−2i2i−2i2i00000000000000000000
χ482-2-22-22-222-200002-2-22-2200200-2000000000−2i2i−2i2i-22-2200002i−2i2i−2i00000000000000000000
χ492-2-22-22-22-220000-222-22-200200-20000000002i−2i−2i2i00002-22-200002i−2i2i−2i0000000000000000
χ502-2-22-22-22-220000-222-22-200200-20000000002i−2i−2i2i0000-22-220000−2i2i−2i2i0000000000000000
χ512-2-22-22-22-220000-222-22-200200-2000000000−2i2i2i−2i00002-22-20000−2i2i−2i2i0000000000000000
χ522-2-22-22-22-220000-222-22-200200-2000000000−2i2i2i−2i0000-22-2200002i−2i2i−2i0000000000000000
χ53444-4-44-4-4004i4i−4i−4i-4400-44000−4i4i0000000000000000000000000000000000000000000000
χ54444-4-44-4-400−4i−4i4i4i-4400-440004i−4i0000000000000000000000000000000000000000000000
χ5544-44-4-44-4-444i−4i4i−4i00-4400−4i4i0000000000000000000000000000000000000000000000000
χ5644-44-4-44-4-44−4i4i−4i4i00-44004i−4i0000000000000000000000000000000000000000000000000
χ5744-4-44-4-44004-4-44000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ5844-4-44-4-44004-4-4400000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ5944-4-44-4-4400-444-4000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ6044-4-44-4-4400-444-400000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ614-4444-4-4-444000000-4-400000000000000000000022−22−22220000000000000000000000000000
χ624-4444-4-4-444000000-4-4000000000000000000000−222222−220000000000000000000000000000
χ634-4444-4-4-4-4-40000004400000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ644-4444-4-4-4-4-4000000440000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ654-4-44-44-444-40000-44-444-400-4004000000000000000000000000000000000000000000000
χ664-4-44-44-44-4400004-44-4-4400-4004000000000000000000000000000000000000000000000
χ674-4-4-4444-40000004400-4-40000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ684-4-4-4444-40000004400-4-4000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ694-4-4-4444-4000000-4-40044000000000000000000000000000000022−22−22220000000000000000
χ704-4-4-4444-4000000-4-400440000000000000000000000000000000−222222−220000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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