Finite Group Databasebeta

← Group #290213

Character table — Group #290213

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444488888888888888884444444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-1-1-111-1-1111111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-111-1-1111111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-111-11
χ111111111111111111-1-1-1-111-1-111111111-1-1-1-11111-1-11111-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-111-1-111111111-1-1-1-11111-1-11111-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111111-1-11111-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111-1
χ172222222222-22-2-2-222222-2-2-2-200000000000000002222-2-2-2-2-20000000000000000000000
χ182222222222-22-2-2-222222-2-2-2-20000000000000000-2-2-2-222-2220000000000000000000000
χ192222222222-22-2-2-22-2-2-2-2-2-222000000000000000022-2-2222-2-20000000000000000000000
χ202222222222-22-2-2-22-2-2-2-2-2-2220000000000000000-2-222-2-22220000000000000000000000
χ2122222222-2-22-2222-222-2-2-2-2220000000022222222000000-200-2-20000-2-200000000000000
χ2222222222-2-22-2222-222-2-2-2-22200000000-2-2-2-2-2-2-2-2000000-2002200002200000000000000
χ2322222222-2-22-2222-2-2-222-2-2-2-2000000002222-2-2-2-2000000200220000-2-200000000000000
χ2422222222-2-22-2222-2-2-222-2-2-2-200000000-2-2-2-22222000000200-2-200002200000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2-22i2i2i2i−2i−2i−2i−2i00000000000000200002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i0000000000000020000−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222222i2i2i2i−2i−2i−2i−2i00000000000000-20000−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222−2i−2i−2i−2i2i2i2i2i00000000000000-200002i2i−2i−2i0000000000000000
χ29222-2-22-2-22-2222-2-2-200002-20022-2-222-2-200000000000000000000000002-2002-200000000
χ30222-2-22-2-22-2222-2-2-200002-20022-2-222-2-20000000000000000000000000-2200-2200000000
χ31222-2-22-2-22-2222-2-2-200002-200-2-222-2-22200000000000000000000000002-200-2200000000
χ32222-2-22-2-22-2222-2-2-200002-200-2-222-2-2220000000000000000000000000-22002-200000000
χ33222-2-22-2-2-22-2-2-222200002-2002i2i−2i−2i−2i−2i2i2i0000000000000000000000000002i−2i002-2000000
χ34222-2-22-2-2-22-2-2-222200002-2002i2i−2i−2i−2i−2i2i2i000000000000000000000000000−2i2i00-22000000
χ35222-2-22-2-2-22-2-2-222200002-200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000002i−2i00-22000000
χ36222-2-22-2-2-22-2-2-222200002-200−2i−2i2i2i2i2i−2i−2i000000000000000000000000000−2i2i002-2000000
χ3722-222-2-2-2220-2000-22-22-200002−22−22−22−222−2−222−2−22-22-2000002−22−22−22−200000000000000
χ3822-222-2-2-2220-2000-22-22-200002−22−22−22−2−2−222−2−222-22-2200000−222−22−2−2200000000000000
χ3922-222-2-2-2220-2000-22-22-20000−22−22−22−2222−2−222−2−2-22-22000002−2−22−222−200000000000000
χ4022-222-2-2-2220-2000-22-22-20000−22−22−22−22−2−222−2−2222-22-200000−22−22−22−2200000000000000
χ4122-222-2-2-2220-2000-2-22-2200002−22−22−22−222−2−2−2−2222-2-2200000−22−22−222−200000000000000
χ4222-222-2-2-2220-2000-2-22-2200002−22−22−22−2−2−22222−2−2-222-2000002−2−22−22−2200000000000000
χ4322-222-2-2-2220-2000-2-22-220000−22−22−22−2222−2−2−2−222-222-200000−222−22−22−200000000000000
χ4422-222-2-2-2220-2000-2-22-220000−22−22−22−22−2−22222−2−22-2-22000002−22−22−2−2200000000000000
χ4522-222-2-2-2-2-20200022-2-220000i2−i2i2−i2−i2i2−i2i222−2−222−2−200002i−2i02i−2i−22i2−i2−i2i2−2200000000000000
χ4622-222-2-2-2-2-20200022-2-220000i2−i2i2−i2−i2i2−i2i2−2−222−2−2220000−2i2i0−2i2i2−2i2−i2−i2i22−200000000000000
χ4722-222-2-2-2-2-20200022-2-220000−i2i2−i2i2i2−i2i2−i222−2−222−2−20000−2i2i0−2i2i−22−i2i2i2−i2−2200000000000000
χ4822-222-2-2-2-2-20200022-2-220000−i2i2−i2i2i2−i2i2−i2−2−222−2−22200002i−2i02i−2i2−2−i2i2i2−i22−200000000000000
χ4922-222-2-2-2-2-2020002-222-20000i2−i2i2−i2−i2i2−i2i222−2−2−2−2220000−2i2i02i−2i2−2−i2i2i2−i2−2200000000000000
χ5022-222-2-2-2-2-2020002-222-20000i2−i2i2−i2−i2i2−i2i2−2−22222−2−200002i−2i0−2i2i−22−i2i2i2−i22−200000000000000
χ5122-222-2-2-2-2-2020002-222-20000−i2i2−i2i2i2−i2i2−i222−2−2−2−22200002i−2i0−2i2i2−2i2−i2−i2i2−2200000000000000
χ5222-222-2-2-2-2-2020002-222-20000−i2i2−i2i2i2−i2i2−i2−2−22222−2−20000−2i2i02i−2i−22i2−i2−i2i22−200000000000000
χ53444-4-44-4-44-4-44-444-40000-440000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-444-44-4-440000-440000000000000000000000000000000000000000000000000
χ5544-4-4-4-4444-40-400040000000022−22−222222−22−2222000000000000000000000000000000000000000
χ5644-4-4-4-4444-40-4000400000000−222222−22−222222−22000000000000000000000000000000000000000
χ5744-4-4-4-444-4404000-4000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ5844-4-4-4-444-4404000-400000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ594-444-4-44-40040-44-40000000000000000000000000000000000000000000000000022−220000
χ604-444-4-44-40040-44-400000000000000000000000000000000000000000000000000−22220000
χ614-444-4-44-400-404-4400000000000000000000000000000000000000000000000000002i2−2i200
χ624-444-4-44-400-404-440000000000000000000000000000000000000000000000000000−2i22i200
χ634-44-44-4-440040-4-44000000000000000004i−4i4i−4i00000000000000000000000000000000000
χ644-44-44-4-440040-4-4400000000000000000−4i4i−4i4i00000000000000000000000000000000000
χ654-44-44-4-4400-4044-40000000000000000000004i−4i4i−4i0000000000000000000000000000000
χ664-44-44-4-4400-4044-4000000000000000000000−4i4i−4i4i0000000000000000000000000000000
χ674-4-4-4444-4000000000000004-4000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000
χ684-4-4-4444-4000000000000004-400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000
χ694-4-4-4444-400000000000000-44000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ704-4-4-4444-400000000000000-4400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ718-8-88-88-88000000000000000000000000000000000000000000000000000000000000000

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