Finite Group Databasebeta

← Group #275367

Character table — Group #275367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888882444488888888888844448888888844
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ91111111111111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-1
χ101111111111111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11
χ111111111111111111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-222-2-2222-2-2-2-2222222-2-2-2-200000000-222-2-200000000000000000000000000
χ18222222222-2-222-2-2222-2-2-2-222-2-2-2-2222200000000-2-2-22200000000000000000000000000
χ19222222222-2-222-2-22-2-222-2-2-2-22222-2-2-2-2000000002-2-22200000000000000000000000000
χ20222222222-2-222-2-22-2-222-2-2-2-2-2-2-2-2222200000000222-2-200000000000000000000000000
χ2122222222-222-2-222-222-2-2-2-2-2-2000000002222-2-2-2-220000-2-2220000000000000000000000
χ2222222222-222-2-222-222-2-2-2-2-2-200000000-2-2-2-222222000022-2-20000000000000000000000
χ2322222222-222-2-222-2-2-222-2-2220000000022222222-20000-2-2-2-20000000000000000000000
χ2422222222-222-2-222-2-2-222-2-22200000000-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-20000000000000000-2000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2222222-2-20000000000000000-200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-22-2-2-22-22-22-2200002-2002i2i−2i−2i2i2i−2i−2i0000000000000000000000000002i−2i00002-20000
χ30222-2-22-2-2-22-22-22-2200002-2002i2i−2i−2i2i2i−2i−2i000000000000000000000000000−2i2i0000-220000
χ31222-2-22-2-2-22-22-22-2200002-200−2i−2i2i2i−2i−2i2i2i0000000000000000000000000002i−2i0000-220000
χ32222-2-22-2-2-22-22-22-2200002-200−2i−2i2i2i−2i−2i2i2i000000000000000000000000000−2i2i00002-20000
χ33222-2-22-2-2-2-222-2-2220000-22002i2i−2i−2i−2i−2i2i2i00000000000000000000000002i−2i002-200000000
χ34222-2-22-2-2-2-222-2-2220000-22002i2i−2i−2i−2i−2i2i2i0000000000000000000000000−2i2i00-2200000000
χ35222-2-22-2-2-2-222-2-2220000-2200−2i−2i2i2i2i2i−2i−2i00000000000000000000000002i−2i00-2200000000
χ36222-2-22-2-2-2-222-2-2220000-2200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000−2i2i002-200000000
χ3722-22-2-2-22200-2-20022i−2i00002i−2i00002-22-222−2−2i2i2−i2−i20002i−2i2−2i2−i22−22−2i2−i2i2−i200000000000000
χ3822-22-2-2-22200-2-20022i−2i00002i−2i00002-22-2−2−222−i2−i2i2i20002i−2i−22−i2i2−22−22−i2i2−i2i200000000000000
χ3922-22-2-2-22200-2-20022i−2i00002i−2i0000-22-2222−2−2i2i2−i2−i2000−2i2i2−2i2−i2−22−22−i2i2−i2i200000000000000
χ4022-22-2-2-22200-2-20022i−2i00002i−2i0000-22-22−2−222−i2−i2i2i2000−2i2i−22−i2i22−22−2i2−i2i2−i200000000000000
χ4122-22-2-2-22200-2-2002−2i2i0000−2i2i00002-22-222−2−2−i2−i2i2i2000−2i2i2−2−i2i22−22−2−i2i2−i2i200000000000000
χ4222-22-2-2-22200-2-2002−2i2i0000−2i2i00002-22-2−2−222i2i2−i2−i2000−2i2i−22i2−i2−22−22i2−i2i2−i200000000000000
χ4322-22-2-2-22200-2-2002−2i2i0000−2i2i0000-22-2222−2−2−i2−i2i2i20002i−2i2−2−i2i2−22−22i2−i2i2−i200000000000000
χ4422-22-2-2-22200-2-2002−2i2i0000−2i2i0000-22-22−2−222i2i2−i2−i20002i−2i−22i2−i22−22−2−i2i2−i2i200000000000000
χ4522-22-2-2-22-2002200-22i−2i0000−2i2i2i−2i2i−2i000022−2−2−i2−i2i2i202-200−22i2−i2i2−i2−i2i2−222−200000000000000
χ4622-22-2-2-22-2002200-22i−2i0000−2i2i2i−2i2i−2i0000−2−222i2i2−i2−i202-2002−2−i2i2−i2i2i2−i22−2−2200000000000000
χ4722-22-2-2-22-2002200-22i−2i0000−2i2i−2i2i−2i2i000022−2−2−i2−i2i2i20-2200−22i2−i2−i2i2i2−i22−2−2200000000000000
χ4822-22-2-2-22-2002200-22i−2i0000−2i2i−2i2i−2i2i0000−2−222i2i2−i2−i20-22002−2−i2i2i2−i2−i2i2−222−200000000000000
χ4922-22-2-2-22-2002200-2−2i2i00002i−2i2i−2i2i−2i000022−2−2i2i2−i2−i20-2200−22−i2i2i2−i2−i2i22−2−2200000000000000
χ5022-22-2-2-22-2002200-2−2i2i00002i−2i2i−2i2i−2i0000−2−222−i2−i2i2i20-22002−2i2−i2−i2i2i2−i2−222−200000000000000
χ5122-22-2-2-22-2002200-2−2i2i00002i−2i−2i2i−2i2i000022−2−2i2i2−i2−i202-200−22−i2i2−i2i2i2−i2−222−200000000000000
χ5222-22-2-2-22-2002200-2−2i2i00002i−2i−2i2i−2i2i0000−2−222−i2−i2i2i202-2002−2i2−i2i2−i2−i2i22−2−2200000000000000
χ53444-4-44-4-444-4-444-4-40000-440000000000000000000000000000000000000000000000000
χ54444-4-44-4-44-44-44-44-400004-40000000000000000000000000000000000000000000000000
χ5544-4-44-44-44004-400-4000000004-4-440000000000000000000000000000000000000000000
χ5644-4-44-44-44004-400-400000000-444-40000000000000000000000000000000000000000000
χ5744-4-44-44-4-400-440040000000000004i−4i−4i4i000000000000000000000000000000000000000
χ5844-4-44-44-4-400-44004000000000000−4i4i4i−4i000000000000000000000000000000000000000
χ594-4444-4-4-404-400-440000000000000000000004-44-40000000000000000000000000000000
χ604-4444-4-4-404-400-44000000000000000000000-44-440000000000000000000000000000000
χ614-4444-4-4-40-44004-4000000000000000004-44-400000000000000000000000000000000000
χ624-4444-4-4-40-44004-400000000000000000-44-4400000000000000000000000000000000000
χ634-44-4-4-44404400-4-40000000000000000000000000000000000000000000000002i2−2i2000000
χ644-44-4-4-44404400-4-4000000000000000000000000000000000000000000000000−2i22i2000000
χ654-44-4-4-4440-4-40044000000000000000000000000000000000000000000000000000022−2200
χ664-44-4-4-4440-4-400440000000000000000000000000000000000000000000000000000−222200
χ674-4-44-444-400000000004i−4i00000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000
χ684-4-44-444-400000000004i−4i000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000
χ694-4-44-444-40000000000−4i4i00000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000
χ704-4-44-444-40000000000−4i4i000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000
χ718-8-8-888-88000000000000000000000000000000000000000000000000000000000000000

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