Finite Group Databasebeta

← Group #276459

Character table — Group #276459

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888882244488888888888822448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ61111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ71111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-11
χ81111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-1
χ9111111111111111111-1-1-1-111-1-1-1-1111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-111-1-1-1-1111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ11111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ12111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ172222222222-22-2-2-22-2-2222222-2-2-2-2-2-2-2-200000000222-2-200000000000000000000000000
χ182222222222-22-2-2-22-2-22222-2-2-2-2-2-2222200000000-2-2-22200000000000000000000000000
χ192222222222-22-2-2-22-2-2-2-2-2-2222222-2-2-2-200000000-2-222200000000000000000000000000
χ202222222222-22-2-2-22-2-2-2-2-2-2-2-2222222220000000022-2-2-200000000000000000000000000
χ2122222222-2-22-2222-2-2-2000022000022-2-22222222200-200-2-2-2-20000000000000000000000
χ2222222222-2-22-2222-2-2-2000022000022-2-2-2-2-2-2-2-2-2-200-20022220000000000000000000000
χ2322222222-2-22-2222-2-2-20000-2-20000-2-2222222-2-2-2-200200-2-2220000000000000000000000
χ2422222222-2-22-2222-2-2-20000-2-20000-2-222-2-2-2-222220020022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000220000-2-2220000000000-20000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2220000220000-2-2220000000000-2000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2220000-2-2000022-2-2000000000020000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2220000-2-2000022-2-200000000002000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-22-2-2-22-22-2-2-2222-22i2i−2i−2i002i2i−2i−2i000000000000000000000000000002-2002i−2i00000000
χ30222-22-2-2-22-22-2-2-2222-22i2i−2i−2i002i2i−2i−2i00000000000000000000000000000-2200−2i2i00000000
χ31222-22-2-2-22-22-2-2-2222-2−2i−2i2i2i00−2i−2i2i2i000000000000000000000000000002-200−2i2i00000000
χ32222-22-2-2-22-22-2-2-2222-2−2i−2i2i2i00−2i−2i2i2i00000000000000000000000000000-22002i−2i00000000
χ33222-22-2-2-22-2-2-222-22-222i2i−2i−2i00−2i−2i2i2i00000000000000000000000000000002i−2i002-2000000
χ34222-22-2-2-22-2-2-222-22-222i2i−2i−2i00−2i−2i2i2i0000000000000000000000000000000−2i2i00-22000000
χ35222-22-2-2-22-2-2-222-22-22−2i−2i2i2i002i2i−2i−2i00000000000000000000000000000002i−2i00-22000000
χ36222-22-2-2-22-2-2-222-22-22−2i−2i2i2i002i2i−2i−2i0000000000000000000000000000000−2i2i002-2000000
χ3722-2-2-2-222220-2000-2002i−2i2i−2i0000002-22-222−2−222−2−20002i−2i2−22−2i2−i2i2−i2i2−i2i2−i200000000000000
χ3822-2-2-2-222220-2000-2002i−2i2i−2i0000002-22-2−2−222−2−2220002i−2i−22−22−i2i2−i2i2−i2i2−i2i200000000000000
χ3922-2-2-2-222220-2000-2002i−2i2i−2i000000-22-2222−2−2−2−222000−2i2i2−2−22i2−i2i2−i2−i2i2−i2i200000000000000
χ4022-2-2-2-222220-2000-2002i−2i2i−2i000000-22-22−2−22222−2−2000−2i2i−222−2−i2i2−i2i2i2−i2i2−i200000000000000
χ4122-2-2-2-222220-2000-200−2i2i−2i2i0000002-22-222−2−222−2−2000−2i2i2−22−2−i2i2−i2i2−i2i2−i2i200000000000000
χ4222-2-2-2-222220-2000-200−2i2i−2i2i0000002-22-2−2−222−2−222000−2i2i−22−22i2−i2i2−i2i2−i2i2−i200000000000000
χ4322-2-2-2-222220-2000-200−2i2i−2i2i000000-22-2222−2−2−2−2220002i−2i2−2−22−i2i2−i2i2i2−i2i2−i200000000000000
χ4422-2-2-2-222220-2000-200−2i2i−2i2i000000-22-22−2−22222−2−20002i−2i−222−2i2−i2i2−i2−i2i2−i2i200000000000000
χ4522-2-2-2-222-2-2020002000000002-22-22-2-2222−2−222−2−22-2000−22−222−2−22−222−200000000000000
χ4622-2-2-2-222-2-2020002000000002-22-22-2-22−2−222−2−2222-20002−22−2−222−22−2−2200000000000000
χ4722-2-2-2-222-2-2020002000000002-22-2-222-222−2−2−2−222-22000−222−22−2−222−2−2200000000000000
χ4822-2-2-2-222-2-2020002000000002-22-2-222-2−2−22222−2−2-220002−2−22−222−2−222−200000000000000
χ4922-2-2-2-222-2-202000200000000-22-222-2-2222−2−222−2−2-22000−22−22−222−22−2−2200000000000000
χ5022-2-2-2-222-2-202000200000000-22-222-2-22−2−222−2−222-220002−22−22−2−22−222−200000000000000
χ5122-2-2-2-222-2-202000200000000-22-22-222-222−2−2−2−2222-2000−222−2−222−2−222−200000000000000
χ5222-2-2-2-222-2-202000200000000-22-22-222-2−2−22222−2−22-20002−2−222−2−222−2−2200000000000000
χ53444-44-4-4-4-4444-4-44-4-4400000000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-44-4444-4-44-400000000000000000000000000000000000000000000000000000
χ5544-44-44-4-44-404000-4004-4-440000000000000000000000000000000000000000000000000
χ5644-44-44-4-44-404000-400-444-40000000000000000000000000000000000000000000000000
χ5744-44-44-4-4-440-40004000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ5844-44-44-4-4-440-4000400000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ594-444-4-44-4000000000000004i−4i0000000022−2222−222i2−2i22i2−2i20000000000000000000000000000000
χ604-444-4-44-4000000000000004i−4i00000000−2222−2222−2i22i2−2i22i20000000000000000000000000000000
χ614-444-4-44-400000000000000−4i4i0000000022−2222−22−2i22i2−2i22i20000000000000000000000000000000
χ624-444-4-44-400000000000000−4i4i00000000−2222−22222i2−2i22i2−2i20000000000000000000000000000000
χ634-4-444-4-4400404-4-400000000000000000000000000000000000000000000000000002i2−2i200
χ644-4-444-4-4400404-4-40000000000000000000000000000000000000000000000000000−2i22i200
χ654-4-444-4-4400-40-4440000000000000000000000000000000000000000000000000022−220000
χ664-4-444-4-4400-40-44400000000000000000000000000000000000000000000000000−22220000
χ674-4-4-4444-40040-44-40000000000000000000004i−4i−4i4i0000000000000000000000000000000
χ684-4-4-4444-40040-44-4000000000000000000000−4i4i4i−4i0000000000000000000000000000000
χ694-4-4-4444-400-404-44000000000000000004-4-4400000000000000000000000000000000000
χ704-4-4-4444-400-404-4400000000000000000-444-400000000000000000000000000000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

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