Finite Group Databasebeta

← Group #279337

Character table — Group #279337

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888884444488888888888844448888888844
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
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-111-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ91111111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-1
χ101111111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11
χ111111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-11
χ121111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-222-22-222-2-2-2-22222-2-2-2-2-2-200000000222-2-200000000000000000000000000
χ18222222222-2-222-22-222-2-2-2-2-2-2-2-22222-2-200000000-2-222200000000000000000000000000
χ19222222222-2-222-22-2-2-2-2-2222222-2-2-2-22200000000-2-2-22200000000000000000000000000
χ20222222222-2-222-22-2-2-2-2-222-2-2-2-22222220000000022-2-2-200000000000000000000000000
χ2122222222-222-2-22-2222-2-2-2-200000000222222222200-200-2-2-2-20000000000000000000000
χ2222222222-222-2-22-2222-2-2-2-20000000022-2-2-2-2-2-2-2-200-20022220000000000000000000000
χ2322222222-222-2-22-22-2-2-2-22200000000-2-22222-2-2-2-200200-2-2220000000000000000000000
χ2422222222-222-2-22-22-2-2-2-22200000000-2-2-2-2-2-222220020022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222222200000000-2-20000000000-20000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-222222200000000-2-20000000000-2000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-20000000022000000000020000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2000000002200000000002000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-2-2-22200-2-202000002i−2i000022-2-22i−2i22−2−2i2i2−i2−i22i−2i0002−2i2−i22−22−2i2−i2i2−i200000000000000
χ30222-2-2-2-22200-2-202000002i−2i000022-2-22i−2i−2−222−i2−i2i2i22i−2i000−22−i2i2−22−22−i2i2−i2i200000000000000
χ31222-2-2-2-22200-2-202000002i−2i0000-2-2222i−2i22−2−2i2i2−i2−i2−2i2i0002−2i2−i2−22−22−i2i2−i2i200000000000000
χ32222-2-2-2-22200-2-202000002i−2i0000-2-2222i−2i−2−222−i2−i2i2i2−2i2i000−22−i2i22−22−2i2−i2i2−i200000000000000
χ33222-2-2-2-22200-2-20200000−2i2i000022-2-2−2i2i22−2−2−i2−i2i2i2−2i2i0002−2−i2i22−22−2−i2i2−i2i200000000000000
χ34222-2-2-2-22200-2-20200000−2i2i000022-2-2−2i2i−2−222i2i2−i2−i2−2i2i000−22i2−i2−22−22i2−i2i2−i200000000000000
χ35222-2-2-2-22200-2-20200000−2i2i0000-2-222−2i2i22−2−2−i2−i2i2i22i−2i0002−2−i2i2−22−22i2−i2i2−i200000000000000
χ36222-2-2-2-22200-2-20200000−2i2i0000-2-222−2i2i−2−222i2i2−i2−i22i−2i000−22i2−i22−22−2−i2i2−i2i200000000000000
χ37222-2-2-2-22-200220-2000002i−2i2i2i−2i−2i0000−2i2i22−2−2−i2−i2i2i20002-2−22i2−i2i2−i2−i2i2−222−200000000000000
χ38222-2-2-2-22-200220-2000002i−2i2i2i−2i−2i0000−2i2i−2−222i2i2−i2−i20002-22−2−i2i2−i2i2i2−i22−2−2200000000000000
χ39222-2-2-2-22-200220-2000002i−2i−2i−2i2i2i0000−2i2i22−2−2−i2−i2i2i2000-22−22i2−i2−i2i2i2−i22−2−2200000000000000
χ40222-2-2-2-22-200220-2000002i−2i−2i−2i2i2i0000−2i2i−2−222i2i2−i2−i2000-222−2−i2i2i2−i2−i2i2−222−200000000000000
χ41222-2-2-2-22-200220-200000−2i2i2i2i−2i−2i00002i−2i22−2−2i2i2−i2−i2000-22−22−i2i2i2−i2−i2i22−2−2200000000000000
χ42222-2-2-2-22-200220-200000−2i2i2i2i−2i−2i00002i−2i−2−222−i2−i2i2i2000-222−2i2−i2−i2i2i2−i2−222−200000000000000
χ43222-2-2-2-22-200220-200000−2i2i−2i−2i2i2i00002i−2i22−2−2i2i2−i2−i20002-2−22−i2i2−i2i2i2−i2−222−200000000000000
χ44222-2-2-2-22-200220-200000−2i2i−2i−2i2i2i00002i−2i−2−222−i2−i2i2i20002-22−2i2−i2i2−i2−i2i22−2−2200000000000000
χ452-222-22-2-22222-2-2-2-2002-2002-22-22-22-20000000000000000000000000002-2002-200000000
χ462-222-22-2-22222-2-2-2-2002-2002-22-22-22-2000000000000000000000000000-2200-2200000000
χ472-222-22-2-22222-2-2-2-2002-200-22-22-22-220000000000000000000000000002-200-2200000000
χ482-222-22-2-22222-2-2-2-2002-200-22-22-22-22000000000000000000000000000-22002-200000000
χ492-222-22-2-22-2-22-22-2200-22002-22-2-22-22000000000000000000000000000002i−2i00002i−2i0000
χ502-222-22-2-22-2-22-22-2200-22002-22-2-22-2200000000000000000000000000000−2i2i0000−2i2i0000
χ512-222-22-2-22-2-22-22-2200-2200-22-222-22-2000000000000000000000000000002i−2i0000−2i2i0000
χ522-222-22-2-22-2-22-22-2200-2200-22-222-22-200000000000000000000000000000−2i2i00002i−2i0000
χ5344-444-4-4-4000000004-40000000000000022−2222−2222−2222−220000000000000000000000000000000
χ5444-444-4-4-4000000004-400000000000000−2222−2222−2222−22220000000000000000000000000000000
χ5544-444-4-4-400000000-440000000000000022−2222−22−2222−22220000000000000000000000000000000
χ5644-444-4-4-400000000-4400000000000000−2222−222222−2222−220000000000000000000000000000000
χ5744-4-4-444-404-40040-400000000000000004-4-4400000000000000000000000000000000000
χ5844-4-4-444-404-40040-40000000000000000-444-400000000000000000000000000000000000
χ5944-4-4-444-40-4400-404000000000000000000004i−4i−4i4i0000000000000000000000000000000
χ6044-4-4-444-40-4400-40400000000000000000000−4i4i4i−4i0000000000000000000000000000000
χ614-444-44-4-4-444-44-44-400-44000000000000000000000000000000000000000000000000000
χ624-444-44-4-4-4-4-4-44444004-4000000000000000000000000000000000000000000000000000
χ634-44-44-44-4400-440-4000000000004-4-4400000000000000000000000000000000000000000
χ644-44-44-44-4400-440-400000000000-444-400000000000000000000000000000000000000000
χ654-44-44-44-4-4004-40400000004i−4i−4i4i000000000000000000000000000000000000000000000
χ664-44-44-44-4-4004-4040000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ674-4-4-444-4404-400-4040000000000000000000000000000000000000000000000022−22000000
χ684-4-4-444-4404-400-40400000000000000000000000000000000000000000000000−2222000000
χ694-4-4-444-440-440040-40000000000000000000000000000000000000000000000000002i2−2i200
χ704-4-4-444-440-440040-4000000000000000000000000000000000000000000000000000−2i22i200
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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