Finite Group Databasebeta

← Group #274792

Character table — Group #274792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888882224488888888888844448888888844
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
χ51111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ61111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-11-1
χ9111111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-111111111-1-111-1-111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-222-2-22-2-222222222-2-2-2-2-2-200000000-222-2-200000000000000000000000000
χ18222222222-2-222-2-22-2-22222-2-2-2-2-2-2-2-222000000002-2-22200000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-2-2-222222222-2-200000000-2-2-22200000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-2-2-2-2-2-2-222222200000000222-2-200000000000000000000000000
χ2122222222-222-2-222-2-2-2000022-2-200002222222222-20000-2-20000-2-2000000000000000000
χ2222222222-222-2-222-2-2-2000022-2-2000022-2-2-2-2-2-2-2-2-2000022000022000000000000000000
χ2322222222-222-2-222-2-2-20000-2-2220000-2-22222-2-2-2-220000-2-2000022000000000000000000
χ2422222222-222-2-222-2-2-20000-2-2220000-2-2-2-2-2-2222220000220000-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-222000022-2-20000-2-20000000020000002i2i−2i−2i002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-222000022-2-20000-2-2000000002000000−2i−2i2i2i00−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2220000-2-22200002200000000-20000002i2i−2i−2i00−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2220000-2-22200002200000000-2000000−2i−2i2i2i002i2i−2i−2i00000000000000
χ2922-22-2-22-2200-2-2002002i2i−2i−2i2i−2i2i−2i00000022−2−2i2i2−i2−i202-2002−2i2−i2i2−i2i2−i22−22−200000000000000
χ3022-22-2-22-2200-2-2002002i2i−2i−2i2i−2i2i−2i000000−2−222−i2−i2i2i202-200−22−i2i2−i2i2−i2i2−22−2200000000000000
χ3122-22-2-22-2200-2-2002002i2i−2i−2i−2i2i−2i2i00000022−2−2−i2−i2i2i20-22002−2i2−i2i2−i2−i2i2−22−2200000000000000
χ3222-22-2-22-2200-2-2002002i2i−2i−2i−2i2i−2i2i000000−2−222i2i2−i2−i20-2200−22−i2i2−i2i2i2−i22−22−200000000000000
χ3322-22-2-22-2200-2-200200−2i−2i2i2i2i−2i2i−2i00000022−2−2i2i2−i2−i20-22002−2−i2i2−i2i2i2−i2−22−2200000000000000
χ3422-22-2-22-2200-2-200200−2i−2i2i2i2i−2i2i−2i000000−2−222−i2−i2i2i20-2200−22i2−i2i2−i2−i2i22−22−200000000000000
χ3522-22-2-22-2200-2-200200−2i−2i2i2i−2i2i−2i2i00000022−2−2−i2−i2i2i202-2002−2−i2i2−i2i2−i2i22−22−200000000000000
χ3622-22-2-22-2200-2-200200−2i−2i2i2i−2i2i−2i2i000000−2−222i2i2−i2−i202-200−22i2−i2i2−i2i2−i2−22−2200000000000000
χ3722-22-2-22-2-2002200-20000002i−2i−2i2i22-2-20022−2−2i2i2−i2−i20002i−2i−222−2−22−i2i2−i2i2i2−i200000000000000
χ3822-22-2-22-2-2002200-20000002i−2i−2i2i22-2-200−2−222−i2−i2i2i20002i−2i2−2−222−2i2−i2i2−i2−i2i200000000000000
χ3922-22-2-22-2-2002200-20000002i−2i−2i2i-2-2220022−2−2i2i2−i2−i2000−2i2i−22−222−2−i2i2i2−i2−i2i200000000000000
χ4022-22-2-22-2-2002200-20000002i−2i−2i2i-2-22200−2−222−i2−i2i2i2000−2i2i2−22−2−22i2−i2−i2i2i2−i200000000000000
χ4122-22-2-22-2-2002200-2000000−2i2i2i−2i22-2-20022−2−2−i2−i2i2i2000−2i2i−222−2−22i2−i2i2−i2−i2i200000000000000
χ4222-22-2-22-2-2002200-2000000−2i2i2i−2i22-2-200−2−222i2i2−i2−i2000−2i2i2−2−222−2−i2i2−i2i2i2−i200000000000000
χ4322-22-2-22-2-2002200-2000000−2i2i2i−2i-2-2220022−2−2−i2−i2i2i20002i−2i−22−222−2i2−i2−i2i2i2−i200000000000000
χ4422-22-2-22-2-2002200-2000000−2i2i2i−2i-2-22200−2−222i2i2−i2−i20002i−2i2−22−2−22−i2i2i2−i2−i2i200000000000000
χ452-2-2-2222-222-22-22-2-22-22-22-200002-22-2000000000000000000000000000002i−2i00002i−2i0000
χ462-2-2-2222-222-22-22-2-22-22-22-200002-22-200000000000000000000000000000−2i2i0000−2i2i0000
χ472-2-2-2222-222-22-22-2-22-2-22-220000-22-22000000000000000000000000000002i−2i0000−2i2i0000
χ482-2-2-2222-222-22-22-2-22-2-22-220000-22-2200000000000000000000000000000−2i2i00002i−2i0000
χ492-2-2-2222-22-222-2-22-2-222-22-20000-22-220000000000000000000000000002i−2i002i−2i00000000
χ502-2-2-2222-22-222-2-22-2-222-22-20000-22-22000000000000000000000000000−2i2i00−2i2i00000000
χ512-2-2-2222-22-222-2-22-2-22-22-2200002-22-20000000000000000000000000002i−2i00−2i2i00000000
χ522-2-2-2222-22-222-2-22-2-22-22-2200002-22-2000000000000000000000000000−2i2i002i−2i00000000
χ53444-44-4-4-404-400-44000000000000000004-44-400000000000000000000000000000000000
χ54444-44-4-4-404-400-4400000000000000000-44-4400000000000000000000000000000000000
χ55444-44-4-4-40-44004-40000000000000000000004-44-40000000000000000000000000000000
χ56444-44-4-4-40-44004-4000000000000000000000-44-440000000000000000000000000000000
χ5744-4-4-44-4400000000000000000000004i−4i22−22−22222i2−2i2−2i22i20000000000000000000000000000000
χ5844-4-4-44-4400000000000000000000004i−4i−222222−22−2i22i22i2−2i20000000000000000000000000000000
χ5944-4-4-44-440000000000000000000000−4i4i22−22−2222−2i22i22i2−2i20000000000000000000000000000000
χ6044-4-4-44-440000000000000000000000−4i4i−222222−222i2−2i2−2i22i20000000000000000000000000000000
χ614-44-4-4-444400-4400-4004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ624-44-4-4-444400-4400-400−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ634-44-4-4-444-4004-400400000000004-4-4400000000000000000000000000000000000000000
χ644-44-4-4-444-4004-40040000000000-444-400000000000000000000000000000000000000000
χ654-4-444-4-4404400-4-400000000000000000000000000000000000000000000000000002i2−2i200
χ664-4-444-4-4404400-4-40000000000000000000000000000000000000000000000000000−2i22i200
χ674-4-444-4-440-4-4004400000000000000000000000000000000000000000000000022−22000000
χ684-4-444-4-440-4-40044000000000000000000000000000000000000000000000000−2222000000
χ694-4-4-4444-4-44-4-444-44-4400000000000000000000000000000000000000000000000000000
χ704-4-4-4444-4-4-44-44-4444-400000000000000000000000000000000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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