Finite Group Databasebeta

← Group #274178

Character table — Group #274178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444444444444888888884444488888888888844448888888824
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
χ51111111111111111111111-1-1-1-111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-111-1-111-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ91111111111111111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-11
χ101111111111111111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-111111-1
χ111111111111111111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1111-1
χ121111111111111111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-11
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-1111111-1-1-1-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-111-1-1-1-11111-1-11-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-11111-1-1-1-111-11
χ17222222222-2-222-2-2222-2-2-2-22222-2-2-2-2-2-200000000222-2-200000000000000000000000000
χ18222222222-2-222-2-2222-2-2-2-2-2-2-2-2-2-2222200000000-2-222200000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-222222222-2-2-2-200000000-2-2-22200000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-222-2-2-2-22222220000000022-2-2-200000000000000000000000000
χ2122222222-222-2-222-222-2-2-2-200002200002222222200-200-2-2-2-20000000000000000000000
χ2222222222-222-2-222-222-2-2-2-20000220000-2-2-2-2-2-2-2-200-20022220000000000000000000000
χ2322222222-222-2-222-2-2-2-2-2220000-2-200002222-2-2-2-200200-2-2220000000000000000000000
χ2422222222-222-2-222-2-2-2-2-2220000-2-20000-2-2-2-222220020022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222220000-2-200000000000000-20000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-22222220000-2-200000000000000-2000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-20000220000000000000020000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2000022000000000000002000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ2922-2-222-2-2200-2-200200002i−2i22-2-22i−2i000022−2−2i2i2−i2−i20002i−2i2−2i2−i22−22−2i2−i2i2−i200000000000000
χ3022-2-222-2-2200-2-200200002i−2i22-2-22i−2i0000−2−222−i2−i2i2i20002i−2i−22−i2i2−22−22−i2i2−i2i200000000000000
χ3122-2-222-2-2200-2-200200002i−2i-2-2222i−2i000022−2−2i2i2−i2−i2000−2i2i2−2i2−i2−22−22−i2i2−i2i200000000000000
χ3222-2-222-2-2200-2-200200002i−2i-2-2222i−2i0000−2−222−i2−i2i2i2000−2i2i−22−i2i22−22−2i2−i2i2−i200000000000000
χ3322-2-222-2-2200-2-20020000−2i2i22-2-2−2i2i000022−2−2−i2−i2i2i2000−2i2i2−2−i2i22−22−2−i2i2−i2i200000000000000
χ3422-2-222-2-2200-2-20020000−2i2i22-2-2−2i2i0000−2−222i2i2−i2−i2000−2i2i−22i2−i2−22−22i2−i2i2−i200000000000000
χ3522-2-222-2-2200-2-20020000−2i2i-2-222−2i2i000022−2−2−i2−i2i2i20002i−2i2−2−i2i2−22−22i2−i2i2−i200000000000000
χ3622-2-222-2-2200-2-20020000−2i2i-2-222−2i2i0000−2−222i2i2−i2−i20002i−2i−22i2−i22−22−2−i2i2−i2i200000000000000
χ3722-2-222-2-2-2002200-200002i−2i0000−2i2i2i2i−2i−2i22−2−2−i2−i2i2i22-2000−22i2−i2i2−i2−i2i2−222−200000000000000
χ3822-2-222-2-2-2002200-200002i−2i0000−2i2i2i2i−2i−2i−2−222i2i2−i2−i22-20002−2−i2i2−i2i2i2−i22−2−2200000000000000
χ3922-2-222-2-2-2002200-200002i−2i0000−2i2i−2i−2i2i2i22−2−2−i2−i2i2i2-22000−22i2−i2−i2i2i2−i22−2−2200000000000000
χ4022-2-222-2-2-2002200-200002i−2i0000−2i2i−2i−2i2i2i−2−222i2i2−i2−i2-220002−2−i2i2i2−i2−i2i2−222−200000000000000
χ4122-2-222-2-2-2002200-20000−2i2i00002i−2i2i2i−2i−2i22−2−2i2i2−i2−i2-22000−22−i2i2i2−i2−i2i22−2−2200000000000000
χ4222-2-222-2-2-2002200-20000−2i2i00002i−2i2i2i−2i−2i−2−222−i2−i2i2i2-220002−2i2−i2−i2i2i2−i2−222−200000000000000
χ4322-2-222-2-2-2002200-20000−2i2i00002i−2i−2i−2i2i2i22−2−2i2i2−i2−i22-2000−22−i2i2−i2i2i2−i2−222−200000000000000
χ4422-2-222-2-2-2002200-20000−2i2i00002i−2i−2i−2i2i2i−2−222−i2−i2i2i22-20002−2i2−i2i2−i2−i2i22−2−2200000000000000
χ452-2-22-222-222-22-22-2-2002-2002i−2i2i−2i002i−2i2i−2i0000000000000000000000000002-200002i−2i0000
χ462-2-22-222-222-22-22-2-2002-2002i−2i2i−2i002i−2i2i−2i000000000000000000000000000-220000−2i2i0000
χ472-2-22-222-222-22-22-2-2002-200−2i2i−2i2i00−2i2i−2i2i0000000000000000000000000002-20000−2i2i0000
χ482-2-22-222-222-22-22-2-2002-200−2i2i−2i2i00−2i2i−2i2i000000000000000000000000000-2200002i−2i0000
χ492-2-22-222-22-222-2-22-200-22002i−2i2i−2i00−2i2i−2i2i00000000000000000000000002-2002i−2i00000000
χ502-2-22-222-22-222-2-22-200-22002i−2i2i−2i00−2i2i−2i2i0000000000000000000000000-2200−2i2i00000000
χ512-2-22-222-22-222-2-22-200-2200−2i2i−2i2i002i−2i2i−2i00000000000000000000000002-200−2i2i00000000
χ522-2-22-222-22-222-2-22-200-2200−2i2i−2i2i002i−2i2i−2i0000000000000000000000000-22002i−2i00000000
χ53444-4-4-44-404400-4-40000000000000000000004-44-40000000000000000000000000000000
χ54444-4-4-44-404400-4-4000000000000000000000-44-440000000000000000000000000000000
χ55444-4-4-44-40-4-40044000000000000000004i−4i4i−4i00000000000000000000000000000000000
χ56444-4-4-44-40-4-4004400000000000000000−4i4i−4i4i00000000000000000000000000000000000
χ5744-44-4-4-44000000004-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000
χ5844-44-4-4-44000000004-400000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000
χ5944-44-4-4-4400000000-44000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ6044-44-4-4-4400000000-4400000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ614-44-4-44-44400-4400-40000004i−4i−4i4i000000000000000000000000000000000000000000000
χ624-44-4-44-44400-4400-4000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ634-44-4-44-44-4004-40040000000000004-4-44000000000000000000000000000000000000000
χ644-44-4-44-44-4004-4004000000000000-444-4000000000000000000000000000000000000000
χ654-4-44-444-4-44-4-444-4400-44000000000000000000000000000000000000000000000000000
χ664-4-44-444-4-4-44-44-444004-4000000000000000000000000000000000000000000000000000
χ674-4-4-44-44404-400-4400000000000000000000000000000000000000000000000022−22000000
χ684-4-4-44-44404-400-44000000000000000000000000000000000000000000000000−2222000000
χ694-4-4-44-4440-44004-4000000000000000000000000000000000000000000000000000022−2200
χ704-4-4-44-4440-44004-40000000000000000000000000000000000000000000000000000−222200
χ718-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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