Finite Group Databasebeta

← Group #274205

Character table — Group #274205

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444444444444888888884444488888888888822228888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111
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
χ111111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-11
χ121111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-11-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-111-1-111-1-1-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-111-1-111-1-1111-1
χ172222222222-2-22-2-2222-2-2-2-22222-2-2-2-22200000000-222-2-200000000000000000000000000
χ182222222222-2-22-2-2222-2-2-2-2-2-2-2-222222200000000-2-2-22200000000000000000000000000
χ192222222222-2-22-2-22-2-2-2-2222222-2-2-2-2-2-2000000002-2-22200000000000000000000000000
χ202222222222-2-22-2-22-2-2-2-222-2-2-2-22222-2-200000000222-2-200000000000000000000000000
χ2122222222-2-222-222-222-2-2-2-200000000-2-22222-2-2-2-220000-2-2220000000000000000000000
χ2222222222-2-222-222-222-2-2-2-200000000-2-2-2-2-2-222222000022-2-20000000000000000000000
χ2322222222-2-222-222-2-2-2-2-222000000002222222222-20000-2-2-2-20000000000000000000000
χ2422222222-2-222-222-2-2-2-2-2220000000022-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222222200000000-2-200000000-2000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-222222200000000-2-200000000-200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-20000000022000000002000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2000000002200000000200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-2-22-22-22-222-2-2002-2002i2i−2i−2i2i2i−2i−2i000000000000000000000000000002-200002i−2i0000
χ30222-2-2-22-22-22-222-2-2002-2002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000-220000−2i2i0000
χ31222-2-2-22-22-22-222-2-2002-200−2i−2i2i2i−2i−2i2i2i000000000000000000000000000002-20000−2i2i0000
χ32222-2-2-22-22-22-222-2-2002-200−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000-2200002i−2i0000
χ33222-2-2-22-22-2-222-22-200-22002i2i−2i−2i−2i−2i2i2i0000000000000000000000000002-200002i−2i000000
χ34222-2-2-22-22-2-222-22-200-22002i2i−2i−2i−2i−2i2i2i000000000000000000000000000-220000−2i2i000000
χ35222-2-2-22-22-2-222-22-200-2200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000002-20000−2i2i000000
χ36222-2-2-22-22-2-222-22-200-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000000-2200002i−2i000000
χ372-2-22-2-2222200-200-22-200002i−2i2i−2i00002-222−2−222−2−202i−2i002−22−2i2−i2i2−i2i2−i2i2−i200000000000000
χ382-2-22-2-2222200-200-22-200002i−2i2i−2i00002-2−2−222−2−22202i−2i00−22−22−i2i2−i2i2−i2i2−i2i200000000000000
χ392-2-22-2-2222200-200-22-20000−2i2i−2i2i00002-222−2−222−2−20−2i2i002−22−2−i2i2−i2i2−i2i2−i2i200000000000000
χ402-2-22-2-2222200-200-22-20000−2i2i−2i2i00002-2−2−222−2−2220−2i2i00−22−22i2−i2i2−i2i2−i2i2−i200000000000000
χ412-2-22-2-2222200-200-2-2200002i−2i2i−2i0000-2222−2−2−2−2220−2i2i002−2−22i2−i2i2−i2−i2i2−i2i200000000000000
χ422-2-22-2-2222200-200-2-2200002i−2i2i−2i0000-22−2−22222−2−20−2i2i00−222−2−i2i2−i2i2i2−i2i2−i200000000000000
χ432-2-22-2-2222200-200-2-220000−2i2i−2i2i0000-2222−2−2−2−22202i−2i002−2−22−i2i2−i2i2i2−i2i2−i200000000000000
χ442-2-22-2-2222200-200-2-220000−2i2i−2i2i0000-22−2−22222−2−202i−2i00−222−2i2−i2i2−i2−i2i2−i2i200000000000000
χ452-2-22-2-222-2-20020022-2000000002-22-2-2222−2−2−2−2220002-2−222−22−2−222−2−2200000000000000
χ462-2-22-2-222-2-20020022-2000000002-22-2-22−2−22222−2−20002-22−2−22−222−2−222−200000000000000
χ472-2-22-2-222-2-20020022-200000000-22-22-2222−2−2−2−222000-22−222−2−222−2−222−200000000000000
χ482-2-22-2-222-2-20020022-200000000-22-22-22−2−22222−2−2000-222−2−222−2−222−2−2200000000000000
χ492-2-22-2-222-2-2002002-22000000002-22-22-222−2−222−2−2000-22−22−222−2−22−222−200000000000000
χ502-2-22-2-222-2-2002002-22000000002-22-22-2−2−222−2−222000-222−22−2−222−22−2−2200000000000000
χ512-2-22-2-222-2-2002002-2200000000-22-222-222−2−222−2−20002-2−22−22−222−22−2−2200000000000000
χ522-2-22-2-222-2-2002002-2200000000-22-222-2−2−222−2−2220002-22−22−22−2−22−222−200000000000000
χ53444-4-4-44-4-444-4-44-4400-44000000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-44-44-4-444004-4000000000000000000000000000000000000000000000000000
χ5544-444-4-4-40000000000004-400000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000000
χ5644-444-4-4-40000000000004-40000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000000
χ5744-444-4-4-4000000000000-4400000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000
χ5844-444-4-4-4000000000000-440000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000
χ594-444-44-4-4004-40-440000000000000000000004i−4i−4i4i0000000000000000000000000000000
χ604-444-44-4-4004-40-44000000000000000000000−4i4i4i−4i0000000000000000000000000000000
χ614-444-44-4-400-4404-4000000000000000004i−4i−4i4i00000000000000000000000000000000000
χ624-444-44-4-400-4404-400000000000000000−4i4i4i−4i00000000000000000000000000000000000
χ634-44-44-4-4400440-4-400000000000000000000000000000000000000000000002i2−2i200000000
χ644-44-44-4-4400440-4-40000000000000000000000000000000000000000000000−2i22i200000000
χ654-44-44-4-4400-4-4044000000000000000000000000000000000000000000000000000022−2200
χ664-44-44-4-4400-4-40440000000000000000000000000000000000000000000000000000−222200
χ674-4-4-4444-44-400-40040000004-4-44000000000000000000000000000000000000000000000
χ684-4-4-4444-44-400-4004000000-444-4000000000000000000000000000000000000000000000
χ694-4-4-4444-4-4400400-400000000004i−4i−4i4i00000000000000000000000000000000000000000
χ704-4-4-4444-4-4400400-40000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ7188-8-8-88-88000000000000000000000000000000000000000000000000000000000000000

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