Finite Group Databasebeta

← Group #309294

Character table — Group #309294

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-1-1-1-11-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-11-1-1-1-1-11-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1111111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-111-1-111-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1111-1-1-1-1-1-1-1111-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11111111-1-11-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-11111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-11-1-111-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-11-1-111-1-1-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-1111111-1-1-1-111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-11-111-1-111-1-11-1
χ172222222222-22-2-2-22-2-2000000002222-2-2-2-2000000002200-2-200-200000200000000000
χ182222222222-22-2-2-22-2-2000000002222-2-2-2-200000000-2-2002200200000-200000000000
χ192222222222-22-2-2-22-2-200000000-2-2-2-22222000000002200-2-200200000-200000000000
χ202222222222-22-2-2-22-2-200000000-2-2-2-2222200000000-2-2002200-200000200000000000
χ2122222222-2-22-2222-2-2-22222-2-2-2-20000000000000000002200220-200000-20000000000
χ2222222222-2-22-2222-2-2-22222-2-2-2-2000000000000000000-2-200-2-2020000020000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-222220000000000000000002200-2-20200000-20000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-22222000000000000000000-2-200220-20000020000000000
χ2522-2-2-222-222-2-222-2-22-222-2-222-2-2000000000000000000000000002-22-2000000000000
χ2622-2-2-222-222-2-222-2-22-222-2-222-2-200000000000000000000000000-22-22000000000000
χ2722-2-2-222-222-2-222-2-22-2-2-222-2-222000000000000000000000000002-2-22000000000000
χ2822-2-2-222-222-2-222-2-22-2-2-222-2-22200000000000000000000000000-222-2000000000000
χ2922-2-2-222-2-2-222-2-2222-200000000000000002i2i2i2i−2i−2i−2i−2i2i−2i002i−2i0000000000002-2000000
χ3022-2-2-222-2-2-222-2-2222-200000000000000002i2i2i2i−2i−2i−2i−2i−2i2i00−2i2i000000000000-22000000
χ3122-2-2-222-2-2-222-2-2222-20000000000000000−2i−2i−2i−2i2i2i2i2i2i−2i002i−2i000000000000-22000000
χ3222-2-2-222-2-2-222-2-2222-20000000000000000−2i−2i−2i−2i2i2i2i2i−2i2i00−2i2i0000000000002-2000000
χ3322-2-2-222-2-2-2-2222-22-2222-2-2-2-22200000000000000002i−2i00−2i2i00000000002i−2i00000000
χ3422-2-2-222-2-2-2-2222-22-2222-2-2-2-2220000000000000000−2i2i002i−2i0000000000−2i2i00000000
χ3522-2-2-222-2-2-2-2222-22-22-2-22222-2-200000000000000002i−2i00−2i2i0000000000−2i2i00000000
χ3622-2-2-222-2-2-2-2222-22-22-2-22222-2-20000000000000000−2i2i002i−2i00000000002i−2i00000000
χ372-222-22-2-200-202-220002i−2i2i−2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2002-2002i−2i0000000000002−2i2−i200
χ382-222-22-2-200-202-220002i−2i2i−2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i200-2200−2i2i000000000000−22−i2i200
χ392-222-22-2-200-202-220002i−2i2i−2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i2002-2002i−2i000000000000−22−i2i200
χ402-222-22-2-200-202-220002i−2i2i−2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i200-2200−2i2i0000000000002−2i2−i200
χ412-222-22-2-200-202-22000−2i2i−2i2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2002-200−2i2i0000000000002−2−i2i200
χ422-222-22-2-200-202-22000−2i2i−2i2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i200-22002i−2i000000000000−22i2−i200
χ432-222-22-2-200-202-22000−2i2i−2i2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i2002-200−2i2i000000000000−22i2−i200
χ442-222-22-2-200-202-22000−2i2i−2i2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i200-22002i−2i0000000000002−2−i2i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-40000000000000022−2222−22000022−2222−222-22-22-22-200000000000000000000000000
χ47444-44-4-4-40000000000000022−2222−220000−2222−2222-22-22-22-2200000000000000000000000000
χ48444-44-4-4-400000000000000−2222−2222000022−2222−22-22-22-22-2200000000000000000000000000
χ49444-44-4-4-400000000000000−2222−22220000−2222−22222-22-22-22-200000000000000000000000000
χ5044-44-4-4-440000000000000022−22−22222i2−2i22i2−2i200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5144-44-4-4-440000000000000022−22−2222−2i22i2−2i22i20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5244-44-4-4-4400000000000000−222222−222i2−2i22i2−2i20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5344-44-4-4-4400000000000000−222222−22−2i22i2−2i22i200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5444-4-4-444-4444-4-4-44-4-4400000000000000000000000000000000000000000000000000
χ554-444-44-4-40040-44-4000000000002222−22−22−22−2222220000000000000000000000000000000000
χ564-444-44-4-40040-44-400000000000−22−2222222222−22−220000000000000000000000000000000000
χ574-44-4-4-4444-404000-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ584-44-4-4-4444-404000-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ594-44-4-4-444-440-40004000000000000004-4-440000000000000000000000000000000000
χ604-44-4-4-444-440-4000400000000000000-444-40000000000000000000000000000000000
χ614-4-444-44-44-40-4000400000000004i−4i−4i4i00000000000000000000000000000000000000
χ624-4-444-44-44-40-400040000000000−4i4i4i−4i00000000000000000000000000000000000000
χ634-4-444-44-4-4404000-400000000000000000022−22−2222−222222−2200000000000000000000000000
χ644-4-444-44-4-4404000-4000000000000000000−222222−2222−22−222200000000000000000000000000
χ654-4-4-444-4400404-4-40004i−4i−4i4i0000000000000000000000000000000000000000000000
χ664-4-4-444-4400404-4-4000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-4-4-444-4400-40-44400000000000000000002222−22−22−22−22222200000000000000000000000000
χ684-4-4-444-4400-40-4440000000000000000000−22−2222222222−22−2200000000000000000000000000

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