Finite Group Databasebeta

← Group #333285

Character table — Group #333285

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444222444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-1-1-11-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-1-1-111-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11-1111-1-1-1-1-1-1111-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-111-1-1-1-111-1-1-1-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-111-1-11111-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111111111-1-11-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-111111-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-11-1-1-1-11111111-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1111111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1111-11111111-1-1-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-11-1-1-1-1-1-11111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111-11-111-1-1-1-11111-1-1
χ17222222222-22-22-22-2-2-222220000-2-2-2-200000000000022002200-20000-2000000000000
χ18222222222-22-22-22-2-2-222220000-2-2-2-2000000000000-2-200-2-200200002000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000022220000000000002200-2-20020000-2000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-200002222000000000000-2-2002200-200002000000000000
χ2122222222-22-22-22-22-2-2000022220000-2-2-2-200000000002200-2-2000-220000000000000
χ2222222222-22-22-22-22-2-2000022220000-2-2-2-20000000000-2-200220002-20000000000000
χ2322222222-22-22-22-22-2-20000-2-2-2-2000022220000000000220022000-2-20000000000000
χ2422222222-22-22-22-22-2-20000-2-2-2-2000022220000000000-2-200-2-2000220000000000000
χ252222-2-2-2-2-20-202020002i2i−2i−2i22−2−2000022−2−2i2i2i2i2−i2−i2−i2−i22-2002i−2i0000000000i2−i2002−20000
χ262222-2-2-2-2-20-202020002i2i−2i−2i22−2−2000022−2−2i2i2i2i2−i2−i2−i2−i2-2200−2i2i0000000000−i2i200−220000
χ272222-2-2-2-2-20-202020002i2i−2i−2i−2−2220000−2−222−i2−i2−i2−i2i2i2i2i22-2002i−2i0000000000−i2i200−220000
χ282222-2-2-2-2-20-202020002i2i−2i−2i−2−2220000−2−222−i2−i2−i2−i2i2i2i2i2-2200−2i2i0000000000i2−i2002−20000
χ292222-2-2-2-2-20-20202000−2i−2i2i2i22−2−2000022−2−2−i2−i2−i2−i2i2i2i2i22-200−2i2i0000000000−i2i2002−20000
χ302222-2-2-2-2-20-20202000−2i−2i2i2i22−2−2000022−2−2−i2−i2−i2−i2i2i2i2i2-22002i−2i0000000000i2−i200−220000
χ312222-2-2-2-2-20-20202000−2i−2i2i2i−2−2220000−2−222i2i2i2i2−i2−i2−i2−i22-200−2i2i0000000000i2−i200−220000
χ322222-2-2-2-2-20-20202000−2i−2i2i2i−2−2220000−2−222i2i2i2i2−i2−i2−i2−i2-22002i−2i0000000000−i2i2002−20000
χ332-22-2-22-22-2-222-2-222-22000000000000000022-2-222-2-20000000002-20002-20000000000
χ342-22-2-22-22-2-222-2-222-22000000000000000022-2-222-2-2000000000-22000-220000000000
χ352-22-2-22-22-2-222-2-222-220000000000000000-2-222-2-2220000000002-2000-220000000000
χ362-22-2-22-22-2-222-2-222-220000000000000000-2-222-2-222000000000-220002-20000000000
χ372-2-22-2-2220-20-20202002−22−2000022−2−22-22-22−22−22−22−2002-2002-200000000002−2002−200
χ382-2-22-2-2220-20-20202002−22−2000022−2−22-22-22−22−22−22−200-2200-220000000000−2200−2200
χ392-2-22-2-2220-20-20202002−22−2000022−2−2-22-22−22−22−22−22002-200-220000000000−22002−200
χ402-2-22-2-2220-20-20202002−22−2000022−2−2-22-22−22−22−22−2200-22002-200000000002−200−2200
χ412-2-22-2-2220-20-2020200−22−220000−2−2222-22-2−22−22−22−22002-2002-20000000000−2200−2200
χ422-2-22-2-2220-20-2020200−22−220000−2−2222-22-2−22−22−22−2200-2200-2200000000002−2002−200
χ432-2-22-2-2220-20-2020200−22−220000−2−222-22-222−22−22−22−2002-200-2200000000002−200−2200
χ442-2-22-2-2220-20-2020200−22−220000−2−222-22-222−22−22−22−200-22002-20000000000−22002−200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-44040-40-400000002222−22−220000−22−2222220000000000000000000000000000000000
χ474444-4-4-4-44040-40-40000000−22−22222200002222−22−220000000000000000000000000000000000
χ4844-4-44-4-44040-40-40400000000000000000022−22−222222−22−222200000000000000000000000000
χ4944-4-44-4-44040-40-404000000000000000000−222222−22−222222−2200000000000000000000000000
χ5044-4-44-4-440-404040-40000004-44-4000000000000000000000000000000000000000000
χ5144-4-44-4-440-404040-4000000-44-44000000000000000000000000000000000000000000
χ5244-4-4-444-40000000000000022−22−22222i2−2i22i2−2i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5344-4-4-444-40000000000000022−22−2222−2i22i2−2i22i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5444-4-4-444-400000000000000−222222−222i2−2i22i2−2i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5544-4-4-444-400000000000000−222222−22−2i22i2−2i22i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ564-44-44-44-440-40-40400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ574-44-44-44-440-40-4040000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ584-44-44-44-4-404040-4000000000004i−4i−4i4i00000000000000000000000000000000000000
χ594-44-44-44-4-404040-400000000000−4i4i4i−4i00000000000000000000000000000000000000
χ604-44-4-44-4444-4-444-4-4-4400000000000000000000000000000000000000000000000000
χ614-44-4-44-444-4-444-4-444-400000000000000000000000000000000000000000000000000
χ624-44-4-44-44-444-4-444-44-400000000000000000000000000000000000000000000000000
χ634-4-4444-4-400000000002i2−2i2−2i22i20000000022−22−22222i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ644-4-4444-4-400000000002i2−2i2−2i22i200000000−222222−22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ654-4-4444-4-40000000000−2i22i22i2−2i20000000022−22−2222−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ664-4-4444-4-40000000000−2i22i22i2−2i200000000−222222−222i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ674-4-44-4-44404040-40-40022−2222−220000−22−22222200000000000000000000000000000000000000
χ684-4-44-4-44404040-40-400−2222−222200002222−22−2200000000000000000000000000000000000000

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