Finite Group Databasebeta

← Group #281365

Character table — Group #281365

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11111-1-1-1-111-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-1-111-1-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1111111-1-111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-111-1-111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11-1-1-111-1-1-1-1-1-11111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-11-1-1-1-111-1-111-1-1111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-111-1-11111-1-111-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111111-1-11111-1-1-1-1-11
χ172222222222-2-22-2-22-2-2000000002222-2-2-2-20000000000002222-2-20000000000000000
χ182222222222-2-22-2-22-2-2000000002222-2-2-2-2000000000000-2-2-2-2220000000000000000
χ192222222222-2-22-2-22-2-200000000-2-2-2-2222200000000000022-2-2-220000000000000000
χ202222222222-2-22-2-22-2-200000000-2-2-2-22222000000000000-2-2222-20000000000000000
χ2122222222-2-222-222-2-2-22222-2-2-2-2000000000000000022-2-20000002-200000000000000
χ2222222222-2-222-222-2-2-22222-2-2-2-20000000000000000-2-222000000-2200000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-22222000000000000000022-2-2000000-2200000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-222220000000000000000-2-2220000002-200000000000000
χ252-2-2222-2-22-2-2-2222-2-2200000000000000002222-2-2-2-22i−2i2i−2i0000000000000000002i−2i00
χ262-2-2222-2-22-2-2-2222-2-2200000000000000002222-2-2-2-2−2i2i−2i2i000000000000000000−2i2i00
χ272-2-2222-2-22-2-2-2222-2-220000000000000000-2-2-2-222222i−2i2i−2i000000000000000000−2i2i00
χ282-2-2222-2-22-2-2-2222-2-220000000000000000-2-2-2-22222−2i2i−2i2i0000000000000000002i−2i00
χ292-2-2222-2-2-2222-2-2-22-220000000022-2-222-2-2000000000000000000002i−2i2i−2i0000000000
χ302-2-2222-2-2-2222-2-2-22-220000000022-2-222-2-200000000000000000000−2i2i−2i2i0000000000
χ312-2-2222-2-2-2222-2-2-22-2200000000-2-222-2-222000000000000000000002i−2i−2i2i0000000000
χ322-2-2222-2-2-2222-2-2-22-2200000000-2-222-2-22200000000000000000000−2i2i2i−2i0000000000
χ332-2-2222-2-2-22-2-2-22222-20000000022-2-2-2-222000000002i−2i−2i2i0000000000002i−2i00000000
χ342-2-2222-2-2-22-2-2-22222-20000000022-2-2-2-22200000000−2i2i2i−2i000000000000−2i2i00000000
χ352-2-2222-2-2-22-2-2-22222-200000000-2-22222-2-2000000002i−2i−2i2i000000000000−2i2i00000000
χ362-2-2222-2-2-22-2-2-22222-200000000-2-22222-2-200000000−2i2i2i−2i0000000000002i−2i00000000
χ372-2-22-2-2222200-200-20022−2−222−2−22-22-2000022−2−222−2−200002i−2i2i−2i0000000000i2−i2i2−i20000
χ382-2-22-2-2222200-200-20022−2−222−2−22-22-2000022−2−222−2−20000−2i2i−2i2i0000000000−i2i2−i2i20000
χ392-2-22-2-2222200-200-20022−2−222−2−2-22-220000−2−222−2−22200002i−2i−2i2i0000000000i2−i2−i2i20000
χ402-2-22-2-2222200-200-20022−2−222−2−2-22-220000−2−222−2−2220000−2i2i2i−2i0000000000−i2i2i2−i20000
χ412-2-22-2-2222200-200-200−2−222−2−2222-22-20000−2−222−2−22200002i−2i2i−2i0000000000−i2i2−i2i20000
χ422-2-22-2-2222200-200-200−2−222−2−2222-22-20000−2−222−2−2220000−2i2i−2i2i0000000000i2−i2i2−i20000
χ432-2-22-2-2222200-200-200−2−222−2−222-22-22000022−2−222−2−200002i−2i−2i2i0000000000−i2i2i2−i20000
χ442-2-22-2-2222200-200-200−2−222−2−222-22-22000022−2−222−2−20000−2i2i2i−2i0000000000i2−i2−i2i20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-44-400-40040000000000000000002222−22−22−22−22222200000000000000000000000000
χ474444-4-4-4-44-400-4004000000000000000000−22−2222222222−22−2200000000000000000000000000
χ484444-4-4-4-4-4400400-400000000004-4-4400000000000000000000000000000000000000
χ494444-4-4-4-4-4400400-40000000000-444-400000000000000000000000000000000000000
χ5044-4-44-44-4000000000000002i2−2i22i2−2i2000022−2222−222i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ5144-4-44-44-4000000000000002i2−2i22i2−2i20000−2222−2222−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ5244-4-44-44-400000000000000−2i22i2−2i22i2000022−2222−22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ5344-4-44-44-400000000000000−2i22i2−2i22i20000−2222−22222i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ5444-4-4-44-44004-404-400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000
χ5544-4-4-44-44004-404-40000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000
χ5644-4-4-44-4400-440-440004i−4i4i−4i0000000000000000000000000000000000000000000000
χ5744-4-4-44-4400-440-44000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ584-44-44-4-4400000000002i2−2i2−2i22i20000000022−22−22222i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ594-44-44-4-4400000000002i2−2i2−2i22i200000000−222222−22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ604-44-44-4-440000000000−2i22i22i2−2i20000000022−22−2222−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ614-44-44-4-440000000000−2i22i22i2−2i200000000−222222−222i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ624-44-4-444-4004-40-4400000004i−4i−4i4i000000000000000000000000000000000000000000
χ634-44-4-444-4004-40-440000000−4i4i4i−4i000000000000000000000000000000000000000000
χ644-44-4-444-400-4404-400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ654-44-4-444-400-4404-40000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ664-4-4444-4-44-4444-4-4-44-400000000000000000000000000000000000000000000000000
χ674-4-44-4-444-4-4004004002222−22−22−22−222222000000000000000000000000000000000000000000
χ684-4-44-4-444-4-400400400−22−2222222222−22−22000000000000000000000000000000000000000000

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