Finite Group Databasebeta

← Group #307704

Character table — Group #307704

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-11111-1-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-111111111-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11-1-1-111-1-1-1-111-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-11-1-1-1-111-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-111-1-11111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111111-1-111-1-111-1-1-11
χ1722222222222-2-2-2-22-2-2000000002222-2-2-2-20000000022-2-20000002-200000000000000
χ1822222222222-2-2-2-22-2-2000000002222-2-2-2-200000000-2-222000000-2200000000000000
χ1922222222222-2-2-2-22-2-200000000-2-2-2-222220000000022-2-2000000-2200000000000000
χ2022222222222-2-2-2-22-2-200000000-2-2-2-2222200000000-2-2220000002-200000000000000
χ2122222222-2-2-22222-2-2-22222-2-2-2-2000000000000000000002222-2-20000000000000000
χ2222222222-2-2-22222-2-2-22222-2-2-2-200000000000000000000-2-2-2-2220000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-222220000000000000000000022-2-2-220000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2222200000000000000000000-2-2222-20000000000000000
χ252-2-222-2-222-2-222-2-222-222-2-222-2-200000000000000000000000000002i−2i2i−2i0000000000
χ262-2-222-2-222-2-222-2-222-222-2-222-2-20000000000000000000000000000−2i2i−2i2i0000000000
χ272-2-222-2-222-2-222-2-222-2-2-222-2-22200000000000000000000000000002i−2i−2i2i0000000000
χ282-2-222-2-222-2-222-2-222-2-2-222-2-2220000000000000000000000000000−2i2i2i−2i0000000000
χ292-2-222-2-22-22222-2-2-2-2222-2-2-2-22200000000000000002i−2i2i−2i0000000000002i−2i00000000
χ302-2-222-2-22-22222-2-2-2-2222-2-2-2-2220000000000000000−2i2i−2i2i000000000000−2i2i00000000
χ312-2-222-2-22-22222-2-2-2-22-2-22222-2-200000000000000002i−2i2i−2i000000000000−2i2i00000000
χ322-2-222-2-22-22222-2-2-2-22-2-22222-2-20000000000000000−2i2i−2i2i0000000000002i−2i00000000
χ332-2-222-2-22-222-2-222-22-200000000000000002i2i2i2i−2i−2i−2i−2i2i−2i−2i2i000000000000002-2000000
χ342-2-222-2-22-222-2-222-22-200000000000000002i2i2i2i−2i−2i−2i−2i−2i2i2i−2i00000000000000-22000000
χ352-2-222-2-22-222-2-222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i2i−2i−2i2i00000000000000-22000000
χ362-2-222-2-22-222-2-222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i−2i2i2i−2i000000000000002-2000000
χ372-2-22-222-20002-22-20002-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i0000000000002−22−200
χ382-2-22-222-20002-22-20002-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i000000000000−22−2200
χ392-2-22-222-20002-22-20002-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i000000000000−22−2200
χ402-2-22-222-20002-22-20002-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i0000000000002−22−200
χ412-2-22-222-20002-22-2000-22-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002i−2i−2i2i0000000000002−2−2200
χ422-2-22-222-20002-22-2000-22-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000−2i2i2i−2i000000000000−222−200
χ432-2-22-222-20002-22-2000-22-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002i−2i−2i2i000000000000−222−200
χ442-2-22-222-20002-22-2000-22-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−2i2i2i−2i0000000000002−2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-40004-4-440004-4-440000000000000000000000000000000000000000000000
χ474444-4-4-4-40004-4-44000-444-40000000000000000000000000000000000000000000000
χ484444-4-4-4-4000-444-400000000000000000002222−22−22−22−22222200000000000000000000000000
χ494444-4-4-4-4000-444-40000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5044-4-444-4-444-40000-400000000000000000022−2222−2222−2222−2200000000000000000000000000
χ5144-4-444-4-444-40000-4000000000000000000−2222−2222−2222−222200000000000000000000000000
χ5244-4-444-4-4-4-440000400000000004i−4i4i−4i00000000000000000000000000000000000000
χ5344-4-444-4-4-4-44000040000000000−4i4i−4i4i00000000000000000000000000000000000000
χ5444-4-4-4-444000000000000002i2−2i22i2−2i200002i2−2i22i2−2i22-2-22-222-200000000000000000000000000
χ5544-4-4-4-444000000000000002i2−2i22i2−2i20000−2i22i2−2i22i2-222-22-2-2200000000000000000000000000
χ5644-4-4-4-44400000000000000−2i22i2−2i22i200002i2−2i22i2−2i2-222-22-2-2200000000000000000000000000
χ5744-4-4-4-44400000000000000−2i22i2−2i22i20000−2i22i2−2i22i22-2-22-222-200000000000000000000000000
χ584-44-44-44-44-440000-4000000000000004-4-440000000000000000000000000000000000
χ594-44-44-44-44-440000-400000000000000-444-40000000000000000000000000000000000
χ604-44-44-44-4-44-4000040000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ614-44-44-44-4-44-400004000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ624-44-4-44-44000000000000002i2−2i2−2i22i222−22−222200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ634-44-4-44-44000000000000002i2−2i2−2i22i2−222222−220000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ644-44-4-44-4400000000000000−2i22i22i2−2i222−22−22220000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ654-44-4-44-4400000000000000−2i22i22i2−2i2−222222−2200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ664-4-444-4-444-4-4-4-4444-4400000000000000000000000000000000000000000000000000
χ674-4-44-444-4000-44-44000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ684-4-44-444-4000-44-4400000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000

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