Finite Group Databasebeta

← Group #345552

Character table — Group #345552

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444224444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1111-1-1-1-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-11-1-1-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1111111-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1111-1
χ9111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11-11111-1-1-1-1-1-1-11
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-111-1-111111-1
χ11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1111-1-111-1-1-1-11-1
χ12111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-1-1-1-1111111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111111-11-1-1-111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11-1-11-1-11111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-111-111-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-11-1111-1-111-1-1-1-1
χ172222222222-2-2-222-2-2-200002222-2-2-2-200000000000000002222000000-2-20000000000
χ182222222222-2-2-222-2-2-200002222-2-2-2-20000000000000000-2-2-2-2000000220000000000
χ192222222222-2-2-222-2-2-20000-2-2-2-22222000000000000000022-2-2000000-220000000000
χ202222222222-2-2-222-2-2-20000-2-2-2-222220000000000000000-2-2220000002-20000000000
χ2122222222-2-2222-2-22-2-2222200000000-2-2-2-200000000222200000000-2-2000000000000
χ2222222222-2-2222-2-22-2-2222200000000-2-2-2-200000000-2-2-2-20000000022000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-20000000022220000000022-2-200000000-22000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-200000000222200000000-2-222000000002-2000000000000
χ252222-2-2-2-22222-2-2-2-2-2200000000000000002222-2-2-2-2000000002-22-200000000000000
χ262222-2-2-2-22222-2-2-2-2-2200000000000000002222-2-2-2-200000000-22-2200000000000000
χ272222-2-2-2-22222-2-2-2-2-220000000000000000-2-2-2-22222000000002-2-2200000000000000
χ282222-2-2-2-22222-2-2-2-2-220000000000000000-2-2-2-2222200000000-222-200000000000000
χ2922-2-222-2-22-20002-2000i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002-22-2000000000000i2−i2i2−i200
χ3022-2-222-2-22-20002-2000i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000-22-22000000000000−i2i2−i2i200
χ3122-2-222-2-22-20002-2000i2i2−i2−i2-2-2220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002-2-22000000000000i2−i2−i2i200
χ3222-2-222-2-22-20002-2000i2i2−i2−i2-2-2220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000-222-2000000000000−i2i2i2−i200
χ3322-2-222-2-22-20002-2000−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002-22-2000000000000−i2i2−i2i200
χ3422-2-222-2-22-20002-2000−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000-22-22000000000000i2−i2i2−i200
χ3522-2-222-2-22-20002-2000−i2−i2i2i2-2-2220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002-2-22000000000000−i2i2i2−i200
χ3622-2-222-2-22-20002-2000−i2−i2i2i2-2-2220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000-222-2000000000000i2−i2−i2i200
χ372-2-222-22-2002-2200-2002-22-22−22−222−2−200002−22−22−22−22i−2i2i−2i000000000000i2−i2i2−i2000000
χ382-2-222-22-2002-2200-2002-22-22−22−222−2−200002−22−22−22−2−2i2i−2i2i000000000000−i2i2−i2i2000000
χ392-2-222-22-2002-2200-2002-22-2−22−22−2−2220000−22−22−22−222i−2i2i−2i000000000000−i2i2−i2i2000000
χ402-2-222-22-2002-2200-2002-22-2−22−22−2−2220000−22−22−22−22−2i2i−2i2i000000000000i2−i2i2−i2000000
χ412-2-222-22-2002-2200-200-22-222−22−222−2−20000−22−22−22−222i−2i−2i2i000000000000i2−i2−i2i2000000
χ422-2-222-22-2002-2200-200-22-222−22−222−2−20000−22−22−22−22−2i2i2i−2i000000000000−i2i2i2−i2000000
χ432-2-222-22-2002-2200-200-22-22−22−22−2−22200002−22−22−22−22i−2i−2i2i000000000000−i2i2i2−i2000000
χ442-2-222-22-2002-2200-200-22-22−22−22−2−22200002−22−22−22−2−2i2i2i−2i000000000000i2−i2−i2i2000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-444-4-44-4-444-400000000000000000000000000000000000000000000000000
χ474444-4-4-4-4-4-444-444-44-400000000000000000000000000000000000000000000000000
χ484444-4-4-4-4-4-4-4-44444-4400000000000000000000000000000000000000000000000000
χ4944-4-444-4-4-44000-440002i22i2−2i2−2i200000000−2i2−2i22i22i20000000000000000000000000000000000
χ5044-4-444-4-4-44000-44000−2i2−2i22i22i2000000002i22i2−2i2−2i20000000000000000000000000000000000
χ5144-4-4-4-4444-4000-4400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5244-4-4-4-4444-4000-440000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5344-4-4-4-444-440004-4000000000004i−4i4i−4i00000000000000000000000000000000000000
χ5444-4-4-4-444-440004-400000000000−4i4i−4i4i00000000000000000000000000000000000000
χ554-44-44-4-4400000000002i2−2i2−2i22i222−22−2222000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ564-44-44-4-4400000000002i2−2i2−2i22i2−222222−2200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ574-44-44-4-440000000000−2i22i22i2−2i222−22−222200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ584-44-44-4-440000000000−2i22i22i2−2i2−222222−22000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ594-44-4-444-40000000000000000002i2−2i2−2i22i222−2222−222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ604-44-4-444-40000000000000000002i2−2i2−2i22i2−2222−2222−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ614-44-4-444-4000000000000000000−2i22i22i2−2i222−2222−22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ624-44-4-444-4000000000000000000−2i22i22i2−2i2−2222−22222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ634-4-444-44-400-44-400400000022−2222−22−22−22222200000000000000000000000000000000000000
χ644-4-444-44-400-44-4004000000−2222−22222222−22−2200000000000000000000000000000000000000
χ654-4-44-44-44004-4-400400000000000000000022−2222−22−2222−222200000000000000000000000000
χ664-4-44-44-44004-4-4004000000000000000000−2222−222222−2222−2200000000000000000000000000
χ674-4-44-44-4400-44400-4000000000000004i−4i−4i4i0000000000000000000000000000000000
χ684-4-44-44-4400-44400-400000000000000−4i4i4i−4i0000000000000000000000000000000000

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