Finite Group Databasebeta

← Group #478575

Character table — Group #478575

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111111111111122222222888888888888888888888888888816161616161616161616161616161616
order12222222222222224444444444444444444488888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ21222-22-2-2-2-22222-2-2-22-2-2-2222-20000000000000000000000002i2i−2i−2i0000002i−2i2-2000000
χ22222-22-2-2-2-22222-2-2-22-2-2-2222-20000000000000000000000002i2i−2i−2i000000−2i2i-22000000
χ23222-22-2-2-2-22222-2-2-22-2-2-2222-2000000000000000000000000−2i−2i2i2i0000002i−2i-22000000
χ24222-22-2-2-2-22222-2-2-22-2-2-2222-2000000000000000000000000−2i−2i2i2i000000−2i2i2-2000000
χ2522-2-2222-2-22-2-2-2-222222-22-2-2-2000000000000000000002i2i−2i−2i00002i−2i00000000002-200
χ2622-2-2222-2-22-2-2-2-222222-22-2-2-2000000000000000000002i2i−2i−2i0000−2i2i0000000000-2200
χ2722-2-2222-2-22-2-2-2-222222-22-2-2-200000000000000000000−2i−2i2i2i00002i−2i0000000000-2200
χ2822-2-2222-2-22-2-2-2-222222-22-2-2-200000000000000000000−2i−2i2i2i0000−2i2i00000000002-200
χ292-22-22-2-222-22-2-2-22222-22-22-2-20000000000002i2i−2i−2i000000000000002i−2i0000002-20000
χ302-22-22-2-222-22-2-2-22222-22-22-2-20000000000002i2i−2i−2i00000000000000−2i2i000000-220000
χ312-22-22-2-222-22-2-2-22222-22-22-2-2000000000000−2i−2i2i2i000000000000002i−2i000000-220000
χ322-22-22-2-222-22-2-2-22222-22-22-2-2000000000000−2i−2i2i2i00000000000000−2i2i0000002-20000
χ332-22-2-22-22-22-22-222-200000000002-22i−2i00002i−2ii2−i2i2−i2i2i2−i2−i22−22−22−22−20000000000000000
χ342-22-2-22-22-22-22-222-200000000002-22i−2i00002i−2i−i2i2−i2i2−i2−i2i2i2−22−22−22−220000000000000000
χ352-22-2-22-22-22-22-222-200000000002-2−2i2i0000−2i2ii2−i2i2−i2i2i2−i2−i2−22−22−22−220000000000000000
χ362-22-2-22-22-22-22-222-200000000002-2−2i2i0000−2i2i−i2i2−i2i2−i2−i2i2i22−22−22−22−20000000000000000
χ372-22-2-22-22-22-22-222-20000000000-222i−2i0000−2i2ii2−i2i2−i2−i2−i2i2i22−22−2−22−220000000000000000
χ382-22-2-22-22-22-22-222-20000000000-222i−2i0000−2i2i−i2i2−i2i2i2i2−i2−i2−22−222−22−20000000000000000
χ392-22-2-22-22-22-22-222-20000000000-22−2i2i00002i−2ii2−i2i2−i2−i2−i2i2i2−22−222−22−20000000000000000
χ402-22-2-22-22-22-22-222-20000000000-22−2i2i00002i−2i−i2i2−i2i2i2i2−i2−i22−22−2−22−220000000000000000
χ412-2-2-222222-2-222-2-2-2-22-2-222-2200000000000000002-22-20000000000002i−2i000000002i−2i
χ422-2-2-222222-2-222-2-2-2-22-2-222-2200000000000000002-22-2000000000000−2i2i00000000−2i2i
χ432-2-2-222222-2-222-2-2-2-22-2-222-220000000000000000-22-220000000000002i−2i00000000−2i2i
χ442-2-2-222222-2-222-2-2-2-22-2-222-220000000000000000-22-22000000000000−2i2i000000002i−2i
χ454444-4-444-4-4-4-44-44-40000000000000000000022−22−22220000000000000000000000000000
χ464444-4-444-4-4-4-44-44-400000000000000000000−222222−220000000000000000000000000000
χ47444-44-4-4-4-44444-4-4-4-4444-4-4-4400000000000000000000000000000000000000000000
χ48444-4-44-4-44-4-4-444-4400000000000000004i−4i0000000000000000000000000000000000
χ49444-4-44-4-44-4-4-444-440000000000000000−4i4i0000000000000000000000000000000000
χ5044-444-4-4444-4-4-44-4-44-4-444-4-4400000000000000000000000000000000000000000000
χ5144-444-4-4444-4-4-44-4-4-444-4-444-400000000000000000000000000000000000000000000
χ5244-44-44-44-4-444-4-4-440000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ5344-44-44-44-4-444-4-4-44000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ5444-4-4444-4-44-4-4-4-444-4-4-44-444400000000000000000000000000000000000000000000
χ5544-4-4-4-44-44-444-444-4000000000000004i−4i000000000000000000000000000000000000
χ5644-4-4-4-44-44-444-444-400000000000000−4i4i000000000000000000000000000000000000
χ574-444444-4-4-44-4-44-4-44-44-4-44-4400000000000000000000000000000000000000000000
χ584-444444-4-4-44-4-44-4-4-44-444-44-400000000000000000000000000000000000000000000
χ594-444-4-44-444-44-4-4-44000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ604-444-4-44-444-44-4-4-4400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ614-44-44-4-444-44-4-4-444-4-44-44-44400000000000000000000000000000000000000000000
χ624-4-444-4-4-4-4-4-44444444-4-4-4-44400000000000000000000000000000000000000000000
χ634-4-444-4-4-4-4-4-444444-4-44444-4-400000000000000000000000000000000000000000000
χ644-4-44-44-4-4444-44-44-400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ654-4-44-44-4-4444-44-44-40000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ664-4-4-444444-4-444-4-4-44-444-4-44-400000000000000000000000000000000000000000000
χ674-4-4-4-4-444-444-444-44000000004-4000000000000000000000000000000000000000000
χ684-4-4-4-4-444-444-444-4400000000-44000000000000000000000000000000000000000000

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