Finite Group Databasebeta

← Group #240125

Character table — Group #240125

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444442444448888888888888888222444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-11-1-1-1-1111-1-11111-11-1-1-1111111111-1-1-1-1-1-1-1-11-111-11-1-111-1-111-1-111-1-111-1-1
χ10111111-1-11-1-1-1-1111-1-11111-11-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-111-11-1-11111-1-1-1-111-1-111
χ11111111-1-11-1-1-1-1111-1-11111-11-1-1-1111111111-1-1-1-1-1-1-1-1-1111-1-11-111-1-1-1-111-1-111-1-111
χ12111111-1-11-1-1-1-1111-1-11111-11-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-11-111-1-111-1-11111-1-111-1-1
χ13111111-1-11-1-1-1-1111-1-11111-11-1-1-11-1-1-1-1-1-1-1-1111111111-111-11-1-1-1-111-1-11111-1-1-1-111
χ14111111-1-11-1-1-1-1111-1-11111-11-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-111-1111-1-1-1-111-1-11111-1-1
χ15111111-1-11-1-1-1-1111-1-11111-11-1-1-11-1-1-1-1-1-1-1-111111111-1111-1-11-1-1-11111-1-1-1-11111-1-1
χ16111111-1-11-1-1-1-1111-1-11111-11-1-1-11-1-1-1-1-1-1-1-111111111-11-1-11-11111-1-111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-222-222-22-2-2-200000000000000002-2000-2200000000000000000
χ1822222222222-2-2-2-2-2-2-222-222-22-2-2-20000000000000000-220002-200000000000000000
χ1922222222-2-2-222-2-2-2-2-2-2-2-2-222-22-220000000000000000000000000000000000002i−2i2i−2i
χ2022222222-2-2-222-2-2-2-2-2-2-2-2-222-22-22000000000000000000000000000000000000−2i2i−2i2i
χ2122222222-2-2-2-2-222222-2-22-22-2-2-22-20000000000000000000000002i−2i2i−2i000000000000
χ2222222222-2-2-2-2-222222-2-22-22-2-2-22-2000000000000000000000000−2i2i−2i2i000000000000
χ23222222-2-22-2-222-2-2-22222-22-2-2-222-2000000000000000022000-2-200000000000000000
χ24222222-2-22-2-222-2-2-22222-22-2-2-222-20000000000000000-2-20002200000000000000000
χ25222222-2-2-22222222-2-2-2-22-2-2-222-2-20000000000000000000000002i−2i−2i2i000000000000
χ26222222-2-2-22222222-2-2-2-22-2-2-222-2-2000000000000000000000000−2i2i2i−2i000000000000
χ27222222-2-2-222-2-2-2-2-222-2-2-2-2-222-2220000000000000000000000000000000000002i−2i−2i2i
χ28222222-2-2-222-2-2-2-2-222-2-2-2-2-222-222000000000000000000000000000000000000−2i2i2i−2i
χ292222-2-2222222222-2-2-2-2-2-22-2-2-2-222000000000000000000000000000000002-22-20000
χ302222-2-2222222222-2-2-2-2-2-22-2-2-2-22200000000000000000000000000000000-22-220000
χ312222-2-222222-2-2-2-2222-2-222-22-22-2-20000000000000000002-2-20020000000000000000
χ322222-2-222222-2-2-2-2222-2-222-22-22-2-2000000000000000000-22200-20000000000000000
χ332222-2-222-2-2-222-2-2222222-2-2-22-2-222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ342222-2-222-2-2-222-2-2222222-2-2-22-2-22-2-2-2-22222-2-2-2-22222000000000000000000000000
χ352222-2-222-2-2-2-2-222-2-2-222-2-2-22222-200000000000000000000000000002i−2i2i−2i00000000
χ362222-2-222-2-2-2-2-222-2-2-222-2-2-22222-20000000000000000000000000000−2i2i−2i2i00000000
χ372222-2-2-2-22-2-222-2-22-2-2-2-222222-22-20000000000000000002-2200-20000000000000000
χ382222-2-2-2-22-2-222-2-22-2-2-2-222222-22-2000000000000000000-22-20020000000000000000
χ392222-2-2-2-22-2-2-2-222-222-2-2-222-222-22000000000000000000000000000000002-2-220000
χ402222-2-2-2-22-2-2-2-222-222-2-2-222-222-2200000000000000000000000000000000-222-20000
χ412222-2-2-2-2-2222222-22222-2-222-2-2-2-200000000000000000000000000002i−2i−2i2i00000000
χ422222-2-2-2-2-2222222-22222-2-222-2-2-2-20000000000000000000000000000−2i2i2i−2i00000000
χ432222-2-2-2-2-222-2-2-2-22-2-2222-22-2-22222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ442222-2-2-2-2-222-2-2-2-22-2-2222-22-2-2222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ4544-4-4000004i−4i4-44i−4i000000000000022-2-22i2i−2i−2i22-2-22i2i−2i−2i000000000000000000000000
χ4644-4-4000004i−4i4-44i−4i0000000000000-2-222−2i−2i2i2i-2-222−2i−2i2i2i000000000000000000000000
χ4744-4-4000004i−4i-44−4i4i000000000000022-2-2−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000
χ4844-4-4000004i−4i-44−4i4i0000000000000-2-2222i2i−2i−2i22-2-2−2i−2i2i2i000000000000000000000000
χ4944-4-400000−4i4i4-4−4i4i000000000000022-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000000000000000000000
χ5044-4-400000−4i4i4-4−4i4i0000000000000-2-2222i2i−2i−2i-2-2222i2i−2i−2i000000000000000000000000
χ5144-4-400000−4i4i-444i−4i000000000000022-2-22i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000
χ5244-4-400000−4i4i-444i−4i0000000000000-2-222−2i−2i2i2i22-2-22i2i−2i−2i000000000000000000000000
χ534-44-44-40040000000004-40-40000000000000022−2222−2222−2222−22000000000000000000000000
χ544-44-44-40040000000004-40-400000000000000−2222−2222−2222−2222000000000000000000000000
χ554-44-44-400-4000000000-440400000022−2222−2222−2222−2200000000000000000000000000000000
χ564-44-44-400-4000000000-4404000000−2222−2222−2222−222200000000000000000000000000000000
χ574-44-4-44004000000000-440-400000022−2222−22−2222−222200000000000000000000000000000000
χ584-44-4-44004000000000-440-4000000−2222−222222−2222−2200000000000000000000000000000000
χ594-44-4-4400-40000000004-4040000000000000022−2222−22−2222−2222000000000000000000000000
χ604-44-4-4400-40000000004-40400000000000000−2222−222222−2222−22000000000000000000000000
χ614-4-44004-4000000044-400-4000000000002i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000
χ624-4-44004-4000000044-400-400000000000−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000
χ634-4-44004-40000000-4-44004000000022−22−22220000−222222−220000000000000000000000000000
χ644-4-44004-40000000-4-440040000000−222222−22000022−22−22220000000000000000000000000000
χ654-4-4400-4400000004-4400-4000000000002i2−2i2−2i22i20000−2i22i22i2−2i2000000000000000000000000
χ664-4-4400-4400000004-4400-400000000000−2i22i22i2−2i200002i2−2i2−2i22i2000000000000000000000000
χ674-4-4400-440000000-44-4004000000022−22−2222000022−22−22220000000000000000000000000000
χ684-4-4400-440000000-44-40040000000−222222−220000−222222−220000000000000000000000000000

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