Finite Group Databasebeta

← Group #242016

Character table — Group #242016

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888224444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-11-11-1-1-1-1-11-1-1-11-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-11-11-1-1-1-1-11-1-1-11-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-1-11-1111-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1111-111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ9111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-1-1111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-11-1-1-111-1-111
χ11111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111-1-111-1111-1-111-1-1-1-111
χ12111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-11111-1-11111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-111-1-111-11-1-1-1-1-1-11111-1-1
χ14111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-11-1-1-1-1111-1-1-11111-1-1-1-111
χ15111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111-111-1-1-1-111-11-1-111-1-111
χ16111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-111111-111-1-111-1-1
χ172222222222-2-2222222-2-2-2-222-2-2-2-200000000000000000020-2000002000-2000000000
χ182222222222-2-2222222-2-2-2-222-2-2-2-2000000000000000000-20200000-20002000000000
χ192222222222-2-2-2-2-2-222-2-222-2-222-2-200000000000000000020-200000-20002000000000
χ202222222222-2-2-2-2-2-222-2-222-2-222-2-2000000000000000000-202000002000-2000000000
χ2122222222-2-2222222-2-222-2-2-2-222-2-2000000000000000000020-2000002000-200000000
χ2222222222-2-2222222-2-222-2-2-2-222-2-20000000000000000000-20200000-2000200000000
χ2322222222-2-222-2-2-2-2-2-2222222-2-2-2-2000000000000000000020200000-2000-200000000
χ2422222222-2-222-2-2-2-2-2-2222222-2-2-2-20000000000000000000-20-2000002000200000000
χ2522222222-2-2-2-22222-2-2-2-222-2-2-2-22200000000000000000000002-22-200000000000000
χ2622222222-2-2-2-22222-2-2-2-222-2-2-2-2220000000000000000000000-22-2200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000002-2-2200000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000-222-200000000000000
χ292-22-222-2-22-22-22i2i−2i−2i2-22-22i−2i2i−2i2i−2i2-200000000000000002-200000000002i−2i0000000000
χ302-22-222-2-22-22-22i2i−2i−2i2-22-22i−2i2i−2i2i−2i2-20000000000000000-220000000000−2i2i0000000000
χ312-22-222-2-22-22-2−2i−2i2i2i2-22-2−2i2i−2i2i−2i2i2-200000000000000002-20000000000−2i2i0000000000
χ322-22-222-2-22-22-2−2i−2i2i2i2-22-2−2i2i−2i2i−2i2i2-20000000000000000-2200000000002i−2i0000000000
χ332-22-222-2-22-2-222i2i−2i−2i2-2-22−2i2i2i−2i−2i2i-220000000000000000000000000000000000002-22i−2i
χ342-22-222-2-22-2-222i2i−2i−2i2-2-22−2i2i2i−2i−2i2i-22000000000000000000000000000000000000-22−2i2i
χ352-22-222-2-22-2-22−2i−2i2i2i2-2-222i−2i−2i2i2i−2i-220000000000000000000000000000000000002-2−2i2i
χ362-22-222-2-22-2-22−2i−2i2i2i2-2-222i−2i−2i2i2i−2i-22000000000000000000000000000000000000-222i−2i
χ372-22-222-2-2-222-22i2i−2i−2i-222-2−2i2i−2i2i2i−2i-22000000000000000000000000000000002i−2i2-20000
χ382-22-222-2-2-222-22i2i−2i−2i-222-2−2i2i−2i2i2i−2i-2200000000000000000000000000000000−2i2i-220000
χ392-22-222-2-2-222-2−2i−2i2i2i-222-22i−2i2i−2i−2i2i-22000000000000000000000000000000002i−2i-220000
χ402-22-222-2-2-222-2−2i−2i2i2i-222-22i−2i2i−2i−2i2i-2200000000000000000000000000000000−2i2i2-20000
χ412-22-222-2-2-22-222i2i−2i−2i-22-222i−2i−2i2i−2i2i2-22222-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ422-22-222-2-2-22-222i2i−2i−2i-22-222i−2i−2i2i−2i2i2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ432-22-222-2-2-22-22−2i−2i2i2i-22-22−2i2i2i−2i2i−2i2-22222-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ442-22-222-2-2-22-22−2i−2i2i2i-22-22−2i2i2i−2i2i−2i2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ45444-4-4-44-444000000-4-40000000000000000002222−22−222222−22−22000000000000000000000000
χ46444-4-4-44-444000000-4-4000000000000000000−22−222222−22−222222000000000000000000000000
χ47444-4-4-44-4-4-40000004400000000002i22i2−2i2−2i22i22i2−2i2−2i200000000000000000000000000000000
χ48444-4-4-44-4-4-4000000440000000000−2i2−2i22i22i2−2i2−2i22i22i200000000000000000000000000000000
χ4944-44-44-4-40044000000-4-40000000022−2222−2222−2222−2200000000000000000000000000000000
χ5044-44-44-4-40044000000-4-400000000−2222−2222−2222−222200000000000000000000000000000000
χ5144-44-44-4-400-4-40000004400000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000
χ5244-44-44-4-400-4-4000000440000000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000
χ5344-4-44-4-4400004-44-40000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ5444-4-44-4-4400004-44-4000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5544-4-44-4-440000-44-440000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5644-4-44-4-440000-44-44000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ574-444-4-4-444-4000000-4400000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000
χ584-444-4-4-444-4000000-440000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000
χ594-444-4-4-44-440000004-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000
χ604-444-4-4-44-440000004-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000
χ614-4-444-44-400004i−4i−4i4i0000000000002i−2i−2i2i−2i2i2i−2i-222-22-2-22000000000000000000000000
χ624-4-444-44-400004i−4i−4i4i000000000000−2i2i2i−2i2i−2i−2i2i2-2-22-222-2000000000000000000000000
χ634-4-444-44-40000−4i4i4i−4i0000000000002i−2i−2i2i−2i2i2i−2i2-2-22-222-2000000000000000000000000
χ644-4-444-44-40000−4i4i4i−4i000000000000−2i2i2i−2i2i−2i−2i2i-222-22-2-22000000000000000000000000
χ654-4-4-4-4444004-4000000-44000000000000000022−2222−22−2222−2222000000000000000000000000
χ664-4-4-4-4444004-4000000-440000000000000000−2222−222222−2222−22000000000000000000000000
χ674-4-4-4-444400-440000004-40000000022−2222−22−2222−222200000000000000000000000000000000
χ684-4-4-4-444400-440000004-400000000−2222−222222−2222−2200000000000000000000000000000000

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