Finite Group Databasebeta

← Group #289167

Character table — Group #289167

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order12222244444488884448888888888444488888888888888888888884444882288
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111
χ8111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1
χ9111111111111-1-1-1-1111-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-11-11-11-1
χ10111111111111-1-1-1-1111-1-11111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-11-11-11-11-11
χ11111111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111-11-11-1-11-11
χ12111111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-11-11-111-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-11-111-11-1-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-11-111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-11-111-1-111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-11-11-1-111-1-11
χ1722222222-2-2220000-2-2-2002222000022-2-2-2-20000-2-2220000000000000000000000
χ1822222222-2-2220000-2-2-20022220000-2-222220000-2-2-2-20000000000000000000000
χ1922222222-2-2220000-2-2-200-2-2-2-2000022-2-222000022-2-20000000000000000000000
χ2022222222-2-2220000-2-2-200-2-2-2-20000-2-222-2-2000022220000000000000000000000
χ21222222-2-222-2-222222-2-2222i2i−2i−2i-2-2-2-200000000002i−2i0000002i2i−2i−2i00000000000000
χ22222222-2-222-2-222222-2-222−2i−2i2i2i-2-2-2-20000000000−2i2i000000−2i−2i2i2i00000000000000
χ23222222-2-222-2-2-2-2-2-22-2-2-2-22i2i−2i−2i222200000000002i−2i000000−2i−2i2i2i00000000000000
χ24222222-2-222-2-2-2-2-2-22-2-2-2-2−2i−2i2i2i22220000000000−2i2i0000002i2i−2i−2i00000000000000
χ25222222-2-2-2-2-2-20000-222002i2i−2i−2i00000000002i2i−2i−2i−2i2i000000000022-2-20000000000
χ26222222-2-2-2-2-2-20000-222002i2i−2i−2i0000000000−2i−2i2i2i−2i2i0000000000-2-2220000000000
χ27222222-2-2-2-2-2-20000-22200−2i−2i2i2i00000000002i2i−2i−2i2i−2i0000000000-2-2220000000000
χ28222222-2-2-2-2-2-20000-22200−2i−2i2i2i0000000000−2i−2i2i2i2i−2i000000000022-2-20000000000
χ292222-2-22-2222-22222-22-2-2-2000022-2-2000000000000002222000000000000-2-20000
χ302222-2-22-2222-22222-22-2-2-2000022-2-200000000000000-2-2-2-2000000000000220000
χ312222-2-22-2222-2-2-2-2-2-22-2220000-2-2220000000000000022-2-2000000000000-220000
χ322222-2-22-2222-2-2-2-2-2-22-2220000-2-22200000000000000-2-2220000000000002-20000
χ332222-2-2-2222-222222-2-22-2-20000-2-2220000000000000000000000000022-2-2000000
χ342222-2-2-2222-222222-2-22-2-20000-2-22200000000000000000000000000-2-222000000
χ352222-2-2-2222-22-2-2-2-2-2-2222000022-2-2000000000000000000000000002-2-22000000
χ362222-2-2-2222-22-2-2-2-2-2-2222000022-2-200000000000000000000000000-222-2000000
χ3722-2-22-22-200-2222−2−20002−22-22-22−22−2002i−2i2i−2ii2−i2i2−i2000000002−22−2i2−i2i2−i20000000000
χ3822-2-22-22-200-2222−2−20002−22-22-22−22−200−2i2i−2i2i−i2i2−i2i2000000002−22−2−i2i2−i2i20000000000
χ3922-2-22-22-200-2222−2−20002−2-22-222−22−2002i−2i−2i2ii2−i2i2−i200000000−22−22−i2i2−i2i20000000000
χ4022-2-22-22-200-2222−2−20002−2-22-222−22−200−2i2i2i−2i−i2i2−i2i200000000−22−22i2−i2i2−i20000000000
χ4122-2-22-22-200-22−2−222000−222-22-2−22−22002i−2i2i−2i−i2i2−i2i200000000−22−22−i2i2−i2i20000000000
χ4222-2-22-22-200-22−2−222000−222-22-2−22−2200−2i2i−2i2ii2−i2i2−i200000000−22−22i2−i2i2−i20000000000
χ4322-2-22-22-200-22−2−222000−22-22-22−22−22002i−2i−2i2i−i2i2−i2i2000000002−22−2i2−i2i2−i20000000000
χ4422-2-22-22-200-22−2−222000−22-22-22−22−2200−2i2i2i−2ii2−i2i2−i2000000002−22−2−i2i2−i2i20000000000
χ4522-2-22-2-22002-222−2−20002−22i−2i−2i2i−22−222-200002−2−22002i−2i0000i2−i2−i2i2−i2i2i2−i20000000000
χ4622-2-22-2-22002-222−2−20002−22i−2i−2i2i−22−22-220000−222−200−2i2i0000i2−i2−i2i2i2−i2−i2i20000000000
χ4722-2-22-2-22002-222−2−20002−2−2i2i2i−2i−22−222-200002−2−2200−2i2i0000−i2i2i2−i2i2−i2−i2i20000000000
χ4822-2-22-2-22002-222−2−20002−2−2i2i2i−2i−22−22-220000−222−2002i−2i0000−i2i2i2−i2−i2i2i2−i20000000000
χ4922-2-22-2-22002-2−2−222000−222i−2i−2i2i2−22−22-20000−222−2002i−2i0000−i2i2i2−i2i2−i2−i2i20000000000
χ5022-2-22-2-22002-2−2−222000−222i−2i−2i2i2−22−2-2200002−2−2200−2i2i0000−i2i2i2−i2−i2i2i2−i20000000000
χ5122-2-22-2-22002-2−2−222000−22−2i2i2i−2i2−22−22-20000−222−200−2i2i0000i2−i2−i2i2−i2i2i2−i20000000000
χ5222-2-22-2-22002-2−2−222000−22−2i2i2i−2i2−22−2-2200002−2−22002i−2i0000i2−i2−i2i2i2−i2−i2i20000000000
χ534444-4-44-4-4-44-400004-440000000000000000000000000000000000000000000000
χ544444-4-4-44-4-4-44000044-40000000000000000000000000000000000000000000000
χ5544-4-4-444400-4-42222−22−22000−2222000022−22−2222000000000000000000000000000000000000
χ5644-4-4-444400-4-4−22−22222200022−220000−222222−22000000000000000000000000000000000000
χ5744-4-4-44-4-400442222−22−22000−22220000−222222−22000000000000000000000000000000000000
χ5844-4-4-44-4-40044−22−22222200022−22000022−22−2222000000000000000000000000000000000000
χ594-44-400004-4004-44-40000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ604-44-400004-4004-44-4000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ614-44-400004-400-44-440000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ624-44-400004-400-44-44000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ638-88-80000-880000000000000000000000000000000000000000000000000000000
χ648-8-880000000042−42−42420000000000000000000000000000000000000000000000000
χ658-8-8800000000−424242−420000000000000000000000000000000000000000000000000

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