Finite Group Databasebeta

← Group #289147

Character table — Group #289147

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order12222244444488884448888888888224488888888888888888888882444882488
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1
χ9111111111111-1-1-1-1111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11-11-11-1
χ10111111111111-1-1-1-1111-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-11-11-11
χ11111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-11-1-11-11
χ12111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-111-111-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1111-11-1-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-11-111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1111-1-111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-111-1-1-111-1-11
χ172222222-2-2-2-2222222-2-2-2-2-2-2222i2i−2i−2i00002i−2i0000000000002i2i−2i−2i00000000000000
χ182222222-2-2-2-2222222-2-2-2-2-2-222−2i−2i2i2i0000−2i2i000000000000−2i−2i2i2i00000000000000
χ192222222-2-2-2-22-2-2-2-22-2-22222-2-22i2i−2i−2i00002i−2i000000000000−2i−2i2i2i00000000000000
χ202222222-2-2-2-22-2-2-2-22-2-22222-2-2−2i−2i2i2i0000−2i2i0000000000002i2i−2i−2i00000000000000
χ21222222-22222-20000-2-2-2000000222222-2-2-2-2000022-2-20000000000000000000000
χ22222222-22222-20000-2-2-20000002222-2-222-2-20000-2-2220000000000000000000000
χ23222222-22222-20000-2-2-2000000-2-2-2-222-2-2220000-2-2220000000000000000000000
χ24222222-22222-20000-2-2-2000000-2-2-2-2-2-22222000022-2-20000000000000000000000
χ25222222-2-2-2-2-2-20000-2220000002i2i−2i−2i0000−2i2i2i2i−2i−2i00000000000022-2-20000000000
χ26222222-2-2-2-2-2-20000-2220000002i2i−2i−2i0000−2i2i−2i−2i2i2i000000000000-2-2220000000000
χ27222222-2-2-2-2-2-20000-222000000−2i−2i2i2i00002i−2i2i2i−2i−2i000000000000-2-2220000000000
χ28222222-2-2-2-2-2-20000-222000000−2i−2i2i2i00002i−2i−2i−2i2i2i00000000000022-2-20000000000
χ292222-2-2222-2-222222-22-222-2-2-2-20000000000000000002222000000000000-2-20000
χ302222-2-2222-2-222222-22-222-2-2-2-2000000000000000000-2-2-2-2000000000000220000
χ312222-2-2222-2-22-2-2-2-2-22-2-2-2222200000000000000000022-2-2000000000000-220000
χ322222-2-2222-2-22-2-2-2-2-22-2-2-22222000000000000000000-2-2220000000000002-20000
χ332222-2-22-2-22222222-2-22-2-222-2-20000000000000000000000000000002-2-22000000
χ342222-2-22-2-22222222-2-22-2-222-2-2000000000000000000000000000000-222-2000000
χ352222-2-22-2-2222-2-2-2-2-2-2222-2-2220000000000000000000000000000002-22-2000000
χ362222-2-22-2-2222-2-2-2-2-2-2222-2-222000000000000000000000000000000-22-22000000
χ3722-2-22-202-22-20i2i2−i2−i2000i2−i2i2−i2i2−i22-22-22-20000i2−i2i2−i22-2000000i2−i2i2−i2i2−i2i2−i20000000000
χ3822-2-22-202-22-20i2i2−i2−i2000i2−i2i2−i2i2−i22-22-2-220000−i2i2−i2i2-22000000i2−i2i2−i2−i2i2−i2i20000000000
χ3922-2-22-202-22-20i2i2−i2−i2000i2−i2i2−i2i2−i2-22-222-20000i2−i2i2−i2-22000000−i2i2−i2i2−i2i2−i2i20000000000
χ4022-2-22-202-22-20i2i2−i2−i2000i2−i2i2−i2i2−i2-22-22-220000−i2i2−i2i22-2000000−i2i2−i2i2i2−i2i2−i20000000000
χ4122-2-22-202-22-20−i2−i2i2i2000−i2i2−i2i2−i2i22-22-22-20000−i2i2−i2i22-2000000−i2i2−i2i2−i2i2−i2i20000000000
χ4222-2-22-202-22-20−i2−i2i2i2000−i2i2−i2i2−i2i22-22-2-220000i2−i2i2−i2-22000000−i2i2−i2i2i2−i2i2−i20000000000
χ4322-2-22-202-22-20−i2−i2i2i2000−i2i2−i2i2−i2i2-22-222-20000−i2i2−i2i2-22000000i2−i2i2−i2i2−i2i2−i20000000000
χ4422-2-22-202-22-20−i2−i2i2i2000−i2i2−i2i2−i2i2-22-22-220000i2−i2i2−i22-2000000i2−i2i2−i2−i2i2−i2i20000000000
χ4522-2-22-20-22-220i2i2−i2−i2000−i2i2−i2i2i2−i22i−2i−2i2i002i−2i002−2−22002-20000−222−2−i2i2i2−i20000000000
χ4622-2-22-20-22-220i2i2−i2−i2000−i2i2−i2i2i2−i22i−2i−2i2i00−2i2i00−222−200-220000−222−2i2−i2−i2i20000000000
χ4722-2-22-20-22-220i2i2−i2−i2000−i2i2−i2i2i2−i2−2i2i2i−2i002i−2i002−2−2200-2200002−2−22i2−i2−i2i20000000000
χ4822-2-22-20-22-220i2i2−i2−i2000−i2i2−i2i2i2−i2−2i2i2i−2i00−2i2i00−222−2002-200002−2−22−i2i2i2−i20000000000
χ4922-2-22-20-22-220−i2−i2i2i2000i2−i2i2−i2−i2i22i−2i−2i2i002i−2i00−222−2002-200002−2−22i2−i2−i2i20000000000
χ5022-2-22-20-22-220−i2−i2i2i2000i2−i2i2−i2−i2i22i−2i−2i2i00−2i2i002−2−2200-2200002−2−22−i2i2i2−i20000000000
χ5122-2-22-20-22-220−i2−i2i2i2000i2−i2i2−i2−i2i2−2i2i2i−2i002i−2i00−222−200-220000−222−2−i2i2i2−i20000000000
χ5222-2-22-20-22-220−i2−i2i2i2000i2−i2i2−i2−i2i2−2i2i2i−2i00−2i2i002−2−22002-20000−222−2i2−i2−i2i20000000000
χ534444-4-4-444-4-4-400004-440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-444-4000044-40000000000000000000000000000000000000000000000
χ5544-4-4-4404-4-4402i22i2−2i2−2i20002i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ5644-4-4-4404-4-440−2i2−2i22i22i2000−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ5744-4-4-440-444-402i22i2−2i2−2i2000−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ5844-4-4-440-444-40−2i2−2i22i22i20002i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ594-4-4400-4000044-44-400000000000000000000000000022−2222−22000000000000000000
χ604-4-4400-4000044-44-4000000000000000000000000000−2222−2222000000000000000000
χ614-4-4400-400004-44-4400000000000000000000000000022−22−2222000000000000000000
χ624-4-4400-400004-44-44000000000000000000000000000−222222−22000000000000000000
χ638-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000
χ648-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000
χ658-8-880080000-800000000000000000000000000000000000000000000000000000

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