Finite Group Databasebeta

← Group #235162

Character table — Group #235162

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
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
χ91111111-1-1-1-1-1-1-1-1111-1-11111-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1111-1-1-11-111-1-1
χ101111111-1-1-1-1-1-1-1-1111-1-11111-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-1-1111-11-1-111
χ111111111-1-1-1-1-1-1-1-1111-1-11111-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-11-1-1-11-1-111
χ121111111-1-1-1-1-1-1-1-1111-1-11111-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-11-1111-111-1-1
χ131111111-1-1-1-1-1-1-1-1111-1-11111-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-11-1111-1-1-111
χ141111111-1-1-1-1-1-1-1-1111-1-11111-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1111-11-1-1-1111-1-1
χ151111111-1-1-1-1-1-1-1-1111-1-11111-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-1-1111-1111-1-1
χ161111111-1-1-1-1-1-1-1-1111-1-11111-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11111-1-1-11-1-1-111
χ17222222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ192222222-2-2-2-2-2-2-2-222222-2-2-2-2222-222-2-2-2-22200000000000000000000000000000000
χ202222222-2-2-2-2-2-2-2-222222-2-2-2-2222-2-2-22222-2-200000000000000000000000000000000
χ21222222-22222-2-2-2-2-2-2-22222-2-22-2-220000000000000000000000000000002-200-220000
χ22222222-22222-2-2-2-2-2-2-22222-2-22-2-22000000000000000000000000000000-22002-20000
χ23222222-22222-2-2-2-2-2-2-2-2-2-2-222-222-20000000000000000000000000000000000002i−2i2i−2i
χ24222222-22222-2-2-2-2-2-2-2-2-2-2-222-222-2000000000000000000000000000000000000−2i2i−2i2i
χ25222222-2-2-2-2-22222-2-2-222-2-2222-2-2-20000000000000000000000000000000000002i−2i−2i2i
χ26222222-2-2-2-2-22222-2-2-222-2-2222-2-2-2000000000000000000000000000000000000−2i2i2i−2i
χ27222222-2-2-2-2-22222-2-2-2-2-222-2-2-22220000000000000000000000000000002200-2-20000
χ28222222-2-2-2-2-22222-2-2-2-2-222-2-2-2222000000000000000000000000000000-2-200220000
χ292222-2-2222-2-222-2-2-2-2222222-2-22-2-20000000022-2-222-2-2000000000000000000000000
χ302222-2-2222-2-222-2-2-2-2222222-2-22-2-200000000-2-222-2-222000000000000000000000000
χ312222-2-2222-2-222-2-2-2-22-2-2-2-2-222-222000000000000000022-2-222-2-20000000000000000
χ322222-2-2222-2-222-2-2-2-22-2-2-2-2-222-2220000000000000000-2-222-2-2220000000000000000
χ332222-2-22-2-222-2-222-2-2222-2-2-22-22-22000000000000000022-2-2-2-2220000000000000000
χ342222-2-22-2-222-2-222-2-2222-2-2-22-22-220000000000000000-2-22222-2-20000000000000000
χ352222-2-22-2-222-2-222-2-22-2-2222-22-22-20000000022-2-2-2-222000000000000000000000000
χ362222-2-22-2-222-2-222-2-22-2-2222-22-22-200000000-2-22222-2-2000000000000000000000000
χ372222-2-2-222-2-2-2-22222-22222-22-2-22-20000000000000000000000002-2-22000000000000
χ382222-2-2-222-2-2-2-22222-22222-22-2-22-2000000000000000000000000-222-2000000000000
χ392222-2-2-222-2-2-2-22222-2-2-2-2-22-222-2200000000000000000000000000002-2002-2000000
χ402222-2-2-222-2-2-2-22222-2-2-2-2-22-222-220000000000000000000000000000-2200-22000000
χ412222-2-2-2-2-22222-2-222-222-2-22-2-2-22200000000000000000000000000002-200-22000000
χ422222-2-2-2-2-22222-2-222-222-2-22-2-2-2220000000000000000000000000000-22002-2000000
χ432222-2-2-2-2-22222-2-222-2-2-222-2222-2-200000000000000000000000022-2-2000000000000
χ442222-2-2-2-2-22222-2-222-2-2-222-2222-2-2000000000000000000000000-2-222000000000000
χ4522-2-22-2-22-22-22-22-22-220000000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ4622-2-22-2-22-22-22-22-22-220000000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ4722-2-22-2-22-22-22-22-22-22000000000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ4822-2-22-2-22-22-22-22-22-22000000000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ4922-2-22-2-2-22-22-22-222-220000000000002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ5022-2-22-2-2-22-22-22-222-220000000000002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ5122-2-22-2-2-22-22-22-222-22000000000000−2i2i002i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ5222-2-22-2-2-22-22-22-222-22000000000000−2i2i002i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ5322-2-2-22-22-2-222-2-22-22200000000002i−2i002i−2i00i2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000000000
χ5422-2-2-22-22-2-222-2-22-22200000000002i−2i002i−2i00−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000000000
χ5522-2-2-22-22-2-222-2-22-2220000000000−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000000000
χ5622-2-2-22-22-2-222-2-22-2220000000000−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000000000
χ5722-2-2-22-2-222-2-222-2-22200000000002i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i22−2−22−222−20000000000000000
χ5822-2-2-22-2-222-2-222-2-22200000000002i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i2−222−22−2−220000000000000000
χ5922-2-2-22-2-222-2-222-2-2220000000000−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i2−222−22−2−220000000000000000
χ6022-2-2-22-2-222-2-222-2-2220000000000−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i22−2−22−222−20000000000000000
χ6144-4-44-444-44-4-44-44-44-400000000000000000000000000000000000000000000000000
χ6244-4-44-44-44-444-44-4-44-400000000000000000000000000000000000000000000000000
χ6344-4-4-4444-4-44-444-44-4-400000000000000000000000000000000000000000000000000
χ6444-4-4-444-444-44-4-444-4-400000000000000000000000000000000000000000000000000
χ658-88-8000000000000008i−8i000000000000000000000000000000000000000000000000
χ668-88-800000000000000−8i8i000000000000000000000000000000000000000000000000
χ678-8-8800000000000000008-80000000000000000000000000000000000000000000000
χ688-8-880000000000000000-880000000000000000000000000000000000000000000000

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