Finite Group Databasebeta

← Group #118426

Character table — Group #118426

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222224444444444444444448888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ91111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iii−i−iii
χ111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1-1-111ii−i−i−i−iii
χ121111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-11111-1-1−i−iiiii−i−i
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1-1-111−i−iiiii−i−i
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-11111-1-1ii−i−i−i−iii
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii−i−iii
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−iii−i−i
χ17222222222222222-2-2-222-22-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ18222222222222222-2-2-222-22-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-2-2-2-2-2222-2-22-2-2-2-222-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ202222222222-2-2-2-2-2222-2-22-2-2-2-222-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ21222222-2-2-2-22222-222-2-2-2-2-222-22-2-20000000000000000000000002-22-2000000000000
χ22222222-2-2-2-22222-222-2-2-2-2-222-22-2-2000000000000000000000000-22-22000000000000
χ23222222-2-2-2-22222-2-2-22-2-22-2-2-22-222000000000000000000000000000000002i−2i2i−2i0000
χ24222222-2-2-2-22222-2-2-22-2-22-2-2-22-22200000000000000000000000000000000−2i2i−2i2i0000
χ25222222-2-2-2-2-2-2-2-2222-222-22-2-222-22000000000000000000000000000000002-2-220000
χ26222222-2-2-2-2-2-2-2-2222-222-22-2-222-2200000000000000000000000000000000-222-20000
χ27222222-2-2-2-2-2-2-2-22-2-22222222-2-22-20000000000000000000000002-2-22000000000000
χ28222222-2-2-2-2-2-2-2-22-2-22222222-2-22-2000000000000000000000000-222-2000000000000
χ292222-2-222-2-222-2-22222-2-2222-2-2-2-220000000000000000000000000000000000002-22-2
χ302222-2-222-2-222-2-22222-2-2222-2-2-2-22000000000000000000000000000000000000-22-22
χ312222-2-222-2-222-2-22-2-2-2-2-2-22-22222-200000000000000000000000000002i−2i2i−2i00000000
χ322222-2-222-2-222-2-22-2-2-2-2-2-22-22222-20000000000000000000000000000−2i2i−2i2i00000000
χ332222-2-222-2-2-2-222-2222222-2-222-2-2-200000000000000000000000000002i−2i−2i2i00000000
χ342222-2-222-2-2-2-222-2222222-2-222-2-2-20000000000000000000000000000−2i2i2i−2i00000000
χ352222-2-222-2-2-2-222-2-2-2-222-2-22-2-22220000000000000000000000000000000000002i−2i−2i2i
χ362222-2-222-2-2-2-222-2-2-2-222-2-22-2-2222000000000000000000000000000000000000−2i2i2i−2i
χ372222-2-2-2-22222-2-2-222-222-2-22-22-22-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382222-2-2-2-22222-2-2-222-222-2-22-22-22-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ392222-2-2-2-22222-2-2-2-2-22222-2-22-22-22000000000000000022-2-222-2-20000000000000000
χ402222-2-2-2-22222-2-2-2-2-22222-2-22-22-220000000000000000-2-222-2-2220000000000000000
χ412222-2-2-2-222-2-222222-2-2-2-22-22-2-222000000000000000022-2-2-2-2220000000000000000
χ422222-2-2-2-222-2-222222-2-2-2-22-22-2-2220000000000000000-2-22222-2-20000000000000000
χ432222-2-2-2-222-2-2222-2-22-2-2222-222-2-20000000022-2-2-2-222000000000000000000000000
χ442222-2-2-2-222-2-2222-2-22-2-2222-222-2-200000000-2-22222-2-2000000000000000000000000
χ4522-2-22-22-22-22-22-220002-20-2000000002-2002-22−22−22−22−22−22−22−22−20000000000000000
χ4622-2-22-22-22-22-22-220002-20-2000000002-2002-2−22−22−22−22−22−22−22−220000000000000000
χ4722-2-22-22-22-22-22-220002-20-200000000-2200-222−22−22−22−2−22−22−22−220000000000000000
χ4822-2-22-22-22-22-22-220002-20-200000000-2200-22−22−22−22−222−22−22−22−20000000000000000
χ4922-2-22-22-22-2-22-22-2000-2202000000002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ5022-2-22-22-22-2-22-22-2000-2202000000002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ5122-2-22-22-22-2-22-22-2000-220200000000−2i2i002i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ5222-2-22-22-22-2-22-22-2000-220200000000−2i2i002i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ5322-2-2-22-222-22-2-22-20002-2020000002i−2i002i−2i00i2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000000000
χ5422-2-2-22-222-22-2-22-20002-2020000002i−2i002i−2i00−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000000000
χ5522-2-2-22-222-22-2-22-20002-202000000−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000000000
χ5622-2-2-22-222-22-2-22-20002-202000000−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000000000
χ5722-2-2-22-222-2-222-22000-220-20000002-200-22002−2−22−222−22−2−22−222−20000000000000000
χ5822-2-2-22-222-2-222-22000-220-20000002-200-2200−222−22−2−22−222−22−2−220000000000000000
χ5922-2-2-22-222-2-222-22000-220-2000000-22002-2002−2−22−222−2−222−22−2−220000000000000000
χ6022-2-2-22-222-2-222-22000-220-2000000-22002-200−222−22−2−222−2−22−222−20000000000000000
χ6144-4-44-4-44-444-44-4-4000-44040000000000000000000000000000000000000000000000
χ6244-4-44-4-44-44-44-4440004-40-40000000000000000000000000000000000000000000000
χ6344-4-4-444-4-444-4-444000-440-40000000000000000000000000000000000000000000000
χ6444-4-4-444-4-44-444-4-40004-4040000000000000000000000000000000000000000000000
χ658-88-80000000000000800-800000000000000000000000000000000000000000000000
χ668-88-80000000000000-800800000000000000000000000000000000000000000000000
χ678-8-88000000000008i−8i000000000000000000000000000000000000000000000000000
χ688-8-8800000000000−8i8i000000000000000000000000000000000000000000000000000

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