Finite Group Databasebeta

← Group #119684

Character table — Group #119684

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222224444444444444444442244444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ911111-1-11-1-111111-1-1-1-1-1-11111-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-1
χ1011111-1-11-1-111111-1-1-1-1-1-11111-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-111
χ1111111-1-11-1-111111-1-1-1-1-1-11111-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111
χ1211111-1-11-1-111111-1-1-1-1-1-11111-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1
χ1311111-1-11-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111
χ1411111-1-11-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1
χ1511111-1-11-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-11111-1-1
χ1611111-1-11-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111
χ172222222222222-2-22222-2-22-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ182222222222222-2-22222-2-22-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-22-2-22-2200000000000000000000000000002-22-200000000
χ202222222222-2-2-222-2-2-2-2-2-2-22-2-22-220000000000000000000000000000-22-2200000000
χ212222222222-2-2-2-2-2-2-2-2-222-2-222-22-20000000000000000000000002-22-2000000000000
χ222222222222-2-2-2-2-2-2-2-2-222-2-222-22-2000000000000000000000000-22-22000000000000
χ2322222-2-22-2-2222-2-2-2-2-2-2222-2-2-222222-2-2-2-22200000000000000000000000000000000
χ2422222-2-22-2-2222-2-2-2-2-2-2222-2-2-2222-2-22222-2-200000000000000000000000000000000
χ2522222-2-22-2-2-2-2-222222222-22-2-2-22-200000000000000000000000000002i−2i−2i2i00000000
χ2622222-2-22-2-2-2-2-222222222-22-2-2-22-20000000000000000000000000000−2i2i2i−2i00000000
χ2722222-2-22-2-2-2-2-2-2-22222-2-2-2-2222-220000000000000000000000002i−2i−2i2i000000000000
χ2822222-2-22-2-2-2-2-2-2-22222-2-2-2-2222-22000000000000000000000000−2i2i2i−2i000000000000
χ292222-22-2-22-222-22222-2-222-2-22-22-2-20000000000000000000000000000000000002i−2i2i−2i
χ302222-22-2-22-222-22222-2-222-2-22-22-2-2000000000000000000000000000000000000−2i2i−2i2i
χ312222-22-2-22-222-2-2-222-2-2-2-2-22-22-222000000000000000000000000000000002i−2i2i−2i0000
χ322222-22-2-22-222-2-2-222-2-2-2-2-22-22-22200000000000000000000000000000000−2i2i−2i2i0000
χ332222-22-2-22-2-2-2222-2-222-2-22-2-2222-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ342222-22-2-22-2-2-2222-2-222-2-22-2-2222-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ352222-22-2-22-2-2-22-2-2-2-22222222-2-2-22000000000000000022-2-222-2-20000000000000000
χ362222-22-2-22-2-2-22-2-2-2-22222222-2-2-220000000000000000-2-222-2-2220000000000000000
χ372222-2-22-2-2222-222-2-222-2-2-2-22-2-2220000000000000000000000000000000000002i−2i−2i2i
χ382222-2-22-2-2222-222-2-222-2-2-2-22-2-222000000000000000000000000000000000000−2i2i2i−2i
χ392222-2-22-2-2222-2-2-2-2-22222-22-222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ402222-2-22-2-2222-2-2-2-2-22222-22-222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ412222-2-22-2-22-2-222222-2-2222-2-22-2-220000000022-2-2-2-222000000000000000000000000
χ422222-2-22-2-22-2-222222-2-2222-2-22-2-2200000000-2-22222-2-2000000000000000000000000
χ432222-2-22-2-22-2-22-2-222-2-2-2-2222-222-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ442222-2-22-2-22-2-22-2-222-2-2-2-2222-222-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ4522-2-2222-2-2-22-22002-22-200-20000002-2002-2002−22−22−22−22−22−22−22−20000000000000000
χ4622-2-2222-2-2-22-22002-22-200-20000002-2002-200−22−22−22−22−22−22−22−220000000000000000
χ4722-2-2222-2-2-22-22002-22-200-2000000-2200-22002−22−22−22−2−22−22−22−220000000000000000
χ4822-2-2222-2-2-22-22002-22-200-2000000-2200-2200−22−22−22−222−22−22−22−20000000000000000
χ4922-2-22-2-2-2222-2200-22-2200-20000002-200-2200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ5022-2-22-2-2-2222-2200-22-2200-20000002-200-2200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ5122-2-22-2-2-2222-2200-22-2200-2000000-22002-200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ5222-2-22-2-2-2222-2200-22-2200-2000000-22002-200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ5322-2-2-22-22-22-22200-222-200-2000000002i−2i002i−2ii2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000000000
χ5422-2-2-22-22-22-22200-222-200-2000000002i−2i002i−2i−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000000000
χ5522-2-2-22-22-22-22200-222-200-200000000−2i2i00−2i2ii2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000000000
χ5622-2-2-22-22-22-22200-222-200-200000000−2i2i00−2i2i−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000000000
χ5722-2-2-2-2222-2-222002-2-2200-2000000002i−2i00−2i2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ5822-2-2-2-2222-2-222002-2-2200-2000000002i−2i00−2i2i−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ5922-2-2-2-2222-2-222002-2-2200-200000000−2i2i002i−2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ6022-2-2-2-2222-2-222002-2-2200-200000000−2i2i002i−2i−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ6144-4-4444-4-4-4-44-400-44-440040000000000000000000000000000000000000000000000
χ6244-4-44-4-4-444-44-4004-44-40040000000000000000000000000000000000000000000000
χ6344-4-4-44-44-444-4-4004-4-440040000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-44-4-400-444-40040000000000000000000000000000000000000000000000
χ658-88-80000000000000008i−8i00000000000000000000000000000000000000000000000
χ668-88-8000000000000000−8i8i00000000000000000000000000000000000000000000000
χ678-8-880000000008i−8i00000000000000000000000000000000000000000000000000000
χ688-8-88000000000−8i8i00000000000000000000000000000000000000000000000000000

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