Finite Group Databasebeta

← Group #433301

Character table — Group #433301

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222222444444888888882244444444448888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-11111
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-111-1-111-1-1-1-1
χ172222222222-2-2-2-2-2-2-22-220000222200002i2i−2i−2i0000000000-2-20000002i−2i000000000000
χ182222222222-2-2-2-2-2-2-22-22000022220000−2i−2i2i2i0000000000-2-2000000−2i2i000000000000
χ192222222222-2-2-2-2-2-2-22-220000-2-2-2-200002i2i−2i−2i000000000022000000−2i2i000000000000
χ202222222222-2-2-2-2-2-2-22-220000-2-2-2-20000−2i−2i2i2i0000000000220000002i−2i000000000000
χ2122222222-2-222-2-22-2-2-22-2222200000000000000000000-2-2002i2i−2i−2i000000000000002i−2i
χ2222222222-2-222-2-22-2-2-22-2222200000000000000000000-2-200−2i−2i2i2i00000000000000−2i2i
χ2322222222-2-222-2-22-2-2-22-2-2-2-2-20000000000000000000022002i2i−2i−2i00000000000000−2i2i
χ2422222222-2-222-2-22-2-2-22-2-2-2-2-2000000000000000000002200−2i−2i2i2i000000000000002i−2i
χ252222-2-2-2-222-2-2-2-2222-22-222-2-2000022-2-20000000000002-20000002-200000000000000
χ262222-2-2-2-222-2-2-2-2222-22-222-2-20000-2-2220000000000002-2000000-2200000000000000
χ272222-2-2-2-222-2-2-2-2222-22-2-2-222000022-2-2000000000000-22000000-2200000000000000
χ282222-2-2-2-222-2-2-2-2222-22-2-2-2220000-2-222000000000000-220000002-200000000000000
χ292222-2-2-2-2-2-222-2-2-2222-22000022-2-20000000000002i2i−2i−2i002-200000000000000002i−2i00
χ302222-2-2-2-2-2-222-2-2-2222-22000022-2-2000000000000−2i−2i2i2i002-20000000000000000−2i2i00
χ312222-2-2-2-2-2-222-2-2-2222-220000-2-2220000000000002i2i−2i−2i00-220000000000000000−2i2i00
χ322222-2-2-2-2-2-222-2-2-2222-220000-2-222000000000000−2i−2i2i2i00-2200000000000000002i−2i00
χ332222-2-2-2-2-2-2-2-2222-2-222222-2-222-2-20000000022-2-20000-22-2200000000000000000000
χ342222-2-2-2-2-2-2-2-2222-2-222222-2-2-2-22200000000-2-2220000-222-200000000000000000000
χ352222-2-2-2-2-2-2-2-2222-2-2222-2-22222-2-200000000-2-22200002-2-2200000000000000000000
χ362222-2-2-2-2-2-2-2-2222-2-2222-2-222-2-2220000000022-2-200002-22-200000000000000000000
χ372-2-2222-2-22-22-22-2-22-2-222000000002-22-2000000002i−2i2i−2i00000000000000002i−2i000000
χ382-2-2222-2-22-22-22-2-22-2-222000000002-22-200000000−2i2i−2i2i0000000000000000−2i2i000000
χ392-2-2222-2-22-22-22-2-22-2-22200000000-22-22000000002i−2i2i−2i0000000000000000−2i2i000000
χ402-2-2222-2-22-22-22-2-22-2-22200000000-22-2200000000−2i2i−2i2i00000000000000002i−2i000000
χ412-2-22-2-2222-22-22-22-222-2-20000000000002i−2i2i−2i0000000000002i−2i2i−2i00002-20000000000
χ422-2-22-2-2222-22-22-22-222-2-20000000000002i−2i2i−2i000000000000−2i2i−2i2i0000-220000000000
χ432-2-22-2-2222-22-22-22-222-2-2000000000000−2i2i−2i2i0000000000002i−2i2i−2i0000-220000000000
χ442-2-22-2-2222-22-22-22-222-2-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i00002-20000000000
χ452-2-22-2-2222-2-22-22-22-222-2000000002-2-222-2-2200000000000000000000002-200000000
χ462-2-22-2-2222-2-22-22-22-222-2000000002-2-22-222-20000000000000000000000-2200000000
χ472-2-22-2-2222-2-22-22-22-222-200000000-222-22-2-220000000000000000000000-2200000000
χ482-2-22-2-2222-2-22-22-22-222-200000000-222-2-222-200000000000000000000002-200000000
χ492-2-22-2-222-222-2-2222-2-2-22000000000000000000002-2-2200002-2-2200000000002-20000
χ502-2-22-2-222-222-2-2222-2-2-22000000000000000000002-2-220000-222-20000000000-220000
χ512-2-22-2-222-222-2-2222-2-2-2200000000000000000000-222-200002-2-220000000000-220000
χ522-2-22-2-222-222-2-2222-2-2-2200000000000000000000-222-20000-222-200000000002-20000
χ5344444444-4-4-4-444-444-4-4-4000000000000000000000000000000000000000000000000
χ544444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ5544-4-44i−4i4i−4i00000000000022−222i2−2i22i2−2i222−22000000002i−2i2-20000000000000000000000000000
χ5644-4-44i−4i4i−4i00000000000022−222i2−2i2−2i22i2−222200000000−2i2i-220000000000000000000000000000
χ5744-4-44i−4i4i−4i000000000000−2222−2i22i22i2−2i222−2200000000−2i2i-220000000000000000000000000000
χ5844-4-44i−4i4i−4i000000000000−2222−2i22i2−2i22i2−2222000000002i−2i2-20000000000000000000000000000
χ5944-4-4−4i4i−4i4i00000000000022−22−2i22i22i2−2i2−2222000000002i−2i-220000000000000000000000000000
χ6044-4-4−4i4i−4i4i00000000000022−22−2i22i2−2i22i222−2200000000−2i2i2-20000000000000000000000000000
χ6144-4-4−4i4i−4i4i000000000000−22222i2−2i22i2−2i2−222200000000−2i2i2-20000000000000000000000000000
χ6244-4-4−4i4i−4i4i000000000000−22222i2−2i2−2i22i222−22000000002i−2i-220000000000000000000000000000
χ634-4-4444-4-44-4-44-444-44-4-44000000000000000000000000000000000000000000000000
χ644-4-4444-4-4-444-4-44-4-4444-4000000000000000000000000000000000000000000000000
χ654-4-4444-4-4-44-444-444-44-4-4000000000000000000000000000000000000000000000000
χ664-4-44-4-444-44-444-4-4-44-444000000000000000000000000000000000000000000000000
χ678-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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