Finite Group Databasebeta

← Group #285708

Character table — Group #285708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444888888888888888822444444488888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ9111111111-1-1-1-11111111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111-1
χ10111111111-1-1-1-11111111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ11111111111-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111-11
χ12111111111-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-11-1
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-1-111111111111111-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-11
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-1-111111111111111-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-11111-1-11-1
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111111111-1-1-1-111-11
χ172222222222222-2-2-2222-2-2-2-2-222000000000000000022-2-2-222-2-200000000000000000000000000
χ182222222222222-2-2-2222-2-2-2-2-2220000000000000000-2-2-222-2-22200000000000000000000000000
χ19222222222-2-2-2-2-2-2-2222-222-2-2-2-20000000000000000222-2-2-2-22200000000000000000000000000
χ20222222222-2-2-2-2-2-2-2222-222-2-2-2-20000000000000000-2-222222-2-200000000000000000000000000
χ2122222222-22222222-2-2-2222-2-2-2-2222222220000000000-2000000-2-2-2-20000000000000000000000
χ2222222222-22222222-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-20000000000-200000022220000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i0020000000000000000002i2i−2i−2i0000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i002000000000000000000−2i−2i2i2i0000000000
χ2522222222-2-2-2-2-2222-2-2-22-2-2-2-2222222-2-2-2-200000000002000000-2-2220000000000000000000000
χ2622222222-2-2-2-2-2222-2-2-22-2-2-2-222-2-2-2-222220000000000200000022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i00-2000000000000000000−2i−2i2i2i0000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i00-20000000000000000002i2i−2i−2i0000000000
χ292-222-22-2-2200002-2-22-2-22002-2000000000022-2-222-2-2000000000000000002i2i−2i−2i0000002i−2i000000
χ302-222-22-2-2200002-2-22-2-22002-2000000000022-2-222-2-200000000000000000−2i−2i2i2i000000−2i2i000000
χ312-222-22-2-2200002-2-22-2-22002-20000000000-2-222-2-222000000000000000002i2i−2i−2i000000−2i2i000000
χ322-222-22-2-2200002-2-22-2-22002-20000000000-2-222-2-22200000000000000000−2i−2i2i2i0000002i−2i000000
χ332-222-22-2-2-20000-222-222-2002-200000000002i2i−2i−2i−2i−2i2i2i000000000000022-2-2000000002i−2i00000000
χ342-222-22-2-2-20000-222-222-2002-200000000002i2i−2i−2i−2i−2i2i2i0000000000000-2-22200000000−2i2i00000000
χ352-222-22-2-2-20000-222-222-2002-20000000000−2i−2i2i2i2i2i−2i−2i000000000000022-2-200000000−2i2i00000000
χ362-222-22-2-2-20000-222-222-2002-20000000000−2i−2i2i2i2i2i−2i−2i0000000000000-2-222000000002i−2i00000000
χ372-22-22-22-222i2i−2i−2i000-2-22000002i−2ii2i2−i2−i222−2−22−22−22−22−22-20002i−2i00i2−i22−200000000i2−i2i2−i20000000000
χ382-22-22-22-222i2i−2i−2i000-2-22000002i−2ii2i2−i2−i222−2−2−22−22−22−22-22000−2i2i00i2−i22−200000000−i2i2−i2i20000000000
χ392-22-22-22-222i2i−2i−2i000-2-22000002i−2i−i2−i2i2i2−2−2222−22−22−22−2-22000−2i2i00−i2i2−2200000000i2−i2i2−i20000000000
χ402-22-22-22-222i2i−2i−2i000-2-22000002i−2i−i2−i2i2i2−2−222−22−22−22−222-20002i−2i00−i2i2−2200000000−i2i2−i2i20000000000
χ412-22-22-22-22−2i−2i2i2i000-2-2200000−2i2ii2i2−i2−i2−2−2222−22−22−22−2-220002i−2i00i2−i2−2200000000−i2i2−i2i20000000000
χ422-22-22-22-22−2i−2i2i2i000-2-2200000−2i2ii2i2−i2−i2−2−222−22−22−22−222-2000−2i2i00i2−i2−2200000000i2−i2i2−i20000000000
χ432-22-22-22-22−2i−2i2i2i000-2-2200000−2i2i−i2−i2i2i222−2−22−22−22−22−22-2000−2i2i00−i2i22−200000000−i2i2−i2i20000000000
χ442-22-22-22-22−2i−2i2i2i000-2-2200000−2i2i−i2−i2i2i222−2−2−22−22−22−22-220002i−2i00−i2i22−200000000i2−i2i2−i20000000000
χ452-22-22-22-2-22i2i−2i−2i00022-200000−2i2ii2i2−i2−i222−2−2i2−i2i2−i2−i2i2−i2i20002i−2i002-2−i2i2−2200000000−222−20000000000
χ462-22-22-22-2-22i2i−2i−2i00022-200000−2i2ii2i2−i2−i222−2−2−i2i2−i2i2i2−i2i2−i2000−2i2i00-22−i2i2−22000000002−2−220000000000
χ472-22-22-22-2-22i2i−2i−2i00022-200000−2i2i−i2−i2i2i2−2−222i2−i2i2−i2−i2i2−i2i2000−2i2i00-22i2−i22−200000000−222−20000000000
χ482-22-22-22-2-22i2i−2i−2i00022-200000−2i2i−i2−i2i2i2−2−222−i2i2−i2i2i2−i2i2−i20002i−2i002-2i2−i22−2000000002−2−220000000000
χ492-22-22-22-2-2−2i−2i2i2i00022-2000002i−2ii2i2−i2−i2−2−222i2−i2i2−i2−i2i2−i2i2000−2i2i002-2−i2i22−2000000002−2−220000000000
χ502-22-22-22-2-2−2i−2i2i2i00022-2000002i−2ii2i2−i2−i2−2−222−i2i2−i2i2i2−i2i2−i20002i−2i00-22−i2i22−200000000−222−20000000000
χ512-22-22-22-2-2−2i−2i2i2i00022-2000002i−2i−i2−i2i2i222−2−2i2−i2i2−i2−i2i2−i2i20002i−2i00-22i2−i2−22000000002−2−220000000000
χ522-22-22-22-2-2−2i−2i2i2i00022-2000002i−2i−i2−i2i2i222−2−2−i2i2−i2i2i2−i2i2−i2000−2i2i002-2i2−i2−2200000000−222−20000000000
χ532-2-22-2-22202-22-222-2000-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000i2−i2i2−i2i2−i2i2−i2000000002−22−200
χ542-2-22-2-22202-22-222-2000-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000−i2i2−i2i2−i2i2−i2i200000000−22−2200
χ552-2-22-2-22202-22-222-2000-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000i2−i2i2−i2i2−i2i2−i200000000−22−2200
χ562-2-22-2-22202-22-222-2000-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000−i2i2−i2i2−i2i2−i2i2000000002−22−200
χ572-2-22-2-2220-22-2222-2000-2-2200002i−2i2i−2i−2i2i−2i2i000000000000000000000i2−i2i2−i2−i2i2−i2i200000000−222−200
χ582-2-22-2-2220-22-2222-2000-2-2200002i−2i2i−2i−2i2i−2i2i000000000000000000000−i2i2−i2i2i2−i2i2−i2000000002−2−2200
χ592-2-22-2-2220-22-2222-2000-2-220000−2i2i−2i2i2i−2i2i−2i000000000000000000000i2−i2i2−i2−i2i2−i2i2000000002−2−2200
χ602-2-22-2-2220-22-2222-2000-2-220000−2i2i−2i2i2i−2i2i−2i000000000000000000000−i2i2−i2i2i2−i2i2−i200000000−222−200
χ61444-4-4-4-4440000000-44-400000000000000022−22−222222−22−222200000000000000000000000000000000000
χ62444-4-4-4-4440000000-44-4000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ63444-4-4-4-44-400000004-440000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ64444-4-4-4-44-400000004-44000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ6544-444-4-4-4000004-44000-400000000000000000000000000000000000000022−22−222200000000000000
χ6644-444-4-4-4000004-44000-4000000000000000000000000000000000000000−222222−2200000000000000
χ6744-444-4-4-400000-44-40004000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ6844-444-4-4-400000-44-4000400000000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ6944-4-4-444-404i−4i−4i4i000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000000
χ7044-4-4-444-404i−4i−4i4i0000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000000
χ7144-4-4-444-40−4i4i4i−4i000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000000
χ7244-4-4-444-40−4i4i4i−4i0000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000000
χ734-444-44-4-440000-4444-4-4-400-4400000000000000000000000000000000000000000000000000000
χ744-444-44-4-4-400004-4-4-444400-4400000000000000000000000000000000000000000000000000000
χ754-4-44-4-44404-44-4-4-440004-440000000000000000000000000000000000000000000000000000000
χ764-4-44-4-4440-44-44-4-4400044-40000000000000000000000000000000000000000000000000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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