Finite Group Databasebeta

← Group #252657

Character table — Group #252657

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444444444444444888888888888888822244444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111-1-1111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111-1-111-1-1-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1111111
χ71111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ81111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-11111-1-1-1-1
χ9111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111-1-1111-1-111-1-1
χ10111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-111
χ11111111111111-1-1-1-11111-1-11111-1-111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-111
χ12111111111111-1-1-1-11111-1-11111-1-111-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-111-1-1-11111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1111-1-111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1-1-11111-1-1-1-11111-111111-1-1-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1111111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-111111111-1-1-1-1111-1-1-111-1-1-1-111
χ172222222222-2-2222222-2-2-2-2222222-2-200-2-2-200-2-222000000000000000000000000000000
χ182222222222-2-2222222-2-2-2-2-2-2-2-222-2-200-2220022-2-2000000000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2222222-2-2-2-20022200-2-2-2-2000000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2002-2-2002222000000000000000000000000000000
χ2122222222-2-2222222-2-222220000-2-2-2-222-2002200000000000000000000-20000-200000000
χ2222222222-2-2222222-2-222220000-2-2-2-2-2-2-200-2-20000000000000000000020000200000000
χ2322222222-2-222-2-2-2-2-2-222-2-2000022-2-222200-2-20000000000000000000020000-200000000
χ2422222222-2-222-2-2-2-2-2-222-2-2000022-2-2-2-22002200000000000000000000-20000200000000
χ2522222222-2-2-2-22222-2-2-2-2-2-20000-2-2220020000000000000000000000000002-202-2000000
χ2622222222-2-2-2-22222-2-2-2-2-2-20000-2-222002000000000000000000000000000-220-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-20000000000000000000000000002-20-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-2000000000000000000000000000-2202-2000000
χ292-2222-2-2-22-2002i2i−2i−2i2-2000022-2-22i−2i000000000002i−2i00000000i2i2−i2−i222−2−20000000000i2−i22−2
χ302-2222-2-2-22-2002i2i−2i−2i2-2000022-2-22i−2i000000000002i−2i00000000−i2−i2i2i2−2−2220000000000−i2i2−22
χ312-2222-2-2-22-2002i2i−2i−2i2-20000-2-2222i−2i00000000000−2i2i00000000i2i2−i2−i222−2−20000000000−i2i2−22
χ322-2222-2-2-22-2002i2i−2i−2i2-20000-2-2222i−2i00000000000−2i2i00000000−i2−i2i2i2−2−2220000000000i2−i22−2
χ332-2222-2-2-22-200−2i−2i2i2i2-2000022-2-2−2i2i00000000000−2i2i00000000i2i2−i2−i2−2−2220000000000i2−i2−22
χ342-2222-2-2-22-200−2i−2i2i2i2-2000022-2-2−2i2i00000000000−2i2i00000000−i2−i2i2i222−2−20000000000−i2i22−2
χ352-2222-2-2-22-200−2i−2i2i2i2-20000-2-222−2i2i000000000002i−2i00000000i2i2−i2−i2−2−2220000000000−i2i22−2
χ362-2222-2-2-22-200−2i−2i2i2i2-20000-2-222−2i2i000000000002i−2i00000000−i2−i2i2i222−2−20000000000i2−i2−22
χ372-22-2-222-200222-22-200-2-22-2000000002i−2i0002i−2i000022−2−222−2−2i2−i2i2−i2i2−i2i2−i200000000000000
χ382-22-2-222-200222-22-200-2-22-2000000002i−2i0002i−2i0000−2−222−2−222−i2i2−i2i2−i2i2−i2i200000000000000
χ392-22-2-222-200222-22-200-2-22-200000000−2i2i000−2i2i000022−2−222−2−2−i2i2−i2i2−i2i2−i2i200000000000000
χ402-22-2-222-200222-22-200-2-22-200000000−2i2i000−2i2i0000−2−222−2−222i2−i2i2−i2i2−i2i2−i200000000000000
χ412-22-2-222-20022-22-2200-2-2-22000000002i−2i000−2i2i000022−2−2−2−222i2−i2i2−i2−i2i2−i2i200000000000000
χ422-22-2-222-20022-22-2200-2-2-22000000002i−2i000−2i2i0000−2−22222−2−2−i2i2−i2i2i2−i2i2−i200000000000000
χ432-22-2-222-20022-22-2200-2-2-2200000000−2i2i0002i−2i000022−2−2−2−222−i2i2−i2i2i2−i2i2−i200000000000000
χ442-22-2-222-20022-22-2200-2-2-2200000000−2i2i0002i−2i0000−2−22222−2−2i2−i2i2−i2−i2i2−i2i200000000000000
χ452-2-22-22-22222-20000-2-22-2002i−2i2i−2i002-200000002i−2i0000002i−2i2i−2i00000000000000002-20000
χ462-2-22-22-22222-20000-2-22-2002i−2i2i−2i002-200000002i−2i000000−2i2i−2i2i0000000000000000-220000
χ472-2-22-22-22222-20000-2-22-200−2i2i−2i2i002-20000000−2i2i0000002i−2i2i−2i0000000000000000-220000
χ482-2-22-22-22222-20000-2-22-200−2i2i−2i2i002-20000000−2i2i000000−2i2i−2i2i00000000000000002-20000
χ492-2-22-22-2222-220000-2-2-22002i−2i2i−2i00-220000000−2i2i002i−2i2i−2i00000000000002-200000000000
χ502-2-22-22-2222-220000-2-2-22002i−2i2i−2i00-220000000−2i2i00−2i2i−2i2i0000000000000-2200000000000
χ512-2-22-22-2222-220000-2-2-2200−2i2i−2i2i00-2200000002i−2i002i−2i2i−2i0000000000000-2200000000000
χ522-2-22-22-2222-220000-2-2-2200−2i2i−2i2i00-2200000002i−2i00−2i2i−2i2i00000000000002-200000000000
χ53444-4-4-4-4400004i−4i−4i4i0000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ54444-4-4-4-4400004i−4i−4i4i000000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ55444-4-4-4-440000−4i4i4i−4i0000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ56444-4-4-4-440000−4i4i4i−4i000000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ5744-44-4-44-44-4000000-4400004i−4i−4i4i000000000000000000000000000000000000000000000
χ5844-44-4-44-44-4000000-440000−4i4i4i−4i000000000000000000000000000000000000000000000
χ5944-44-4-44-4-440000004-40000000000000004i−4i000000000000000000000000000000000000
χ6044-44-4-44-4-440000004-4000000000000000−4i4i000000000000000000000000000000000000
χ6144-4-444-4-4004-4000000-4400000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ6244-4-444-4-4004-4000000-440000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ6344-4-444-4-400-440000004-40000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ6444-4-444-4-400-440000004-4000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ654-4444-4-4-4-44004i4i−4i−4i-4400000000−4i4i0000000000000000000000000000000000000000000
χ664-4444-4-4-4-4400−4i−4i4i4i-44000000004i−4i0000000000000000000000000000000000000000000
χ674-44-4-444-400-4-44-44-40044-440000000000000000000000000000000000000000000000000
χ684-44-4-444-400-4-4-44-4400444-40000000000000000000000000000000000000000000000000
χ694-4-44-44-44-4-44-40000444-400000000-4400000000000000000000000000000000000000000
χ704-4-44-44-44-4-4-44000044-44000000004-400000000000000000000000000000000000000000
χ718-8-8-88-888000000000000000000000000000000000000000000000000000000000000000

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