Finite Group Databasebeta

← Group #271925

Character table — Group #271925

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222222244444444444444444448888888888888888888888161616161616161616323232
order12222244444422444444444444488882444448888888888888888224444888488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1-1
χ4111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ51111111111111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-1
χ61111111111111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-11-11
χ71111111111111111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-11
χ81111111111111111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11-1
χ9111111111111-1-1-1-11-1-1111-1-1111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11
χ10111111111111-1-1-1-11-1-1111-1-1111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1
χ11111111111111-1-1-1-11-1-1111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111-1
χ12111111111111-1-1-1-11-1-1111-1-1111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-11
χ13111111111111-1-1-1-11-1-1-1-11-1-1-1-111111-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1
χ14111111111111-1-1-1-11-1-1-1-11-1-1-1-111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-111
χ15111111111111-1-1-1-11-1-1-1-11-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-1-11-111
χ16111111111111-1-1-1-11-1-1-1-11-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-11-1-1
χ172222222-222-222222-2-2-222-2-2-222-20000-2-2-2-2220000000000000000000000000000
χ182222222-222-222222-2-2-2-2-2-2-2-2-2-2-200002222-2-20000000000000000000000000000
χ192222222-222-22-2-2-2-2-22222-22222-20000-2-222-2-20000000000000000000000000000
χ202222222-222-22-2-2-2-2-222-2-2-222-2-2-2000022-2-2220000000000000000000000000000
χ212222-2-2222-22-20000-20022-200-2-222222-220000-2-222000000-2-20000000000000000
χ222222-2-2222-22-20000-20022-200-2-22-2-2-2-2-22000022-2-2000000220000000000000000
χ232222-2-2222-22-20000-200-2-2-20022222222-2000022-2-2000000-2-20000000000000000
χ242222-2-2222-22-20000-200-2-2-200222-2-2-2-22-20000-2-222000000220000000000000000
χ252222-2-22-22-2-2-2000020022200-2-2-200002-2000000002i2i−2i−2i00002i2i−2i−2i000000000000
χ262222-2-22-22-2-2-2000020022200-2-2-200002-200000000−2i−2i2i2i0000−2i−2i2i2i000000000000
χ272222-2-22-22-2-2-20000200-2-220022-20000-22000000002i2i−2i−2i0000−2i−2i2i2i000000000000
χ282222-2-22-22-2-2-20000200-2-220022-20000-2200000000−2i−2i2i2i00002i2i−2i−2i000000000000
χ292222-2-2-22-222222-2-22-2-200-22200-200000000000000000022000000002-20000-2000
χ302222-2-2-22-222222-2-22-2-200-22200-2000000000000000000-2-200000000-2200002000
χ312222-2-2-22-2222-2-22222200-2-2-200-20000000000000000002200000000-220000-2000
χ322222-2-2-22-2222-2-22222200-2-2-200-2000000000000000000-2-2000000002-200002000
χ332222-2-2-2-2-22-2222-2-2-222002-2-2002000000000000000000000000002-200002-20000
χ342222-2-2-2-2-22-2222-2-2-222002-2-200200000000000000000000000000-220000-220000
χ352222-2-2-2-2-22-22-2-222-2-2-200222002000000000000000000000000002-20000-220000
χ362222-2-2-2-2-22-22-2-222-2-2-20022200200000000000000000000000000-2200002-20000
χ3722-2-22-2-202-202000002i−2i2i−2i02i−2i2i−2i0i2i2−i2−i2002-2002−22−2i2−i2i2−i200i2−i22−22−2000000000000
χ3822-2-22-2-202-202000002i−2i2i−2i02i−2i2i−2i0−i2−i2i2i2002-200−22−22−i2i2−i2i200−i2i2−22−22000000000000
χ3922-2-22-2-202-202000002i−2i−2i2i02i−2i−2i2i0i2i2−i2−i200-2200−22−22−i2i2−i2i200i2−i22−22−2000000000000
χ4022-2-22-2-202-202000002i−2i−2i2i02i−2i−2i2i0−i2−i2i2i200-22002−22−2i2−i2i2−i200−i2i2−22−22000000000000
χ4122-2-22-2-202-20200000−2i2i2i−2i0−2i2i2i−2i0i2i2−i2−i200-22002−22−2−i2i2−i2i200i2−i2−22−22000000000000
χ4222-2-22-2-202-20200000−2i2i2i−2i0−2i2i2i−2i0−i2−i2i2i200-2200−22−22i2−i2i2−i200−i2i22−22−2000000000000
χ4322-2-22-2-202-20200000−2i2i−2i2i0−2i2i−2i2i0i2i2−i2−i2002-200−22−22i2−i2i2−i200i2−i2−22−22000000000000
χ4422-2-22-2-202-20200000−2i2i−2i2i0−2i2i−2i2i0−i2−i2i2i2002-2002−22−2−i2i2−i2i200−i2i22−22−2000000000000
χ4522-2-2-22-20220-22-22-20002i−2i000−2i2i0i2i2−i2−i200002i−2i−222−22−2−2200−i2i2−i2i2i2−i2000000000000
χ4622-2-2-22-20220-22-22-20002i−2i000−2i2i0−i2−i2i2i200002i−2i2−2−22−222−200i2−i2i2−i2−i2i2000000000000
χ4722-2-2-22-20220-22-22-2000−2i2i0002i−2i0i2i2−i2−i20000−2i2i2−2−22−222−200−i2i2−i2i2i2−i2000000000000
χ4822-2-2-22-20220-22-22-2000−2i2i0002i−2i0−i2−i2i2i20000−2i2i−222−22−2−2200i2−i2i2−i2−i2i2000000000000
χ4922-2-2-22-20220-2-22-220002i−2i000−2i2i0i2i2−i2−i20000−2i2i−222−2−222−200−i2i2i2−i2−i2i2000000000000
χ5022-2-2-22-20220-2-22-220002i−2i000−2i2i0−i2−i2i2i20000−2i2i2−2−222−2−2200i2−i2−i2i2i2−i2000000000000
χ5122-2-2-22-20220-2-22-22000−2i2i0002i−2i0i2i2−i2−i200002i−2i2−2−222−2−2200−i2i2i2−i2−i2i2000000000000
χ5222-2-2-22-20220-2-22-22000−2i2i0002i−2i0−i2−i2i2i200002i−2i−222−2−222−200i2−i2−i2i2i2−i2000000000000
χ53444444-44-4-44-40000-4000040000-400000000000000000000000000000000000000
χ54444444-4-4-4-4-4-4000040000-40000400000000000000000000000000000000000000
χ5544-4-44-440-440-44-4-440000000000000000000000000000000000000000000000000
χ5644-4-44-440-440-4-444-40000000000000000000000000000000000000000000000000
χ5744-4-4-4440-4-404000004i−4i000−4i4i00000000000000000000000000000000000000000
χ5844-4-4-4440-4-40400000−4i4i0004i−4i00000000000000000000000000000000000000000
χ594-4-44000400-4000000000000000022−2222−22000000000000002i2−2i200000000002i−2i000000
χ604-4-44000400-4000000000000000022−2222−2200000000000000−2i22i20000000000−2i2i000000
χ614-4-44000400-40000000000000000−2222−2222000000000000002i2−2i20000000000−2i2i000000
χ624-4-44000400-40000000000000000−2222−222200000000000000−2i22i200000000002i−2i000000
χ638-88-8000000000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ648-88-800000000000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ658-8-88000-8008000000000000000000000000000000000000000000000000000000

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