Finite Group Databasebeta

← Group #271913

Character table — Group #271913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222222244444444444444444448888888888888888888888161616161616161616323232
order12222244444422444444444444488882224448888888888888888444444888488
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
χ51111111111111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-11-11-1
χ61111111111111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-111-11-11
χ71111111111111111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-11-1-1-1-111-11
χ81111111111111111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11111-1-11-1
χ9111111111111-1-11-1-1-1-1111-1-111111111-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11
χ10111111111111-1-11-1-1-1-1111-1-111111111-1-11-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1
χ11111111111111-1-11-1-1-1-1111-1-1111-1-1-1-11-1-11-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111-1
χ12111111111111-1-11-1-1-1-1111-1-1111-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-11
χ13111111111111-1-11-1-1-1-1-1-11-1-1-1-111111-111-111-1-1-1-111111111-1-1-1-1-111-111-1-111-1-1
χ14111111111111-1-11-1-1-1-1-1-11-1-1-1-111111-111-111-1-1-1-11111-1-111-1-1-1-11-1-11-1-111-1-111
χ15111111111111-1-11-1-1-1-1-1-11-1-1-1-11-1-1-1-1-111-1111111-1-1-1-111-1-11111-111-1-1-1-1-11-111
χ16111111111111-1-11-1-1-1-1-1-11-1-1-1-11-1-1-1-1-111-1111111-1-1-1-1-1-1-1-111111-1-111111-11-1-1
χ172222222-222-2222-222-2-222-2-2-222-20000-2-2-2-2220000000000000000000000000000
χ182222222-222-2222-222-2-2-2-2-2-2-2-2-2-200002222-2-20000000000000000000000000000
χ192222222-222-22-2-2-2-2-22222-22222-20000-222-2-2-20000000000000000000000000000
χ202222222-222-22-2-2-2-2-222-2-2-222-2-2-200002-2-22220000000000000000000000000000
χ212222-2-2222-22-200-2000022-200-2-222222200-200-2-222000000-2-20000000000000000
χ222222-2-2222-22-200-2000022-200-2-22-2-2-2-2200-20022-2-2000000220000000000000000
χ232222-2-2222-22-200-20000-2-2-2002222222-20020022-2-2000000-2-20000000000000000
χ242222-2-2222-22-200-20000-2-2-200222-2-2-2-2-200200-2-222000000220000000000000000
χ252222-2-22-22-2-2-2002000022200-2-2-20000-20020000002i2i−2i−2i00002i2i−2i−2i000000000000
χ262222-2-22-22-2-2-2002000022200-2-2-20000-2002000000−2i−2i2i2i0000−2i−2i2i2i000000000000
χ272222-2-22-22-2-2-20020000-2-220022-20000200-20000002i2i−2i−2i0000−2i−2i2i2i000000000000
χ282222-2-22-22-2-2-20020000-2-220022-20000200-2000000−2i−2i2i2i00002i2i−2i−2i000000000000
χ292222-2-2-22-222222-2-2-222002-2-200-200000000000000000022000000-20020000-2000
χ302222-2-2-22-222222-2-2-222002-2-200-2000000000000000000-2-2000000200-200002000
χ312222-2-2-22-2222-2-2-222-2-20022200-200000000000000000022000000200-20000-2000
χ322222-2-2-22-2222-2-2-222-2-20022200-2000000000000000000-2-2000000-200200002000
χ332222-2-2-2-2-22-22222-2-2-2-200-2220020000000000000000000000000002-20002-20000
χ342222-2-2-2-2-22-22222-2-2-2-200-222002000000000000000000000000000-22000-220000
χ352222-2-2-2-2-22-22-2-22222200-2-2-20020000000000000000000000000002-2000-220000
χ362222-2-2-2-2-22-22-2-22222200-2-2-2002000000000000000000000000000-220002-20000
χ3722-2-22-2-202-202000002i−2i2i−2i02i−2i2i−2i0i2i2−i2−i202-20002−22−2i2−i2i2−i200i2−i22−22−2000000000000
χ3822-2-22-2-202-202000002i−2i2i−2i02i−2i2i−2i0−i2−i2i2i202-2000−22−22−i2i2−i2i200−i2i2−22−22000000000000
χ3922-2-22-2-202-202000002i−2i−2i2i02i−2i−2i2i0i2i2−i2−i20-22000−22−22−i2i2−i2i200i2−i22−22−2000000000000
χ4022-2-22-2-202-202000002i−2i−2i2i02i−2i−2i2i0−i2−i2i2i20-220002−22−2i2−i2i2−i200−i2i2−22−22000000000000
χ4122-2-22-2-202-20200000−2i2i2i−2i0−2i2i2i−2i0i2i2−i2−i20-220002−22−2−i2i2−i2i200i2−i2−22−22000000000000
χ4222-2-22-2-202-20200000−2i2i2i−2i0−2i2i2i−2i0−i2−i2i2i20-22000−22−22i2−i2i2−i200−i2i22−22−2000000000000
χ4322-2-22-2-202-20200000−2i2i−2i2i0−2i2i−2i2i0i2i2−i2−i202-2000−22−22i2−i2i2−i200i2−i2−22−22000000000000
χ4422-2-22-2-202-20200000−2i2i−2i2i0−2i2i−2i2i0−i2−i2i2i202-20002−22−2−i2i2−i2i200−i2i22−22−2000000000000
χ4522-2-2-22-20220-22-202-2002i−2i000−2i2i0i2i2−i2−i200002i−2i−222−22−2−2200−i2i2−i2i2i2−i2000000000000
χ4622-2-2-22-20220-22-202-2002i−2i000−2i2i0−i2−i2i2i200002i−2i2−2−22−222−200i2−i2i2−i2−i2i2000000000000
χ4722-2-2-22-20220-22-202-200−2i2i0002i−2i0i2i2−i2−i20000−2i2i2−2−22−222−200−i2i2−i2i2i2−i2000000000000
χ4822-2-2-22-20220-22-202-200−2i2i0002i−2i0−i2−i2i2i20000−2i2i−222−22−2−2200i2−i2i2−i2−i2i2000000000000
χ4922-2-2-22-20220-2-220-22002i−2i000−2i2i0i2i2−i2−i20000−2i2i−222−2−222−200−i2i2i2−i2−i2i2000000000000
χ5022-2-2-22-20220-2-220-22002i−2i000−2i2i0−i2−i2i2i20000−2i2i2−2−222−2−2200i2−i2−i2i2i2−i2000000000000
χ5122-2-2-22-20220-2-220-2200−2i2i0002i−2i0i2i2−i2−i200002i−2i2−2−222−2−2200−i2i2i2−i2−i2i2000000000000
χ5222-2-2-22-20220-2-220-2200−2i2i0002i−2i0−i2−i2i2i200002i−2i−222−2−222−200i2−i2−i2i2i2−i2000000000000
χ53444444-44-4-44-4004000000-40000-400000000000000000000000000000000000000
χ54444444-4-4-4-4-4-400-400000040000400000000000000000000000000000000000000
χ5544-4-44-440-440-44-40-44000000000000000000000000000000000000000000000000
χ5644-4-44-440-440-4-4404-4000000000000000000000000000000000000000000000000
χ5744-4-4-4440-4-404000004i−4i000−4i4i00000000000000000000000000000000000000000
χ5844-4-4-4440-4-40400000−4i4i0004i−4i00000000000000000000000000000000000000000
χ594-44-4000-4004000000000000000022−2222−22000000000000002i2−2i200000000002i−2i000000
χ604-44-4000-4004000000000000000022−2222−2200000000000000−2i22i20000000000−2i2i000000
χ614-44-4000-40040000000000000000−2222−2222000000000000002i2−2i20000000000−2i2i000000
χ624-44-4000-40040000000000000000−2222−222200000000000000−2i22i200000000002i−2i000000
χ638-88-8000800-8000000000000000000000000000000000000000000000000000000
χ648-8-88000000000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ658-8-8800000000000000000000000−4i4i4i−4i0000000000000000000000000000000000

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