Finite Group Databasebeta

← Group #122608

Character table — Group #122608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222224444442444448888888844888816161616161616161616161616161616888888882444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ61111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ91111-1-1111-1-1-1-11-1111-1-11111-1-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-1111-1-1-1-11-1111-1-11111-1-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-1111-1-1-1-11-1111-1-11111-1-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-1111-1-1-1-11-1111-1-11111-1-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-1111-1-1-1-11-11-1-111-1-1-1-111111-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111-1-1111-1-1-1-11-11-1-111-1-1-1-111111-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111-1-1111-1-1-1-11-11-1-111-1-1-1-111111-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ161111-1-1111-1-1-1-11-11-1-111-1-1-1-111111-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-222222222-2-2-2-2-2-20000000000000000000000000000
χ1922222222-2-2-2-2-2-22-222-2-2000000002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2022222222-2-2-2-2-2-22-222-2-2000000002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2122222222-2-2-2-2-2-22-2-2-22200000000-22000022−2−222−2−2−2−222−2−222000000000000
χ2222222222-2-2-2-2-2-22-2-2-22200000000-220000−2−222−2−22222−2−222−2−2000000000000
χ23222222-2-2-222-2-2-2-2200002i2i−2i−2i2i2i−2i−2i00000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ24222222-2-2-222-2-2-2-2200002i2i−2i−2i2i2i−2i−2i0000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ25222222-2-2-222-2-2-2-220000−2i−2i2i2i−2i−2i2i2i00000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ26222222-2-2-222-2-2-2-220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ272222-2-2222-2-2-2-22-2222-2-2-2-2-2-22222-22-2-2220000000000000000000000000000
χ282222-2-2222-2-2-2-22-22-2-2222222-2-2-2-22-2-2-2220000000000000000000000000000
χ292222-2-222-22222-2-2-2222200000000-2-2000022−2−2−2−22222−2−2−2−222000000000000
χ302222-2-222-22222-2-2-2222200000000-2-20000−2−22222−2−2−2−22222−2−2000000000000
χ312222-2-222-22222-2-2-2-2-2-2-200000000220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ322222-2-222-22222-2-2-2-2-2-2-200000000220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ332222-2-2-2-2-2-2-222-22200002i2i−2i−2i−2i−2i2i2i00000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ342222-2-2-2-2-2-2-222-22200002i2i−2i−2i−2i−2i2i2i0000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ352222-2-2-2-2-2-2-222-2220000−2i−2i2i2i2i2i−2i−2i00000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ362222-2-2-2-2-2-2-222-2220000−2i−2i2i2i2i2i−2i−2i0000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ3722-2-2002-202i−2i2i−2i0002-22i−2i2−22−2i2−i2i2−i2002−2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ3822-2-2002-202i−2i2i−2i0002-22i−2i2−22−2i2−i2i2−i2002−2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ3922-2-2002-202i−2i2i−2i0002-22i−2i−22−22−i2i2−i2i200−22−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3000000000000
χ4022-2-2002-202i−2i2i−2i0002-22i−2i−22−22−i2i2−i2i200−22−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3000000000000
χ4122-2-2002-202i−2i2i−2i000-22−2i2i2−22−2i2−i2i2−i200−22−i2i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ4222-2-2002-202i−2i2i−2i000-22−2i2i2−22−2i2−i2i2−i200−22−i2i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ4322-2-2002-202i−2i2i−2i000-22−2i2i−22−22−i2i2−i2i2002−2i2−i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3000000000000
χ4422-2-2002-202i−2i2i−2i000-22−2i2i−22−22−i2i2−i2i2002−2i2−i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3000000000000
χ4522-2-2002-20−2i2i−2i2i0002-2−2i2i2−22−2−i2i2−i2i2002−2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3000000000000
χ4622-2-2002-20−2i2i−2i2i0002-2−2i2i2−22−2−i2i2−i2i2002−2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3000000000000
χ4722-2-2002-20−2i2i−2i2i0002-2−2i2i−22−22i2−i2i2−i200−22i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ4822-2-2002-20−2i2i−2i2i0002-2−2i2i−22−22i2−i2i2−i200−22i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ4922-2-2002-20−2i2i−2i2i000-222i−2i2−22−2−i2i2−i2i200−22i2−i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3000000000000
χ5022-2-2002-20−2i2i−2i2i000-222i−2i2−22−2−i2i2−i2i200−22i2−i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3000000000000
χ5122-2-2002-20−2i2i−2i2i000-222i−2i−22−22i2−i2i2−i2002−2−i2i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ5222-2-2002-20−2i2i−2i2i000-222i−2i−22−22i2−i2i2−i2002−2−i2i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ53444444-4-44-4-4444-4-40000000000000000000000000000000000000000000000
χ544444-4-4-4-4444-4-444-40000000000000000000000000000000000000000000000
χ5544-4-400-4404i−4i−4i4i00000002i2−2i2−2i22i2−222222−220000000000000000000000000000000000
χ5644-4-400-4404i−4i−4i4i0000000−2i22i22i2−2i222−22−22220000000000000000000000000000000000
χ5744-4-400-440−4i4i4i−4i00000002i2−2i2−2i22i222−22−22220000000000000000000000000000000000
χ5844-4-400-440−4i4i4i−4i0000000−2i22i22i2−2i2−222222−220000000000000000000000000000000000
χ598-88-8000080000-8000000000000000000000000000000000000000000000000
χ608-88-80000-800008000000000000000000000000000000000000000000000000
χ618-8-888-800000000000000000000000000000000000000000000000000000000
χ628-8-88-8800000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.