Finite Group Databasebeta

← Group #136309

Character table — Group #136309

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order122244442244444444888888888888888888161616161616161616161616161616162444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-111-1-11-1ii−i−i11-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1i−ii−iii−i−i
χ101111-1-1-1-111-1-111-1-11-1ii−i−i11-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−ii−ii−i−iii
χ111111-1-1-1-111-1-111-1-11-1ii−i−i11-1-111-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiii11-1-1-1-111i−ii−i−i−iii
χ121111-1-1-1-111-1-111-1-11-1ii−i−i11-1-111-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−ii−iiii−i−i
χ131111-1-1-1-111-1-111-1-11-1−i−iii11-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−ii−ii−i−iii
χ141111-1-1-1-111-1-111-1-11-1−i−iii11-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111i−ii−iii−i−i
χ151111-1-1-1-111-1-111-1-11-1−i−iii11-1-111-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−i11-1-1-1-111−ii−iiii−i−i
χ161111-1-1-1-111-1-111-1-11-1−i−iii11-1-111-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−i-1-11111-1-1i−ii−i−i−iii
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2222200000000-2-2000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-2-2-2-2-2222200000000-2-20000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-22222-2-2000022-2-2-2-22200000000000000000000002-22-2000000000000
χ2422222222-2-2-2-22222-2-2000022-2-2-2-2220000000000000000000000-22-22000000000000
χ2522222222-2-2-2-22222-2-20000-2-22222-2-200000000000000000000000000000022-2-20000
χ2622222222-2-2-2-22222-2-20000-2-22222-2-2000000000000000000000000000000-2-2220000
χ272222-2-2-2-222-2-222-2-22-22i2i−2i−2i-2-222-2-2222i−2i−2i−2i2i2i00000000000000000000000000000000
χ282222-2-2-2-222-2-222-2-22-2−2i−2i2i2i-2-222-2-222−2i2i2i2i−2i−2i00000000000000000000000000000000
χ292222-2-2-2-222-2-2-2-222-222i2i−2i−2i00000000−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ302222-2-2-2-222-2-2-2-222-222i2i−2i−2i00000000−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ312222-2-2-2-222-2-2-2-222-22−2i−2i2i2i000000002i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ322222-2-2-2-222-2-2-2-222-22−2i−2i2i2i000000002i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ332222-2-2-2-2-2-22222-2-2-2200002222-2-2-2-200000000000000000000002-2-22000000000000
χ342222-2-2-2-2-2-22222-2-2-2200002222-2-2-2-20000000000000000000000-222-2000000000000
χ352222-2-2-2-2-2-22222-2-2-220000-2-2-2-222220000000000000000000000000000002i−2i−2i2i0000
χ362222-2-2-2-2-2-22222-2-2-220000-2-2-2-22222000000000000000000000000000000−2i2i2i−2i0000
χ3722-2-22i−2i2i−2i2-22i−2i0000002ζ2−2ζ22ζ6−2ζ62−2i2−i22−2i2−i2001+i−1−i1−i−1+iζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000000000
χ3822-2-22i−2i2i−2i2-22i−2i0000002ζ2−2ζ22ζ6−2ζ62−2i2−i22−2i2−i2001+i−1−i1−i−1+i−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000000000
χ3922-2-22i−2i2i−2i2-22i−2i0000002ζ2−2ζ22ζ6−2ζ6−22−i2i2−22−i2i200−1−i1+i−1+i1−iζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000000000
χ4022-2-22i−2i2i−2i2-22i−2i0000002ζ2−2ζ22ζ6−2ζ6−22−i2i2−22−i2i200−1−i1+i−1+i1−i−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000000000
χ4122-2-22i−2i2i−2i2-22i−2i000000−2ζ22ζ2−2ζ62ζ62−2i2−i22−2i2−i200−1−i1+i−1+i1−iζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000000000
χ4222-2-22i−2i2i−2i2-22i−2i000000−2ζ22ζ2−2ζ62ζ62−2i2−i22−2i2−i200−1−i1+i−1+i1−i−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000000000
χ4322-2-22i−2i2i−2i2-22i−2i000000−2ζ22ζ2−2ζ62ζ6−22−i2i2−22−i2i2001+i−1−i1−i−1+iζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000000000
χ4422-2-22i−2i2i−2i2-22i−2i000000−2ζ22ζ2−2ζ62ζ6−22−i2i2−22−i2i2001+i−1−i1−i−1+i−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000000000
χ4522-2-2−2i2i−2i2i2-2−2i2i0000002ζ6−2ζ62ζ2−2ζ22−2−i2i22−2−i2i200−1+i1−i−1−i1+iζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000000000
χ4622-2-2−2i2i−2i2i2-2−2i2i0000002ζ6−2ζ62ζ2−2ζ22−2−i2i22−2−i2i200−1+i1−i−1−i1+i−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000000000
χ4722-2-2−2i2i−2i2i2-2−2i2i0000002ζ6−2ζ62ζ2−2ζ2−22i2−i2−22i2−i2001−i−1+i1+i−1−iζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000000000
χ4822-2-2−2i2i−2i2i2-2−2i2i0000002ζ6−2ζ62ζ2−2ζ2−22i2−i2−22i2−i2001−i−1+i1+i−1−i−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000000000
χ4922-2-2−2i2i−2i2i2-2−2i2i000000−2ζ62ζ6−2ζ22ζ22−2−i2i22−2−i2i2001−i−1+i1+i−1−iζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000000000
χ5022-2-2−2i2i−2i2i2-2−2i2i000000−2ζ62ζ6−2ζ22ζ22−2−i2i22−2−i2i2001−i−1+i1+i−1−i−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000000000
χ5122-2-2−2i2i−2i2i2-2−2i2i000000−2ζ62ζ6−2ζ22ζ2−22i2−i2−22i2−i200−1+i1−i−1−i1+iζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000000000
χ5222-2-2−2i2i−2i2i2-2−2i2i000000−2ζ62ζ6−2ζ22ζ2−22i2−i2−22i2−i200−1+i1−i−1−i1+i−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-444-4-4444-400000000000000000000000000000000000000000000000000
χ5544-4-44i−4i4i−4i-44−4i4i000000000022−22−2i22i2−22222i2−2i200000000000000000000000000000000000000
χ5644-4-44i−4i4i−4i-44−4i4i0000000000−22222i2−2i222−22−2i22i200000000000000000000000000000000000000
χ5744-4-4−4i4i−4i4i-444i−4i000000000022−222i2−2i2−2222−2i22i200000000000000000000000000000000000000
χ5844-4-4−4i4i−4i4i-444i−4i0000000000−2222−2i22i222−222i2−2i200000000000000000000000000000000000000
χ594-44-44i−4i−4i4i00004-44i−4i0000000000000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ6
χ604-44-44i−4i−4i4i00004-44i−4i000000000000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ6
χ614-44-44i−4i−4i4i0000-44−4i4i00000000000000000000000000000000000000002-22i−2i00000000
χ624-44-44i−4i−4i4i0000-44−4i4i0000000000000000000000000000000000000000-22−2i2i00000000
χ634-44-4−4i4i4i−4i00004-4−4i4i0000000000000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ2
χ644-44-4−4i4i4i−4i00004-4−4i4i000000000000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ2
χ654-44-4−4i4i4i−4i0000-444i−4i00000000000000000000000000000000000000002-2−2i2i00000000
χ664-44-4−4i4i4i−4i0000-444i−4i0000000000000000000000000000000000000000-222i−2i00000000
χ678-8-8888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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