Finite Group Databasebeta

← Group #138913

Character table — Group #138913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order122222444444888822488888888882244444488161616161616161616161616161616162488882488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ811111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1
χ911111111-1-1-1-11111-1-1111-1-1ii−i−i-1-111-1-1ii−i−ii−i1111-1-1-1-1iiii−i−i−i−i1-1ii−i−i1-1i−i
χ1011111111-1-1-1-11111-1-1111-1-1ii−i−i-1-111-1-1ii−i−ii−i-1-1-1-11111−i−i−i−iiiii1-1ii−i−i-11−ii
χ1111111111-1-1-1-11111-1-1111-1-1ii−i−i-1-1-1-111ii−i−ii−i1111-1-1-1-1iiii−i−i−i−i-11−i−iii-11−ii
χ1211111111-1-1-1-11111-1-1111-1-1ii−i−i-1-1-1-111ii−i−ii−i-1-1-1-11111−i−i−i−iiiii-11−i−iii1-1i−i
χ1311111111-1-1-1-11111-1-1111-1-1−i−iii-1-111-1-1−i−iii−ii1111-1-1-1-1−i−i−i−iiiii1-1−i−iii1-1−ii
χ1411111111-1-1-1-11111-1-1111-1-1−i−iii-1-111-1-1−i−iii−ii-1-1-1-11111iiii−i−i−i−i1-1−i−iii-11i−i
χ1511111111-1-1-1-11111-1-1111-1-1−i−iii-1-1-1-111−i−iii−ii1111-1-1-1-1−i−i−i−iiiii-11ii−i−i-11i−i
χ1611111111-1-1-1-11111-1-1111-1-1−i−iii-1-1-1-111−i−iii−ii-1-1-1-11111iiii−i−i−i−i-11ii−i−i1-1−ii
χ17222222222222-2-2-2-2222-2-2-2-22222-2-20000-2-2-2-22200000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-200002222-2-200000000000000000000000000
χ1922222222-2-2-2-2-2-2-2-2-2-22-2-2222i2i−2i−2i220000−2i−2i2i2i2i−2i00000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2-2-22-2-222−2i−2i2i2i2200002i2i−2i−2i−2i2i00000000000000000000000000
χ21222222-2-222220000-2-2-2000022220000000000-2-222−2−222−2−222−2−222−2−20000000000
χ22222222-2-222220000-2-2-2000022220000000000-2-2−2−222−2−222−2−222−2−2220000000000
χ23222222-2-222220000-2-2-20000-2-2-2-200000000002222−2−222−2−2−2−222−2−2220000000000
χ24222222-2-222220000-2-2-20000-2-2-2-2000000000022−2−222−2−22222−2−222−2−20000000000
χ25222222-2-2-2-2-2-2000022-200002i2i−2i−2i0000000000−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000
χ26222222-2-2-2-2-2-2000022-200002i2i−2i−2i0000000000−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000
χ27222222-2-2-2-2-2-2000022-20000−2i−2i2i2i00000000002i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000
χ28222222-2-2-2-2-2-2000022-20000−2i−2i2i2i00000000002i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000
χ292222-2-22222-2-222222-2-2-2-2-2-200002222-2-20000000000000000000000-2200000000
χ302222-2-22222-2-222222-2-2-2-2-2-2000022-2-22200000000000000000000002-200000000
χ312222-2-22222-2-2-2-2-2-22-2-222220000-2-200000000000000000000000000002i−2i2i−2i0000
χ322222-2-22222-2-2-2-2-2-22-2-222220000-2-20000000000000000000000000000−2i2i−2i2i0000
χ332222-2-222-2-2222222-22-2-2-2220000-2-222220000000000000000000000-2-200000000
χ342222-2-222-2-2222222-22-2-2-2220000-2-2-2-2-2-200000000000000000000002200000000
χ352222-2-222-2-222-2-2-2-2-22-222-2-200002200000000000000000000000000002-2-220000
χ362222-2-222-2-222-2-2-2-2-22-222-2-20000220000000000000000000000000000-222-20000
χ3722-2-22-2002i−2i2i−2i22−2−20002−2i2−i22ζ2−2ζ22ζ6−2ζ6i2−i200001+i−1−i1−i−1+i00ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000
χ3822-2-22-2002i−2i2i−2i22−2−20002−2i2−i22ζ2−2ζ22ζ6−2ζ6i2−i200001+i−1−i1−i−1+i00−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000
χ3922-2-22-2002i−2i2i−2i22−2−20002−2i2−i2−2ζ22ζ2−2ζ62ζ6i2−i20000−1−i1+i−1+i1−i00ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000
χ4022-2-22-2002i−2i2i−2i22−2−20002−2i2−i2−2ζ22ζ2−2ζ62ζ6i2−i20000−1−i1+i−1+i1−i00−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000
χ4122-2-22-2002i−2i2i−2i−2−222000−22−i2i22ζ2−2ζ22ζ6−2ζ6−i2i20000−1−i1+i−1+i1−i00ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000
χ4222-2-22-2002i−2i2i−2i−2−222000−22−i2i22ζ2−2ζ22ζ6−2ζ6−i2i20000−1−i1+i−1+i1−i00−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000
χ4322-2-22-2002i−2i2i−2i−2−222000−22−i2i2−2ζ22ζ2−2ζ62ζ6−i2i200001+i−1−i1−i−1+i00ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000
χ4422-2-22-2002i−2i2i−2i−2−222000−22−i2i2−2ζ22ζ2−2ζ62ζ6−i2i200001+i−1−i1−i−1+i00−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000
χ4522-2-22-200−2i2i−2i2i22−2−20002−2−i2i22ζ6−2ζ62ζ2−2ζ2−i2i20000−1+i1−i−1−i1+i00ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000
χ4622-2-22-200−2i2i−2i2i22−2−20002−2−i2i22ζ6−2ζ62ζ2−2ζ2−i2i20000−1+i1−i−1−i1+i00−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000
χ4722-2-22-200−2i2i−2i2i22−2−20002−2−i2i2−2ζ62ζ6−2ζ22ζ2−i2i200001−i−1+i1+i−1−i00ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000
χ4822-2-22-200−2i2i−2i2i22−2−20002−2−i2i2−2ζ62ζ6−2ζ22ζ2−i2i200001−i−1+i1+i−1−i00−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000
χ4922-2-22-200−2i2i−2i2i−2−222000−22i2−i22ζ6−2ζ62ζ2−2ζ2i2−i200001−i−1+i1+i−1−i00ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000
χ5022-2-22-200−2i2i−2i2i−2−222000−22i2−i22ζ6−2ζ62ζ2−2ζ2i2−i200001−i−1+i1+i−1−i00−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000
χ5122-2-22-200−2i2i−2i2i−2−222000−22i2−i2−2ζ62ζ6−2ζ22ζ2i2−i20000−1+i1−i−1−i1+i00ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000
χ5222-2-22-200−2i2i−2i2i−2−222000−22i2−i2−2ζ62ζ6−2ζ22ζ2i2−i20000−1+i1−i−1−i1+i00−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000
χ534444-4-4-4-444-4-40000-4440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-44400004-440000000000000000000000000000000000000000000000
χ5544-4-4-44004i−4i−4i4i2222−22−22000−2222−2i22i200002i2−2i2000000000000000000000000000000000000
χ5644-4-4-44004i−4i−4i4i−22−22222200022−222i2−2i20000−2i22i2000000000000000000000000000000000000
χ5744-4-4-4400−4i4i4i−4i2222−22−22000−22222i2−2i20000−2i22i2000000000000000000000000000000000000
χ5844-4-4-4400−4i4i4i−4i−22−22222200022−22−2i22i200002i2−2i2000000000000000000000000000000000000
χ594-4-4400-4400004-44-40000000000000004-400000000000000000000000000000000
χ604-4-4400-4400004-44-4000000000000000-4400000000000000000000000000000000
χ614-4-4400-440000-44-4400000000000004-40000000000000000000000000000000000
χ624-4-4400-440000-44-440000000000000-440000000000000000000000000000000000
χ638-88-80000000042−42−42420000000000000000000000000000000000000000000000000
χ648-88-800000000−424242−420000000000000000000000000000000000000000000000000
χ658-8-88008-8000000000000000000000000000000000000000000000000000000000

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