Finite Group Databasebeta

← Group #130511

Character table — Group #130511

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222244444444444444488888888888881616161616161616161616161632323232
order12222244444444444444444222244444444424444444444448888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-111-1-1111-1-11111-1-1-1-1-1iiii−i−i−i−iii−i−i
χ41111111111111111111-1-1-1-111-1-1111-1-11111-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111-1-1-1-11111-1-1111-1-111-1-1111-1-1-1-111111111-1-1-1-1
χ6111111111111111-1-1-1-11111-1-1111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-11111iiii−i−i−i−i−i−iii
χ8111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-11111−i−i−i−iiiiiii−i−i
χ911111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-111-1-111-1-111-1-11-11-1
χ1011111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-111-1-1-1-111-1-111-11-11
χ1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-11-1-111ii−i−i−i−iiii−i−ii
χ1211111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-11-1-111−i−iiiii−i−i−iii−i
χ1311111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-11
χ1411111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1-111-1-1111-11-1
χ1511111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1111-1-1ii−i−i−i−iii−iii−i
χ1611111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1111-1-1−i−iiiii−i−ii−i−ii
χ1722222222-2-220000222222-2-2002-2-20000-2-20002-200000000000000
χ1822222222-2-2200002222-2-22200-22-20000-2-2000-2200000000000000
χ1922222222-2-220000-2-2-2-222-2-2002-2-2000022000-2200000000000000
χ2022222222-2-220000-2-2-2-2-2-22200-22-20000220002-200000000000000
χ21222222-2-222-222220000222200-2-2-2002200-2-2-20000000000000000
χ22222222-2-222-222220000-2-2-2-20022-200-2-200-2-220000000000000000
χ23222222-2-222-2-2-2-2-20000222200-2-2-200-2-2002220000000000000000
χ24222222-2-222-2-2-2-2-20000-2-2-2-20022-200220022-20000000000000000
χ25222222-2-2-2-2-20000000022-2-222-222-2-20000000002-2000000000000
χ26222222-2-2-2-2-20000000022-2-2-2-2-22222000000000-22000000000000
χ27222222-2-2-2-2-200000000-2-222222-22-2-2000000000-22000000000000
χ28222222-2-2-2-2-200000000-2-222-2-22-22220000000002-2000000000000
χ292-22-22-2002-2022-2-200002i−2i2i−2i00000002i−2i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ302-22-22-2002-2022-2-200002i−2i2i−2i00000002i−2i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ312-22-22-2002-2022-2-20000−2i2i−2i2i0000000−2i2i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ322-22-22-2002-2022-2-20000−2i2i−2i2i0000000−2i2i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ332-22-22-2002-20-2-22200002i−2i2i−2i0000000−2i2i0000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ342-22-22-2002-20-2-22200002i−2i2i−2i0000000−2i2i000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ352-22-22-2002-20-2-2220000−2i2i−2i2i00000002i−2i0000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ362-22-22-2002-20-2-2220000−2i2i−2i2i00000002i−2i000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ374444-4-44400-40000000000000000000004i−4i0000000000000000000
χ384444-4-44400-4000000000000000000000−4i4i0000000000000000000
χ394444-4-4-4-400400004i4i−4i−4i0000000000000000000000000000000000
χ404444-4-4-4-40040000−4i−4i4i4i0000000000000000000000000000000000
χ4144-4-4004i−4i0002-22-22+2i−2−2i2−2i−2+2i00002-20002i−2i00002i−2i00000000000000000
χ4244-4-4004i−4i0002-22-2−2−2i2+2i−2+2i2−2i0000-22000−2i2i00002i−2i00000000000000000
χ4344-4-4004i−4i000-22-222+2i−2−2i2−2i−2+2i0000-22000−2i2i0000−2i2i00000000000000000
χ4444-4-4004i−4i000-22-22−2−2i2+2i−2+2i2−2i00002-20002i−2i0000−2i2i00000000000000000
χ4544-4-400−4i4i0002-22-22−2i−2+2i2+2i−2−2i00002-2000−2i2i0000−2i2i00000000000000000
χ4644-4-400−4i4i0002-22-2−2+2i2−2i−2−2i2+2i0000-220002i−2i0000−2i2i00000000000000000
χ4744-4-400−4i4i000-22-222−2i−2+2i2+2i−2−2i0000-220002i−2i00002i−2i00000000000000000
χ4844-4-400−4i4i000-22-22−2+2i2−2i−2−2i2+2i00002-2000−2i2i00002i−2i00000000000000000
χ494-44-44-400-440000000004i−4i−4i4i000000000000000000000000000000
χ504-44-44-400-44000000000−4i4i4i−4i000000000000000000000000000000
χ518-88-8-8800000000000000000000000000000000000000000000000
χ528-8-8800000004-4-4400000000000000000000000000000000000000
χ538-8-880000000-444-400000000000000000000000000000000000000

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