Finite Group Databasebeta

← Group #152012

Character table — Group #152012

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222244224444444222222444444444428888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-11111111111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ6111111111111-1-1-1-11111111111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ7111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−iii
χ8111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111ii−i−i
χ9111111-1-1-1-11-1111111111-1-1-1-111-1-1-1-111-111-1-111-1-111-1-11-11-1
χ10111111-1-1-1-11-1111111111-1-1-1-111-1-1-1-111-1-1-111-1-11111-1-1-11-11
χ11111111-1-1-1-11-11111111-1-111-1-1-1-111-1-111-111-1-111-1-1-1-111-11-11
χ12111111-1-1-1-11-11111111-1-111-1-1-1-111-1-111-1-1-111-1-111-1-1111-11-1
χ13111111-1-1-1-11-1-1-1-1-111111-1-1-1-111-1-111-1-11ii−i−i−i−iii-1-111i−i−ii
χ14111111-1-1-1-11-1-1-1-1-111111-1-1-1-111-1-111-1-11−i−iiiii−i−i-1-111−iii−i
χ15111111-1-1-1-11-1-1-1-1-1111-1-111-1-1-1-11111-1-11ii−i−i−i−iii11-1-1−iii−i
χ16111111-1-1-1-11-1-1-1-1-1111-1-111-1-1-1-11111-1-11−i−iiiii−i−i11-1-1i−i−ii
χ1722222222222222222-2-20000-2-2000022-2-2-20000000000000000
χ18222222222222-2-2-2-22-2-20000-2-20000-2-22220000000000000000
χ19222222-2-2-2-22-222222-2-20000220000-2-2-2-220000000000000000
χ20222222-2-2-2-22-2-2-2-2-22-2-200002200002222-20000000000000000
χ212-2-22-220000-2022-2-222-2002-200002-2002-2000000000002-20000
χ222-2-22-220000-2022-2-222-200-220000-22002-200000000000-220000
χ232-2-22-220000-2022-2-22-222-200002-20000-220000000002-2000000
χ242-2-22-220000-2022-2-22-22-220000-220000-22000000000-22000000
χ252-2-22-220000-20-2-22222-2002-200002-200-2200000000000-220000
χ262-2-22-220000-20-2-22222-200-220000-2200-22000000000002-20000
χ272-2-22-220000-20-2-2222-222-200002-200002-2000000000-22000000
χ282-2-22-220000-20-2-2222-22-220000-2200002-20000000002-2000000
χ2944444444-4-4-440000-4000000000000000000000000000000000
χ30444444-4-444-4-40000-4000000000000000000000000000000000
χ314444-4-444000-4000000022-2-200-2-222000000000000000000000
χ324444-4-444000-40000000-2-2220022-2-2000000000000000000000
χ334444-4-4-4-400040000000222200-2-2-2-2000000000000000000000
χ344444-4-4-4-400040000000-2-2-2-2002222000000000000000000000
χ3544-4-4004i−4i00002i−2i2i−2i00000000000002-20001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ3644-4-4004i−4i00002i−2i2i−2i00000000000002-2000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ3744-4-4004i−4i0000−2i2i−2i2i0000000000000-220001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ3844-4-4004i−4i0000−2i2i−2i2i0000000000000-22000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ3944-4-400−4i4i00002i−2i2i−2i0000000000000-220001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ4044-4-400−4i4i00002i−2i2i−2i0000000000000-22000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ4144-4-400−4i4i0000−2i2i−2i2i00000000000002-20001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ4244-4-400−4i4i0000−2i2i−2i2i00000000000002-2000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ434-4-444-4004-40000000002-22-200-22-22000000000000000000000
χ444-4-444-4004-4000000000-22-22002-22-2000000000000000000000
χ454-4-444-400-440000000002-2-2200-222-2000000000000000000000
χ464-4-444-400-44000000000-222-2002-2-22000000000000000000000
χ474-4-44-440000400000-40000004-40000000000000000000000000
χ484-4-44-440000400000-4000000-440000000000000000000000000
χ498-88-8000000004i−4i−4i4i0000000000000000000000000000000000
χ508-88-800000000−4i4i4i−4i0000000000000000000000000000000000

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