Finite Group Databasebeta

← Group #150258

Character table — Group #150258

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1122244448881616161616161616161616161611222444488816161616161616161616161616
order12222222224444444444488882222222222444444444448888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111-1-1-1-11111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1
χ41111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111
χ51111111-1-1-1-1-1111-1-1ii−i−iii−i−i1111111-1-1-1-1-1111-1-1ii−i−iii−i−i
χ61111111-1-1-1-1-1111-1-1−i−iii−i−iii1111111-1-1-1-1-1111-1-1−i−iii−i−iii
χ71111111-1-1-1-1-11-1-111ii−i−i−i−iii1111111-1-1-1-1-11-1-111ii−i−i−i−iii
χ81111111-1-1-1-1-11-1-111−i−iiiii−i−i1111111-1-1-1-1-11-1-111−i−iiiii−i−i
χ92222222222-2-2-20000000000002222222222-2-2-2000000000000
χ102222222-2-2-222-20000000000002222222-2-2-222-2000000000000
χ11222-2-22-222-200000000000i2−i2i2−i2222-2-22-222-200000000000i2−i2i2−i2
χ12222-2-22-222-200000000000−i2i2−i2i2222-2-22-222-200000000000−i2i2−i2i2
χ13222-2-22-2-2-22000000000002−2−22222-2-22-2-2-22000000000002−2−22
χ14222-2-22-2-2-2200000000000−222−2222-2-22-2-2-2200000000000−222−2
χ15222-2-2-220002i−2i000001+i−1−i1−i−1+i0000222-2-2-220002i−2i000001+i−1−i1−i−1+i0000
χ16222-2-2-220002i−2i00000−1−i1+i−1+i1−i0000222-2-2-220002i−2i00000−1−i1+i−1+i1−i0000
χ17222-2-2-22000−2i2i000001−i−1+i1+i−1−i0000222-2-2-22000−2i2i000001−i−1+i1+i−1−i0000
χ18222-2-2-22000−2i2i00000−1+i1−i−1−i1+i0000222-2-2-22000−2i2i00000−1+i1−i−1−i1+i0000
χ1944444-4-400000000000000000044444-4-4000000000000000000
χ2044-44-400000000002i−2i0000000044-44-400000000002i−2i00000000
χ2144-44-40000000000−2i2i0000000044-44-40000000000−2i2i00000000
χ2244-4-44000000002-2000000000044-4-44000000002-20000000000
χ2344-4-4400000000-22000000000044-4-4400000000-220000000000
χ248-8000004-400000000000000008-8000004-40000000000000000
χ258-800000-4400000000000000008-800000-440000000000000000
χ261111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2711111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ281111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ291111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ301111111-1-1-1-1-1111-1-1ii−i−iii−i−i-1-1-1-1-1-1-111111-1-1-111−i−iii−i−iii
χ311111111-1-1-1-1-1111-1-1−i−iii−i−iii-1-1-1-1-1-1-111111-1-1-111ii−i−iii−i−i
χ321111111-1-1-1-1-11-1-111ii−i−i−i−iii-1-1-1-1-1-1-111111-111-1-1−i−iiiii−i−i
χ331111111-1-1-1-1-11-1-111−i−iiiii−i−i-1-1-1-1-1-1-111111-111-1-1ii−i−i−i−iii
χ342222222222-2-2-2000000000000-2-2-2-2-2-2-2-2-2-2222000000000000
χ352222222-2-2-222-2000000000000-2-2-2-2-2-2-2222-2-22000000000000
χ36222-2-22-222-200000000000i2−i2i2−i2-2-2-222-22-2-2200000000000−i2i2−i2i2
χ37222-2-22-222-200000000000−i2i2−i2i2-2-2-222-22-2-2200000000000i2−i2i2−i2
χ38222-2-22-2-2-22000000000002−2−22-2-2-222-2222-200000000000−222−2
χ39222-2-22-2-2-2200000000000−222−2-2-2-222-2222-2000000000002−2−22
χ40222-2-2-220002i−2i000001+i−1−i1−i−1+i0000-2-2-2222-2000−2i2i00000−1−i1+i−1+i1−i0000
χ41222-2-2-220002i−2i00000−1−i1+i−1+i1−i0000-2-2-2222-2000−2i2i000001+i−1−i1−i−1+i0000
χ42222-2-2-22000−2i2i000001−i−1+i1+i−1−i0000-2-2-2222-20002i−2i00000−1+i1−i−1−i1+i0000
χ43222-2-2-22000−2i2i00000−1+i1−i−1−i1+i0000-2-2-2222-20002i−2i000001−i−1+i1+i−1−i0000
χ4444444-4-4000000000000000000-4-4-4-4-444000000000000000000
χ4544-44-400000000002i−2i00000000-4-44-440000000000−2i2i00000000
χ4644-44-40000000000−2i2i00000000-4-44-4400000000002i−2i00000000
χ4744-4-44000000002-20000000000-4-444-400000000-220000000000
χ4844-4-4400000000-220000000000-4-444-4000000002-20000000000
χ498-8000004-40000000000000000-8800000-440000000000000000
χ508-800000-440000000000000000-88000004-40000000000000000

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