Finite Group Databasebeta

← Group #150712

Character table — Group #150712

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222244444444488881616161616161616161616161616161616161632323232
order12222244444444444444422444448888888888888888
χ111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-111-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-111-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iii−i−i
χ611111111111-1-111-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−iii
χ711111111111-1-111-1-1-1-1-1-1-1-111-1-1-11111iiii−i−i−i−i−i−iii
χ811111111111-1-111-1-1-1-1-1-1-1-111-1-1-11111−i−i−i−iiiiiii−i−i
χ9111111-1-1-1-1-1111111-1-111-111-11-1-111-1-111-1-111-1-11-11-1
χ10111111-1-1-1-1-1111111-1-111-111-11-1-111-1-1-1-111-1-111-11-11
χ11111111-1-1-1-1-1111111-1-111-1-11-1-111-1-11111-1-111-1-1-11-11
χ12111111-1-1-1-1-1111111-1-111-1-11-1-111-1-111-1-111-1-1111-11-1
χ13111111-1-1-1-1-1-1-111-1-111-1-1111-11-1-1-1-111ii−i−i−i−iiii−i−ii
χ14111111-1-1-1-1-1-1-111-1-111-1-1111-11-1-1-1-111−i−iiiii−i−i−iii−i
χ15111111-1-1-1-1-1-1-111-1-111-1-11-11-1-11111-1-1ii−i−i−i−iii−iii−i
χ16111111-1-1-1-1-1-1-111-1-111-1-11-11-1-11111-1-1−i−iiiii−i−ii−i−ii
χ172222222222222222222-2-2-20-2-20000000000000000000
χ1822222222222-2-222-2-2-2-22220-2-20000000000000000000
χ19222222-2-2-2-2-2222222-2-2-2-220-220000000000000000000
χ20222222-2-2-2-2-2-2-222-2-22222-20-220000000000000000000
χ21444444444-4-400-4-400000000000000000000000000000
χ22444444-4-4-44400-4-400000000000000000000000000000
χ234444-4-444-40000000000000200-22-20000000000000000
χ244444-4-444-40000000000000-2002-220000000000000000
χ254444-4-4-4-440000000000000200-2-220000000000000000
χ264444-4-4-4-440000000000000-20022-20000000000000000
χ2744-4-4004i−4i0002i−2i002i−2i2-200000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ2844-4-4004i−4i0002i−2i002i−2i2-20000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ2944-4-4004i−4i000−2i2i00−2i2i-2200000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ3044-4-4004i−4i000−2i2i00−2i2i-220000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ3144-4-400−4i4i0002i−2i002i−2i-2200000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ3244-4-400−4i4i0002i−2i002i−2i-220000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ3344-4-400−4i4i000−2i2i00−2i2i2-200000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ3444-4-400−4i4i000−2i2i00−2i2i2-20000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ354-44-44-400000004-400004i−4i00000000000000000000000
χ364-44-44-400000004-40000−4i4i00000000000000000000000
χ374-44-44-40000044-44-4-4000000000000000000000000000
χ384-44-44-400000-4-4-4444000000000000000000000000000
χ394-44-4-440004i−4i000000000000000002i−2i2-2000000000000
χ404-44-4-440004i−4i00000000000000000−2i2i-22000000000000
χ414-44-4-44000−4i4i000000000000000002i−2i-22000000000000
χ424-44-4-44000−4i4i00000000000000000−2i2i2-2000000000000
χ438-8-8800000004i−4i00−4i4i000000000000000000000000000
χ448-8-880000000−4i4i004i−4i000000000000000000000000000

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