Finite Group Databasebeta

← Group #129849

Character table — Group #129849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244444444444488888888888816161616161616161616161616161616161616161616
order12222222222222444444444444444444442444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11-111ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11-111−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-11-1-1ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-11-1-1−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1111ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-200-2-222-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000000000
χ192222222222-2-2-2-222222222-2-200-2-2-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-2002222-2-2000000000000000000000000
χ212222-2-2-2-2222-22-2000022-2-22-200000000002-2002-20000000000000000
χ222222-2-2-2-2222-22-2000022-2-22-20000000000-2200-220000000000000000
χ232222-2-2-2-2222-22-20000-2-222-22220000002200-2-2000000000000000000
χ242222-2-2-2-2222-22-20000-2-222-22-2-2000000-2-20022000000000000000000
χ252222-2-2-2-222-22-22000022-2-2-2222000000-2-200-22000000000000000000
χ262222-2-2-2-222-22-22000022-2-2-22-2-200000022002-2000000000000000000
χ272222-2-2-2-222-22-220000-2-2222-200000000002-200-220000000000000000
χ282222-2-2-2-222-22-220000-2-2222-20000000000-22002-20000000000000000
χ2922-2-222-2-22-2000022-2-22i−2i2i−2i000000002i−2i000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ3022-2-222-2-22-2000022-2-22i−2i2i−2i000000002i−2i00000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ3122-2-222-2-22-2000022-2-2−2i2i−2i2i00000000−2i2i000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ3222-2-222-2-22-2000022-2-2−2i2i−2i2i00000000−2i2i00000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ3322-2-222-2-22-20000-2-2222i−2i2i−2i00000000−2i2i000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ3422-2-222-2-22-20000-2-2222i−2i2i−2i00000000−2i2i00000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ3522-2-222-2-22-20000-2-222−2i2i−2i2i000000002i−2i000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ3622-2-222-2-22-20000-2-222−2i2i−2i2i000000002i−2i00000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ3722-2-22-22-2-222-2-222i−2i2i−2i00000000002i−2i0000000000000000002−22−2i2−i2i2−i2
χ3822-2-22-22-2-222-2-222i−2i2i−2i00000000002i−2i000000000000000000−22−22−i2i2−i2i2
χ3922-2-22-22-2-222-2-22−2i2i−2i2i0000000000−2i2i0000000000000000002−22−2−i2i2−i2i2
χ4022-2-22-22-2-222-2-22−2i2i−2i2i0000000000−2i2i000000000000000000−22−22i2−i2i2−i2
χ4122-2-22-22-2-22-222-22i−2i2i−2i0000000000−2i2i000000000000000000i2−i2−i2i2−222−2
χ4222-2-22-22-2-22-222-22i−2i2i−2i0000000000−2i2i000000000000000000−i2i2i2−i22−2−22
χ4322-2-22-22-2-22-222-2−2i2i−2i2i00000000002i−2i000000000000000000i2−i2−i2i22−2−22
χ4422-2-22-22-2-22-222-2−2i2i−2i2i00000000002i−2i000000000000000000−i2i2i2−i2−222−2
χ4544444-4-44-4-400004i−4i−4i4i00000000000000000000000000000000000000
χ4644444-4-44-4-40000−4i4i4i−4i00000000000000000000000000000000000000
χ474444-444-4-4-400000000000000004i−4i0000000000000000000000000000
χ484444-444-4-4-40000000000000000−4i4i0000000000000000000000000000
χ4944-4-4-44-44-4444-4-4000000000000000000000000000000000000000000
χ5044-4-4-44-44-44-4-444000000000000000000000000000000000000000000
χ5144-4-4-4-4444-4000000004i−4i−4i4i0000000000000000000000000000000000
χ5244-4-4-4-4444-400000000−4i4i4i−4i0000000000000000000000000000000000
χ538-88-800000000000000000000000000004i−4i0000000000000000000000
χ548-88-80000000000000000000000000000−4i4i0000000000000000000000
χ558-8-88000000000000000000004-4000000000000000000000000000000
χ568-8-8800000000000000000000-44000000000000000000000000000000

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