Finite Group Databasebeta

← Group #100950

Character table — Group #100950

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224444448888888888161616161616161616161616161616161616161616161616
order12222222222244442222444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-22222-2-222-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-222-2-222-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-22222-2-222-2-2-2-2-2-222000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ2122222222-2-2-2-222222-22-2-2-20000002-20000000000000000002-22-20000
χ2222222222-2-2-2-222222-22-2-2-20000002-2000000000000000000-22-220000
χ2322222222-2-2-2-22222-22-22-2-2000000-2200000000000000000000002-22-2
χ2422222222-2-2-2-22222-22-22-2-2000000-220000000000000000000000-22-22
χ2522222222-2-2-2-2-2-2-2-22-22-222000000-2200000000000000000000002i−2i−2i2i
χ2622222222-2-2-2-2-2-2-2-22-22-222000000-220000000000000000000000−2i2i2i−2i
χ2722222222-2-2-2-2-2-2-2-2-22-22220000002-20000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-22-22220000002-2000000000000000000−2i2i2i−2i0000
χ29222-2-2-2-222-22-22i2i−2i−2i00002i−2i002i−2i00002-2000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ30222-2-2-2-222-22-22i2i−2i−2i00002i−2i002i−2i00002-200000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ31222-2-2-2-222-22-22i2i−2i−2i00002i−2i00−2i2i0000-22000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ32222-2-2-2-222-22-22i2i−2i−2i00002i−2i00−2i2i0000-2200000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ33222-2-2-2-222-22-2−2i−2i2i2i0000−2i2i002i−2i0000-22000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ34222-2-2-2-222-22-2−2i−2i2i2i0000−2i2i002i−2i0000-2200000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ35222-2-2-2-222-22-2−2i−2i2i2i0000−2i2i00−2i2i00002-2000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ36222-2-2-2-222-22-2−2i−2i2i2i0000−2i2i00−2i2i00002-200000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ37444-4-4-4-44-44-444i4i−4i−4i0000−4i4i0000000000000000000000000000000000
χ38444-4-4-4-44-44-44−4i−4i4i4i00004i−4i0000000000000000000000000000000000
χ3944-444-4-4-444-4-400004-4-44000000000000000000000000000000000000
χ4044-444-4-4-444-4-40000-444-4000000000000000000000000000000000000
χ4144-444-4-4-4-4-444000044-4-4000000000000000000000000000000000000
χ4244-444-4-4-4-4-4440000-4-444000000000000000000000000000000000000
χ4344-4-4-444-44-4-4400000000004i−4i00000000000000000000000000000000
χ4444-4-4-444-44-4-440000000000−4i4i00000000000000000000000000000000
χ4544-4-4-444-4-444-4000000000000004i−4i0000000000000000000000000000
χ4644-4-4-444-4-444-400000000000000−4i4i0000000000000000000000000000
χ474-444-44-4-400004-44-400000000000000002i−2i2i−2i00000000000000000000
χ484-444-44-4-400004-44-40000000000000000−2i2i−2i2i00000000000000000000
χ494-444-44-4-40000-44-4400000000000000002i−2i−2i2i00000000000000000000
χ504-444-44-4-40000-44-440000000000000000−2i2i2i−2i00000000000000000000
χ514-44-44-44-400004i−4i−4i4i000000000000000000002-22i−2i0000000000000000
χ524-44-44-44-400004i−4i−4i4i00000000000000000000-22−2i2i0000000000000000
χ534-44-44-44-40000−4i4i4i−4i000000000000000000002-2−2i2i0000000000000000
χ544-44-44-44-40000−4i4i4i−4i00000000000000000000-222i−2i0000000000000000
χ558-8-88-8-888000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

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