Finite Group Databasebeta

← Group #122677

Character table — Group #122677

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order1222224444444444444488882488888844444444888888881616161616161616
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
χ51111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111-1-1-1-1-1-1111-111-1-1-1-1-1-11-111-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-1-1-1-1-1111-111-1-1-1-1-1-11-111-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-1-1-1-1-1111-111-1-1-1-1-1-11-111-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111-1-1-1-1-1-1111-111-1-1-1-1-1-11-111-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111-1-1-1-1-1-1111-1-1-1111111-1111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ14111111-1-1-1-1-1-1111-1-1-1111111-1111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ15111111-1-1-1-1-1-1111-1-1-1111111-1111-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1
χ16111111-1-1-1-1-1-1111-1-1-1111111-1111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-22222-2-2-2-2-2-222000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-20000-220000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ202222222222-2-2-2-2-2-222-2-20000-220000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ212222222222-2-2-2-2-2-2-2-22200002-200000000000000000000002−22−2−22−22
χ222222222222-2-2-2-2-2-2-2-22200002-20000000000000000000000−22−222−22−2
χ23222222-2-2-2-222-2-2-2222220000-2-200000000000000000000002−2−222−2−22
χ24222222-2-2-2-222-2-2-2222220000-2-20000000000000000000000−222−2−222−2
χ25222222-2-2-2-222-2-2-22-2-2-2-20000220000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ26222222-2-2-2-222-2-2-22-2-2-2-20000220000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ27222222-2-2-2-2-2-2222-222-2-222222-2-2-222-2-2000000000000000000000000
χ28222222-2-2-2-2-2-2222-2-2-222-2-2-2-2-22-2-22222000000000000000000000000
χ292222-2-222-2-222-2-22-200002i2i−2i−2i0000002i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ302222-2-222-2-222-2-22-200002i2i−2i−2i0000002i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ312222-2-222-2-222-2-22-20000−2i−2i2i2i000000−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ322222-2-222-2-222-2-22-20000−2i−2i2i2i000000−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ332222-2-2-2-222-2-2-2-22200002i2i−2i−2i000000−2i2i000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ342222-2-2-2-222-2-2-2-22200002i2i−2i−2i000000−2i2i00000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ352222-2-2-2-222-2-2-2-2220000−2i−2i2i2i0000002i−2i000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ362222-2-2-2-222-2-2-2-2220000−2i−2i2i2i0000002i−2i00000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ374444-4-444-4-4-4-444-440000000000000000000000000000000000000000
χ384444-4-4-4-4444444-4-40000000000000000000000000000000000000000
χ3944-4-44-40000000000004-422−2222−220022−220000000000000000000000000000
χ4044-4-44-40000000000004-4−2222−222200−22220000000000000000000000000000
χ4144-4-44-4000000000000-4422−2222−2200−22220000000000000000000000000000
χ4244-4-44-4000000000000-44−2222−22220022−220000000000000000000000000000
χ4344-4-4-4400000000004i−4i002i2−2i2−2i22i2000022−2200000000000000000000000000
χ4444-4-4-4400000000004i−4i00−2i22i22i2−2i20000−222200000000000000000000000000
χ4544-4-4-440000000000−4i4i002i2−2i2−2i22i20000−222200000000000000000000000000
χ4644-4-4-440000000000−4i4i00−2i22i22i2−2i2000022−2200000000000000000000000000
χ474-44-400004i−4i4i−4i4-40000000000000000002-22i−2i00000000000000000000
χ484-44-400004i−4i4i−4i4-4000000000000000000-22−2i2i00000000000000000000
χ494-44-400004i−4i−4i4i-4400000000000000000000002-22i−2i0000000000000000
χ504-44-400004i−4i−4i4i-440000000000000000000000-22−2i2i0000000000000000
χ514-44-40000−4i4i4i−4i-4400000000000000000000002-2−2i2i0000000000000000
χ524-44-40000−4i4i4i−4i-440000000000000000000000-222i−2i0000000000000000
χ534-44-40000−4i4i−4i4i4-40000000000000000002-2−2i2i00000000000000000000
χ544-44-40000−4i4i−4i4i4-4000000000000000000-222i−2i00000000000000000000
χ558-8-88008i−8i000000000000000000000000000000000000000000000000
χ568-8-8800−8i8i000000000000000000000000000000000000000000000000

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