Finite Group Databasebeta

← Group #299654

Character table — Group #299654

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222224444444888888888888881616161616161616161616161616161616163232
order12222244444444488882244888888888822244444444488888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ3111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ51111111111111111111-1-1-1-1111111111111-1-1-111-11111-1-1-1-1-1-1-1-1
χ61111111111111111111-1-1-1-11111111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-111
χ71111111111111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-1-111-1-1-1-1-111-1-11111
χ81111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1111-1-11111111-1-111-1-1
χ9111111111111111-1-1-1-11111-11111-1-1-1-1-11-11-1-11-1111-1-111-1-1-1-1-11
χ10111111111111111-1-1-1-11111-11111-1-1-1-1-1-11-111-11-1-1-11111-1-1-1-11-1
χ11111111111111111-1-1-1-11111-1-1-1-1-1-111111-11-1-11-11-1-111-1-1-1-1111-1
χ12111111111111111-1-1-1-11111-1-1-1-1-1-11111-11-111-11-111-1-1-1-1-1-111-11
χ13111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1111-1-111-1-1-1-111111-1
χ14111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-111-1-11111-11
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1111111-1-1-11
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-11111-1-11111-1-11-1
χ172222222-2-2-2-222-2-222-2-22-22-220000-20000000000000000002-20000
χ182222222-2-2-2-222-2-222-2-2-22-2220000-2000000000000000000-220000
χ192222222-2-2-2-222-2-2-2-2222-22-2-200002000000000000000000-220000
χ202222222-2-2-2-222-2-2-2-222-22-22-2000020000000000000000002-20000
χ21222222-22222-2-2-2-2000022-2-2022-2-2000000000000000002-2000000
χ22222222-22222-2-2-2-2000022-2-20-2-22200000000000000000-22000000
χ23222222-22222-2-2-2-20000-2-222022-2-200000000000000000-22000000
χ24222222-22222-2-2-2-20000-2-2220-2-222000000000000000002-2000000
χ25222222-2-2-2-2-2-2-22200002-2-2200000022-2-200000000000000002-200
χ26222222-2-2-2-2-2-2-22200002-2-22000000-2-2220000000000000000-2200
χ27222222-2-2-2-2-2-2-2220000-222-200000022-2-20000000000000000-2200
χ28222222-2-2-2-2-2-2-2220000-222-2000000-2-22200000000000000002-200
χ292222-2-2222-2-22-22-222220000-20000-200000022-200-2000000000000
χ302222-2-2222-2-22-22-222220000-20000-2000000-2-22002000000000000
χ312222-2-2222-2-22-22-2-2-2-2-200002000020000002-2200-2000000000000
χ322222-2-2222-2-22-22-2-2-2-2-20000200002000000-22-2002000000000000
χ332222-2-22-2-2222-2-2222-2-20000-20000200002-2000-220000000000000
χ342222-2-22-2-2222-2-2222-2-20000-2000020000-220002-20000000000000
χ352222-2-22-2-2222-2-22-2-222000020000-2000022000-2-20000000000000
χ362222-2-22-2-2222-2-22-2-222000020000-20000-2-2000220000000000000
χ374444-4-4-444-4-4-44-4400000000000000000000000000000000000000
χ384444-4-4-4-4-444-444-400000000000000000000000000000000000000
χ3944-4-400-400004000004-400000000000000000000002i−2i2i−2i00000000
χ4044-4-400-400004000004-40000000000000000000000−2i2i−2i2i00000000
χ4144-4-400-40000400000-4400000000000000000000002i−2i−2i2i00000000
χ4244-4-400-40000400000-440000000000000000000000−2i2i2i−2i00000000
χ434-4-444-404-44-40000000000000000002i2−2i22i2−2i200000000000000000000
χ444-4-444-404-44-4000000000000000000−2i22i2−2i22i200000000000000000000
χ454-4-444-40-44-440000000000000000002i2−2i2−2i22i200000000000000000000
χ464-4-444-40-44-44000000000000000000−2i22i22i2−2i200000000000000000000
χ474-4-44-4404-4-4400000000000004-4000000000000000000000000000
χ484-4-44-4404-4-440000000000000-44000000000000000000000000000
χ494-4-44-440-444-40000000000000004-40000000000000000000000000
χ504-4-44-440-444-4000000000000000-440000000000000000000000000
χ5188-8-80080000-800000000000000000000000000000000000000000
χ528-88-8000000000004i2−4i2000000000000000000000000000000000000
χ538-88-800000000000−4i24i2000000000000000000000000000000000000

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