Finite Group Databasebeta

← Group #306306

Character table — Group #306306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224488888888888888888888161616161616161616161616161616163232
order12222222444444444422444444888888888888444444448888888844
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11-1111-111-1-111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-11-1-1-1-1-1-111-1-11-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-1-1-111-11
χ51111111111111111111111-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1-1-1-111-11
χ61111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-11111-1-111-1-11-1
χ71111111111111111111111-1-1-1-1111111111111-11-1-1-11-1-11111-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ9111111111111111111-1-1-1-111111111111111111-1-1-11-1-1-1-1-1-1-11111-1-1
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111
χ11111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-111111111-1-1-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-1-1111-1
χ13111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111-1-1-11111-1-1111-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-111111-1-1-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-111111-1-11111-1-1
χ172222222222-2-2-222-2-2-222-2-20000000022-2-2000002000-2000000000000
χ182222222222-2-2-222-2-2-222-2-200000000-2-22200000-20002000000000000
χ192222222222-2-2-222-2-2-2-2-2220000000022-2-200000-20002000000000000
χ202222222222-2-2-222-2-2-2-2-22200000000-2-222000002000-2000000000000
χ2122222222-2-2222-2-22-2-200002222-2-22200000000-2000-20000000000000
χ2222222222-2-2222-2-22-2-2000022-2-222-2-200000000-200020000000000000
χ2322222222-2-2222-2-22-2-20000-2-22222-2-2000000002000-20000000000000
χ2422222222-2-2222-2-22-2-20000-2-2-2-2-2-22200000000200020000000000000
χ25222-22-2-2-2222-22-2-2-2-222-22-200000000000022-2-2000000002-200000000
χ26222-22-2-2-2222-22-2-2-2-222-22-2000000000000-2-22200000000-2200000000
χ27222-22-2-2-2222-22-2-2-2-22-22-2200000000000022-2-200000000-2200000000
χ28222-22-2-2-2222-22-2-2-2-22-22-22000000000000-2-222000000002-200000000
χ29222-22-2-2-222-22-2-2-222-22-2-2200002-22-20000000000000000002-2000000
χ30222-22-2-2-222-22-2-2-222-22-2-220000-22-22000000000000000000-22000000
χ31222-22-2-2-222-22-2-2-222-2-222-200002-22-2000000000000000000-22000000
χ32222-22-2-2-222-22-2-2-222-2-222-20000-22-220000000000000000002-2000000
χ33222-22-2-2-2-2-2-22-2222-22000000002-2-2200000000002i−2i002i−2i0000000000
χ34222-22-2-2-2-2-2-22-2222-22000000002-2-220000000000−2i2i00−2i2i0000000000
χ35222-22-2-2-2-2-2-22-2222-2200000000-222-200000000002i−2i00−2i2i0000000000
χ36222-22-2-2-2-2-2-22-2222-2200000000-222-20000000000−2i2i002i−2i0000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000
χ38444-44-4-4-4-4-44-4444-44-400000000000000000000000000000000000000
χ3944-44-44-4-44-40004-4000000000000000000022−2222−22000000000000000000
χ4044-44-44-4-44-40004-40000000000000000000−2222−2222000000000000000000
χ4144-44-44-4-4-44000-440000000000000004-4000000000000000000000000
χ4244-44-44-4-4-44000-44000000000000000-44000000000000000000000000
χ4344-4-4-4-4444-4000-44000000000000000000022−22−2222000000000000000000
χ4444-4-4-4-4444-4000-440000000000000000000−222222−22000000000000000000
χ4544-4-4-4-444-440004-4000000000000000004-40000000000000000000000
χ4644-4-4-4-444-440004-400000000000000000-440000000000000000000000
χ474-4-444-4-440044-400-40000004i−4i00000000000000000000000000000000
χ484-4-444-4-440044-400-4000000−4i4i00000000000000000000000000000000
χ494-4-444-4-4400-4-44004000000000000000000000000000000000022−220000
χ504-4-444-4-4400-4-440040000000000000000000000000000000000−22220000
χ514-4-4-4444-4004-4-40040000000000000000000000000000000000002i2−2i200
χ524-4-4-4444-4004-4-4004000000000000000000000000000000000000−2i22i200
χ534-4-4-4444-400-44400-4000000004i−4i000000000000000000000000000000
χ544-4-4-4444-400-44400-400000000−4i4i000000000000000000000000000000
χ558-888-8-88-8000000000000000000000000000000000000000000000000
χ568-88-8-88-88000000000000000000000000000000000000000000000000

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