Finite Group Databasebeta

← Group #309115

Character table — Group #309115

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882244444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-1-1-11-1-1-1111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-11111-1-11-1
χ911111111111111111-1-1-1-11111111-1-1111111-1-1-1-1111111-1-11-1-1-11-1-1-11111-1-1
χ1011111111111111111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1111-11111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11-111-1-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11111-11-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-11-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-11-1-111-1-111-1-1-11
χ172222222222-22-2-2-22-22222-2000000-2-20000220000-2-200000002000-200000000
χ182222222222-22-2-2-22-22222-2000000-2-20000-2-20000220000000-2000200000000
χ192222222222-22-2-2-22-2-2-2-2-2-2000000220000220000-2-20000000-2000200000000
χ202222222222-22-2-2-22-2-2-2-2-2-2000000220000-2-200002200000002000-200000000
χ2122222222-2-22-2222-2-20000-22222220022-2-200000000000000-2000-2000000000
χ2222222222-2-22-2222-2-20000-22222-2-200-2-2-2-20000000000000020002000000000
χ2322222222-2-22-2222-2-20000-2-2-2-2-22200-2-22200000000000000-20002000000000
χ2422222222-2-22-2222-2-20000-2-2-2-2-2-2-2002222000000000000002000-2000000000
χ25222-2-22-2-222-2-222-2-220000-222-2-20000002-20000000000002-2002-20000000000
χ26222-2-22-2-222-2-222-2-220000-222-2-20000002-2000000000000-2200-220000000000
χ27222-2-22-2-222-2-222-2-220000-2-2-222000000-220000000000002-200-220000000000
χ28222-2-22-2-222-2-222-2-220000-2-2-222000000-22000000000000-22002-20000000000
χ29222-2-22-2-2-2-222-2-22222i2i−2i−2i-20000002i−2i0000000000002i2i−2i−2i000000002-2000000
χ30222-2-22-2-2-2-222-2-22222i2i−2i−2i-20000002i−2i000000000000−2i−2i2i2i00000000-22000000
χ31222-2-22-2-2-2-222-2-2222−2i−2i2i2i-2000000−2i2i0000000000002i2i−2i−2i00000000-22000000
χ32222-2-22-2-2-2-222-2-2222−2i−2i2i2i-2000000−2i2i000000000000−2i−2i2i2i000000002-2000000
χ33222-2-22-2-2-2-2-2222-22-22i2i−2i−2i222-2-200−2i2i00-22002i2i−2i−2i0000000000000000000000
χ34222-2-22-2-2-2-2-2222-22-22i2i−2i−2i2-2-22200−2i2i002-200−2i−2i2i2i0000000000000000000000
χ35222-2-22-2-2-2-2-2222-22-2−2i−2i2i2i222-2-2002i−2i00-2200−2i−2i2i2i0000000000000000000000
χ36222-2-22-2-2-2-2-2222-22-2−2i−2i2i2i2-2-222002i−2i002-2002i2i−2i−2i0000000000000000000000
χ3744444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ38444-4-44-4-4444-4-4-44-4-4000040000000000000000000000000000000000000000
χ3944-444-4-4-44-404000-404-44-400000000000000000000000000000000000000000
χ4044-444-4-4-44-404000-40-44-4400000000000000000000000000000000000000000
χ4144-444-4-4-4-440-40004000000000000000000002i2−2i22i2−2i20000000000000000000000
χ4244-444-4-4-4-440-4000400000000000000000000−2i22i2−2i22i20000000000000000000000
χ4344-4-4-4-4444-40-400040000000000000000000022−22−22220000000000000000000000
χ4444-4-4-4-4444-40-4000400000000000000000000−222222−220000000000000000000000
χ4544-4-4-4-444-4404000-404i−4i−4i4i00000000000000000000000000000000000000000
χ4644-4-4-4-444-4404000-40−4i4i4i−4i00000000000000000000000000000000000000000
χ474-444-4-44-4000000000000002i2−2i22i2−2i2000000002i2−2i20000002-22-20000000000000000
χ484-444-4-44-4000000000000002i2−2i22i2−2i200000000−2i22i2000000-22-220000000000000000
χ494-444-4-44-400000000000000−2i22i2−2i22i2000000002i2−2i2000000-22-220000000000000000
χ504-444-4-44-400000000000000−2i22i2−2i22i200000000−2i22i20000002-22-20000000000000000
χ514-44-44-4-44000000000000002i2−2i2−2i22i20000000000000022−222i−2i−2i2i0000000000000000
χ524-44-44-4-44000000000000002i2−2i2−2i22i200000000000000−2222−2i2i2i−2i0000000000000000
χ534-44-44-4-4400000000000000−2i22i22i2−2i20000000000000022−22−2i2i2i−2i0000000000000000
χ544-44-44-4-4400000000000000−2i22i22i2−2i200000000000000−22222i−2i−2i2i0000000000000000
χ554-4-44-44-4400404-4-400000000000000000000000000000000000000000002i2−2i200
χ564-4-44-44-4400404-4-40000000000000000000000000000000000000000000−2i22i200
χ574-4-44-44-4400-40-4440000000000000004-4000000000000000000000000000000
χ584-4-44-44-4400-40-444000000000000000-44000000000000000000000000000000
χ594-4-4-4444-40040-44-4000000000004i−4i0000000000000000000000000000000000
χ604-4-4-4444-40040-44-400000000000−4i4i0000000000000000000000000000000000
χ614-4-4-4444-400-404-440000000000000000000000000000000000000000022−220000
χ624-4-4-4444-400-404-4400000000000000000000000000000000000000000−22220000

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