Finite Group Databasebeta

← Group #311478

Character table — Group #311478

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882224444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-1111-1111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-11-1-1-11-1-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11-1-111-1-1-111111-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-11111-1-11-11-1-1-11111-1-1-1-1
χ1011111111111111111-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11-1111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-11111-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1-11-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111-1-1-1-1-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-11-1-111-1-1-11
χ17222222222-222-2-2-22-20000-22222002222-2-200000000000000-20-200000000000
χ18222222222-222-2-2-22-20000-2222200-2-2-2-2-2-20000000000000020200000000000
χ19222222222-222-2-2-22-20000-2-2-2-2-20022-2-2220000000000000020-200000000000
χ20222222222-222-2-2-22-20000-2-2-2-2-200-2-2222200000000000000-20200000000000
χ2122222222-22-2-2222-2-22222-20000-2-200000022-2-200000000000-2000200000000
χ2222222222-22-2-2222-2-22222-20000-2-2000000-2-222000000000002000-200000000
χ2322222222-22-2-2222-2-2-2-2-2-2-200002200000022-2-2000000000002000-200000000
χ2422222222-22-2-2222-2-2-2-2-2-2-2000022000000-2-22200000000000-2000200000000
χ25222-2-2-22-222-2-2-22-22-2000022i2i−2i−2i0000002i−2i0000000000002-20002i−2i000000000
χ26222-2-2-22-222-2-2-22-22-2000022i2i−2i−2i0000002i−2i000000000000-22000−2i2i000000000
χ27222-2-2-22-222-2-2-22-22-200002−2i−2i2i2i000000−2i2i0000000000002-2000−2i2i000000000
χ28222-2-2-22-222-2-2-22-22-200002−2i−2i2i2i000000−2i2i000000000000-220002i−2i000000000
χ29222-2-2-22-22-2-2-22-22222i2i−2i−2i-22i2i−2i−2i2i−2i0000−2i2i000022-2-200000000000000000000
χ30222-2-2-22-22-2-2-22-22222i2i−2i−2i-2−2i−2i2i2i2i−2i00002i−2i0000-2-22200000000000000000000
χ31222-2-2-22-22-2-2-22-2222−2i−2i2i2i-22i2i−2i−2i−2i2i0000−2i2i0000-2-22200000000000000000000
χ32222-2-2-22-22-2-2-22-2222−2i−2i2i2i-2−2i−2i2i2i−2i2i00002i−2i000022-2-200000000000000000000
χ33222-2-2-22-2-2-2222-22-2-22i2i−2i−2i20000−2i2i0000000000000022-2-20000000000002i−2i00
χ34222-2-2-22-2-2-2222-22-2-22i2i−2i−2i20000−2i2i00000000000000-2-222000000000000−2i2i00
χ35222-2-2-22-2-2-2222-22-2-2−2i−2i2i2i200002i−2i0000000000000022-2-2000000000000−2i2i00
χ36222-2-2-22-2-2-2222-22-2-2−2i−2i2i2i200002i−2i00000000000000-2-2220000000000002i−2i00
χ3744444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ38444-4-4-44-4-4444-44-4-440000-40000000000000000000000000000000000000000
χ3944-444-4-4-4404-4000-40000000000004-400000000000000000000000000000000
χ4044-444-4-4-4404-4000-4000000000000-4400000000000000000000000000000000
χ4144-444-4-4-4-40-44000400000000000000000000000000000000000000002i2−2i20000
χ4244-444-4-4-4-40-4400040000000000000000000000000000000000000000−2i22i20000
χ4344-4-4-44-4440-44000-4000000000000004i−4i000000000000000000000000000000
χ4444-4-4-44-4440-44000-400000000000000−4i4i000000000000000000000000000000
χ4544-4-4-44-44-404-400040000000000000000000000000000000000000022−22000000
χ4644-4-4-44-44-404-4000400000000000000000000000000000000000000−2222000000
χ474-444-4-4-440000000000000022−2222−22000000002i2−2i20000002i−2i2i−2i0000000000000000
χ484-444-4-4-440000000000000022−2222−2200000000−2i22i2000000−2i2i−2i2i0000000000000000
χ494-444-4-4-4400000000000000−2222−2222000000002i2−2i2000000−2i2i−2i2i0000000000000000
χ504-444-4-4-4400000000000000−2222−222200000000−2i22i20000002i−2i2i−2i0000000000000000
χ514-44-444-4-4000000000000002i2−2i2−2i22i2000000000022−2200002i−2i−2i2i0000000000000000
χ524-44-444-4-4000000000000002i2−2i2−2i22i20000000000−22220000−2i2i2i−2i0000000000000000
χ534-44-444-4-400000000000000−2i22i22i2−2i2000000000022−220000−2i2i2i−2i0000000000000000
χ544-44-444-4-400000000000000−2i22i22i2−2i20000000000−222200002i−2i−2i2i0000000000000000
χ554-4-44-444-404004-4-4004i−4i4i−4i00000000000000000000000000000000000000000
χ564-4-44-444-404004-4-400−4i4i−4i4i00000000000000000000000000000000000000000
χ574-4-44-444-40-400-4440000000000000000000000022−2222−2200000000000000000000
χ584-4-44-444-40-400-44400000000000000000000000−2222−222200000000000000000000
χ594-4-4-44-4440400-4-440000000000000000000000022−22−222200000000000000000000
χ604-4-4-44-4440400-4-4400000000000000000000000−222222−2200000000000000000000
χ614-4-4-44-4440-40044-4004-4-4400000000000000000000000000000000000000000
χ624-4-4-44-4440-40044-400-444-400000000000000000000000000000000000000000

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