Finite Group Databasebeta

← Group #315213

Character table — Group #315213

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444444444444444444441616161616161616161616161616161632323232
order12222222444444444488888888888888888888888824444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-111-1-1-1111-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-11-1-1111-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-1-1-11-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1111-1-1-1-111-1-1-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-11111-1-111-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111111-11-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-111111111-1-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-111-1-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-1111-1-111-1-1-111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111111-1-1-1-11-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-111111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-1-1-111-1-111-111-1
χ17222222222-2-22-2-222-2-2000000002222-2-2-2-2000000000200-22-20000000000000
χ18222222222-2-22-2-222-2-2000000002222-2-2-2-2000000000-2002-220000000000000
χ19222222222-2-22-2-222-2-200000000-2-2-2-22222000000000200-2-220000000000000
χ20222222222-2-22-2-222-2-200000000-2-2-2-22222000000000-20022-20000000000000
χ2122222222-222-222-2-2-2-22222-2-2-2-20000000000000000202-2000-2000000000000
χ2222222222-222-222-2-2-2-22222-2-2-2-20000000000000000-20-220002000000000000
χ2322222222-222-222-2-2-2-2-2-2-2-22222000000000000000020-22000-2000000000000
χ2422222222-222-222-2-2-2-2-2-2-2-222220000000000000000-202-20002000000000000
χ25222-2-2-2-222-2-2-2222-2-222i2i−2i−2i2i2i−2i−2i0000000000000000000000002-200002i−2i0000
χ26222-2-2-2-222-2-2-2222-2-222i2i−2i−2i2i2i−2i−2i000000000000000000000000-220000−2i2i0000
χ27222-2-2-2-222-2-2-2222-2-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-20000−2i2i0000
χ28222-2-2-2-222-2-2-2222-2-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000-2200002i−2i0000
χ29222-2-2-2-22-2222-2-2-22-220000000022-2-222-2-20000000000000000002i−2i2i−2i000000
χ30222-2-2-2-22-2222-2-2-22-220000000022-2-222-2-2000000000000000000−2i2i−2i2i000000
χ31222-2-2-2-22-2222-2-2-22-2200000000-2-222-2-2220000000000000000002i−2i−2i2i000000
χ32222-2-2-2-22-2222-2-2-22-2200000000-2-222-2-222000000000000000000−2i2i2i−2i000000
χ33222-2-2-2-22-2-2-2222-222-22i2i−2i−2i−2i−2i2i2i22-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000000000
χ34222-2-2-2-22-2-2-2222-222-22i2i−2i−2i−2i−2i2i2i-2-22222-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ35222-2-2-2-22-2-2-2222-222-2−2i−2i2i2i2i2i−2i−2i22-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ36222-2-2-2-22-2-2-2222-222-2−2i−2i2i2i2i2i−2i−2i-2-22222-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ38444-4-4-4-44444-4-4-44-44-400000000000000000000000000000000000000000000
χ3944-444-4-4-40000000000000022−2222−2222−2222−22000022-2-222-2-200000000000000000000
χ4044-444-4-4-40000000000000022−2222−22−2222−22220000-2-222-2-22200000000000000000000
χ4144-444-4-4-400000000000000−2222−222222−2222−220000-2-222-2-22200000000000000000000
χ4244-444-4-4-400000000000000−2222−2222−2222−2222000022-2-222-2-200000000000000000000
χ4344-4-4-444-4000000000000002i2−2i2−2i22i222−22−22220000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4444-4-4-444-4000000000000002i2−2i2−2i22i2−222222−2200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4544-4-4-444-400000000000000−2i22i22i2−2i222−22−222200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4644-4-4-444-400000000000000−2i22i22i2−2i2−222222−220000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ474-444-44-4-404-404-40000000000000000000022−2222−2222−2222−2200000000000000000000
χ484-444-44-4-404-404-400000000000000000000−2222−2222−2222−222200000000000000000000
χ494-444-44-4-40-440-4400004-44-40000000000000000000000000000000000000000
χ504-444-44-4-40-440-440000-44-440000000000000000000000000000000000000000
χ514-44-44-44-404-40-4400004i−4i−4i4i0000000000000000000000000000000000000000
χ524-44-44-44-404-40-440000−4i4i4i−4i0000000000000000000000000000000000000000
χ534-44-44-44-40-4404-4000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000
χ544-44-44-44-40-4404-400000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000
χ554-4-44-4-444400-400-44000000000000004-44-40000000000000000000000000000
χ564-4-44-4-444400-400-4400000000000000-44-440000000000000000000000000000
χ574-4-44-4-444-4004004-400000000000000000022−22−222222−22−222200000000000000000000
χ584-4-44-4-444-4004004-4000000000000000000−222222−22−222222−2200000000000000000000
χ594-4-4-444-44400400-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000
χ604-4-4-444-44400400-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000
χ614-4-4-444-44-400-40044000000000000004-4-440000000000000000000000000000
χ624-4-4-444-44-400-4004400000000000000-444-40000000000000000000000000000

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