Finite Group Databasebeta

← Group #325248

Character table — Group #325248

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222222244444488888888888888888816161616161616161616161632323232
order12222222444444444444444488888888888888884444888888884444
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1
χ9111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ11111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ12111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-111-1-11-1-11
χ1722222222222-2-2-2-22-2-222-2-22-222-2-22200000000-2-20000000000000000
χ1822222222222-2-2-2-22-2-222-2-22-2-2-222-2-200000000220000000000000000
χ1922222222222-2-2-2-22-2-2-2-222-2222-2-2-2-200000000220000000000000000
χ2022222222222-2-2-2-22-2-2-2-222-22-2-2222200000000-2-20000000000000000
χ2122222222-2-2-22222-2-2-22222-2-200000000000000002-22-2000000000000
χ2222222222-2-2-22222-2-2-22222-2-20000000000000000-22-22000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-22200000000000000002-2-22000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2220000000000000000-222-2000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-220000000000000000000000002i−2i2i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-22000000000000000000000000−2i2i−2i2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-2222-20000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-222-2-2222-2000000000000000000000000−2i2i2i−2i0000
χ292222-2-2-2-222-222-2-2-22-20000002-22-200000022-2-2000000002-200000000
χ302222-2-2-2-222-222-2-2-22-20000002-22-2000000-2-22200000000-2200000000
χ312222-2-2-2-222-222-2-2-22-2000000-22-2200000022-2-200000000-2200000000
χ322222-2-2-2-222-222-2-2-22-2000000-22-22000000-2-222000000002-200000000
χ332222-2-2-2-222-2-2-222-2-220000002-2-220022-2-200000000002-20000000000
χ342222-2-2-2-222-2-2-222-2-220000002-2-2200-2-2220000000000-220000000000
χ352222-2-2-2-222-2-2-222-2-22000000-222-20022-2-20000000000-220000000000
χ362222-2-2-2-222-2-2-222-2-22000000-222-200-2-22200000000002-20000000000
χ374444-4-4-4-4-4-4444-4-44-4400000000000000000000000000000000000000
χ384444-4-4-4-4-4-44-4-44444-400000000000000000000000000000000000000
χ3944-4-444-4-44-440000-40000000000000022−2222−220000000000000000000000
χ4044-4-444-4-44-440000-400000000000000−2222−22220000000000000000000000
χ4144-4-444-4-4-44-4000040000000000000000002i2−2i22i2−2i2000000000000000000
χ4244-4-444-4-4-44-400004000000000000000000−2i22i2−2i22i2000000000000000000
χ4344-4-4-4-4444-4-4000040000000000000022−22−22220000000000000000000000
χ4444-4-4-4-4444-4-40000400000000000000−222222−220000000000000000000000
χ4544-4-4-4-444-4440000-40000000000000000002i2−2i2−2i22i2000000000000000000
χ4644-4-4-4-444-4440000-4000000000000000000−2i22i22i2−2i2000000000000000000
χ474-44-44-4-440004-44-40004i−4i4i−4i0000000000000000000000000000000000
χ484-44-44-4-440004-44-4000−4i4i−4i4i0000000000000000000000000000000000
χ494-44-44-4-44000-44-440004i−4i−4i4i0000000000000000000000000000000000
χ504-44-44-4-44000-44-44000−4i4i4i−4i0000000000000000000000000000000000
χ514-44-4-444-40004-4-4400000000000002i2−2i2000000002i2−2i20000000000000000
χ524-44-4-444-40004-4-440000000000000−2i22i200000000−2i22i20000000000000000
χ534-44-4-444-4000-444-400000000000002i2−2i200000000−2i22i20000000000000000
χ544-44-4-444-4000-444-40000000000000−2i22i2000000002i2−2i20000000000000000
χ558-8-888-88-8000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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