Finite Group Databasebeta

← Group #291306

Character table — Group #291306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222222244444444444444888888884444444444444444448888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-11-111-1-1111111-1-1-1-1
χ5111111111111111111111-1-1-1-1111111111-111-11-1-1-1-1-11-1-1-11111-1-1-1-1
χ6111111111111111111111-1-1-1-1111111111-1-1-11-11-1111-1111-1-1-1-1-1-1-1-1
χ7111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-111-11-1-1-1111-111-1-1-1-11111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-11-1-111111111
χ9111111111111-1-111-1-111-11111-11111-1-1-1-1-111-1-11-1-111-11-1-111-1-111-1-1
χ10111111111111-1-111-1-111-11111-11111-1-1-1-1-1-1-111-1-11-1-11-111-1-11111-1-1
χ11111111111111-1-111-1-111-11111-1-1-1-1-11111-111-1-11-1-1-1-1-1111-1-111-1-111
χ12111111111111-1-111-1-111-11111-1-1-1-1-11111-1-1-111-1-11111-1-1-111-1-1-1-111
χ13111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ14111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1111-11111-1-1-1-111-1-111
χ15111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1
χ16111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1111-1-1-1111111-1-111-1-1
χ1722222222222222-2-2-2-2-2-2222-2-2-200000000200000-2000000000000000
χ1822222222222222-2-2-2-2-2-22-2-222-200000000-2000002000000000000000
χ19222222222222-2-2-2-222-2-2-222-2-2200000000-2000002000000000000000
χ20222222222222-2-2-2-222-2-2-2-2-222200000000200000-2000000000000000
χ2122222222-2-2-2-2222-2222-2-20000-2000000000002020-2000-20000000000
χ2222222222-2-2-2-2222-2222-2-20000-200000000000-20-20200020000000000
χ2322222222-2-2-2-222-22-2-2-22-2000020000000002-20200000-200000000000
χ2422222222-2-2-2-222-22-2-2-22-200002000000000-220-200000200000000000
χ2522222222-2-2-2-2-2-22-2-2-22-22000020000000000020-20-200020000000000
χ2622222222-2-2-2-2-2-22-2-2-22-220000200000000000-20202000-20000000000
χ2722222222-2-2-2-2-2-2-2222-2220000-20000000002-20-200000200000000000
χ2822222222-2-2-2-2-2-2-2222-2220000-2000000000-220200000-200000000000
χ2922-2-2-22-222-22-2002-200-2202i−2i2i−2i02i2i−2i−2i00000000000000000000002-200
χ3022-2-2-22-222-22-2002-200-2202i−2i2i−2i0−2i−2i2i2i0000000000000000000000-2200
χ3122-2-2-22-222-22-2002-200-220−2i2i−2i2i02i2i−2i−2i0000000000000000000000-2200
χ3222-2-2-22-222-22-2002-200-220−2i2i−2i2i0−2i−2i2i2i00000000000000000000002-200
χ3322-2-2-22-222-22-200-22002-202i−2i−2i2i0000022-2-2000000000000000000002i−2i
χ3422-2-2-22-222-22-200-22002-202i−2i−2i2i00000-2-22200000000000000000000−2i2i
χ3522-2-2-22-222-22-200-22002-20−2i2i2i−2i0000022-2-200000000000000000000−2i2i
χ3622-2-2-22-222-22-200-22002-20−2i2i2i−2i00000-2-222000000000000000000002i−2i
χ374444-4-4-4-44-4-4400000000000000000022−2222−220000000000000000000000
χ384444-4-4-4-44-4-44000000000000000000−2222−22220000000000000000000000
χ394444-4-4-4-4-444-40000000000000022−2222−2200000000000000000000000000
χ404444-4-4-4-4-444-400000000000000−2222−222200000000000000000000000000
χ4144-4-44-44-444-4-400000000000000000022−22−22220000000000000000000000
χ4244-4-44-44-444-4-4000000000000000000−222222−220000000000000000000000
χ4344-4-44-44-4-4-444000000000000002i2−2i2−2i22i200000000000000000000000000
χ4444-4-44-44-4-4-44400000000000000−2i22i22i2−2i200000000000000000000000000
χ4544-4-4-44-44-44-44004400-4-4000000000000000000000000000000000000
χ4644-4-4-44-44-44-4400-4-40044000000000000000000000000000000000000
χ474-44-44-4-4400004i−4i00000000000000000000000000000000002i−2i2-20000
χ484-44-44-4-4400004i−4i0000000000000000000000000000000000−2i2i-220000
χ494-44-44-4-440000−4i4i00000000000000000000000000000000002i−2i-220000
χ504-44-44-4-440000−4i4i0000000000000000000000000000000000−2i2i2-20000
χ514-44-4-444-4000000004i−4i0000000000000000000000002-2002i−2i00000000
χ524-44-4-444-4000000004i−4i000000000000000000000000-2200−2i2i00000000
χ534-44-4-444-400000000−4i4i0000000000000000000000002-200−2i2i00000000
χ544-44-4-444-400000000−4i4i000000000000000000000000-22002i−2i00000000
χ558-8-8888-8-8000000000000000000000000000000000000000000000000
χ568-8-88-8-888000000000000000000000000000000000000000000000000

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