Finite Group Databasebeta

← Group #394686

Character table — Group #394686

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size112222222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222244444444222244442244444444444444888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111
χ911111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111
χ1011111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111
χ1211111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1
χ1411111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111
χ1511111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1
χ1611111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111
χ172222-22-2-2-222-2-222-2-222-2-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ182222-22-2-2-222-2-222-2-222-2-222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ192222-22-2-2-222-2-222-2-2-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ202222-22-2-2-222-2-222-2-2-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ21222-22-22-2-22-22-22-22-22-22-22-22-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ22222-22-22-2-22-22-22-22-22-22-22-22-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ23222-22-22-2-22-22-22-22-2-22-22-22-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ24222-22-22-2-22-22-22-22-2-22-22-22-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ25222-2-2-2-2222-2-222-2-222-2-222-2-222-22-222-2-200000000000000000000000000000000
χ26222-2-2-2-2222-2-222-2-222-2-222-2-22-22-22-2-22200000000000000000000000000000000
χ27222-2-2-2-2222-2-222-2-22-222-2-222-22-22-2-2-22200000000000000000000000000000000
χ28222-2-2-2-2222-2-222-2-22-222-2-222-2-22-2222-2-200000000000000000000000000000000
χ2922-222-2-2-222-2-2-2-22220000000022-2-2000000002-22-200002-22-20000000000000000
χ3022-222-2-2-222-2-2-2-22220000000022-2-200000000-22-220000-22-220000000000000000
χ3122-222-2-2-222-2-2-2-222200000000-2-222000000002-22-20000-22-220000000000000000
χ3222-222-2-2-222-2-2-2-222200000000-2-22200000000-22-2200002-22-20000000000000000
χ3322-222-2-2-22-22222-2-2-22222-2-2-2-20000000000000000000000000000002i−2i00002i−2i00
χ3422-222-2-2-22-22222-2-2-22222-2-2-2-2000000000000000000000000000000−2i2i0000−2i2i00
χ3522-222-2-2-22-22222-2-2-2-2-2-2-222220000000000000000000000000000002i−2i0000−2i2i00
χ3622-222-2-2-22-22222-2-2-2-2-2-2-22222000000000000000000000000000000−2i2i00002i−2i00
χ3722-22-2-222-22-222-22-2-20000000000002-22-22i−2i2i−2i000000002i−2i−2i2i0000000000000000
χ3822-22-2-222-22-222-22-2-20000000000002-22-2−2i2i−2i2i00000000−2i2i2i−2i0000000000000000
χ3922-22-2-222-22-222-22-2-2000000000000-22-222i−2i2i−2i00000000−2i2i2i−2i0000000000000000
χ4022-22-2-222-22-222-22-2-2000000000000-22-22−2i2i−2i2i000000002i−2i−2i2i0000000000000000
χ4122-22-2-222-2-22-2-22-22222-2-2-2-2220000000000000000000000002-20000002-2000000
χ4222-22-2-222-2-22-2-22-22222-2-2-2-222000000000000000000000000-22000000-22000000
χ4322-22-2-222-2-22-2-22-222-2-22222-2-20000000000000000000000002-2000000-22000000
χ4422-22-2-222-2-22-2-22-222-2-22222-2-2000000000000000000000000-220000002-2000000
χ4522-2-222-22-222-22-2-22-20000000000002-2-2200002i−2i−2i2i2i−2i2i−2i00000000000000000000
χ4622-2-222-22-222-22-2-22-20000000000002-2-220000−2i2i2i−2i−2i2i−2i2i00000000000000000000
χ4722-2-222-22-222-22-2-22-2000000000000-222-200002i−2i−2i2i−2i2i−2i2i00000000000000000000
χ4822-2-222-22-222-22-2-22-2000000000000-222-20000−2i2i2i−2i2i−2i2i−2i00000000000000000000
χ4922-2-222-22-2-2-22-222-222-22-2-22-22000000000000000000000000002-200000000002-2
χ5022-2-222-22-2-2-22-222-222-22-2-22-2200000000000000000000000000-220000000000-22
χ5122-2-222-22-2-2-22-222-22-22-222-22-2000000000000000000000000002-20000000000-22
χ5222-2-222-22-2-2-22-222-22-22-222-22-200000000000000000000000000-2200000000002-2
χ5322-2-2-222-22222-2-2-2-22000000002-2-2200002-2-2200002-2-2200000000000000000000
χ5422-2-2-222-22222-2-2-2-22000000002-2-220000-222-20000-222-200000000000000000000
χ5522-2-2-222-22222-2-2-2-2200000000-222-200002-2-220000-222-200000000000000000000
χ5622-2-2-222-22222-2-2-2-2200000000-222-20000-222-200002-2-2200000000000000000000
χ5722-2-2-222-22-2-2-22222-22-2-22-222-200000000000000000000000000002-200002-20000
χ5822-2-2-222-22-2-2-22222-22-2-22-222-20000000000000000000000000000-220000-220000
χ5922-2-2-222-22-2-2-22222-2-222-22-2-2200000000000000000000000000002-20000-220000
χ6022-2-2-222-22-2-2-22222-2-222-22-2-220000000000000000000000000000-2200002-20000
χ61444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ624444-44-4-4-4-4-444-4-444000000000000000000000000000000000000000000000000
χ63444-44-44-4-4-44-44-44-44000000000000000000000000000000000000000000000000
χ64444-4-4-4-444-444-4-444-4000000000000000000000000000000000000000000000000
χ6516-16000000000000000000000000000000000000000000000000000000000000000

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