Finite Group Databasebeta

← Group #499385

Character table — Group #499385

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222244448888888888881616161616161616111122222244448888888888881616161616161616
order122222444488882488161616161616161644448888222222444488882488161616161616161644448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-11111-1-1-1-111-1-111-1-111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ92222222222-2-2-2-222-2-200000000000000002222222222-2-2-2-222-2-20000000000000000
χ102222222222-2-2-2-2-2-22200000000000000002222222222-2-2-2-2-2-2220000000000000000
χ11222222-2-2-2-200002-200i2i2−i2−i2i2i2−i2−i200000000222222-2-2-2-200002-200i2i2−i2−i2i2i2−i2−i200000000
χ12222222-2-2-2-200002-200−i2−i2i2i2−i2−i2i2i200000000222222-2-2-2-200002-200−i2−i2i2i2−i2−i2i2i200000000
χ13222222-2-2-2-20000-2200i2i2−i2−i2−i2−i2i2i200000000222222-2-2-2-20000-2200i2i2−i2−i2−i2−i2i2i200000000
χ14222222-2-2-2-20000-2200−i2−i2i2i2i2i2−i2−i200000000222222-2-2-2-20000-2200−i2−i2i2i2i2i2−i2−i200000000
χ152222-2-222-2-22-22-20000000000000000002i−2i2222-2-222-2-22-22-20000000000000000002i−2i
χ162222-2-222-2-22-22-2000000000000000000−2i2i2222-2-222-2-22-22-2000000000000000000−2i2i
χ172222-2-222-2-2-22-2200000000000000002i−2i002222-2-222-2-2-22-2200000000000000002i−2i00
χ182222-2-222-2-2-22-220000000000000000−2i2i002222-2-222-2-2-22-220000000000000000−2i2i00
χ192-22-22-2-222-22-2-22000000000000002i−2i00002-22-22-2-222-22-2-22000000000000002i−2i0000
χ202-22-22-2-222-22-2-2200000000000000−2i2i00002-22-22-2-222-22-2-2200000000000000−2i2i0000
χ212-22-22-2-222-2-222-20000000000002i−2i0000002-22-22-2-222-2-222-20000000000002i−2i000000
χ222-22-22-2-222-2-222-2000000000000−2i2i0000002-22-22-2-222-2-222-2000000000000−2i2i000000
χ232-22-2-222-22-20000002i−2i2−22−2i2−i2i2−i2000000002-22-2-222-22-20000002i−2i2−22−2i2−i2i2−i200000000
χ242-22-2-222-22-20000002i−2i−22−22−i2i2−i2i2000000002-22-2-222-22-20000002i−2i−22−22−i2i2−i2i200000000
χ252-22-2-222-22-2000000−2i2i2−22−2−i2i2−i2i2000000002-22-2-222-22-2000000−2i2i2−22−2−i2i2−i2i200000000
χ262-22-2-222-22-2000000−2i2i−22−22i2−i2i2−i2000000002-22-2-222-22-2000000−2i2i−22−22i2−i2i2−i200000000
χ272-22-2-22-22-2222-2-200002i−2i−2i2i0000000000002-22-2-22-22-2222-2-200002i−2i−2i2i000000000000
χ282-22-2-22-22-2222-2-20000−2i2i2i−2i0000000000002-22-2-22-22-2222-2-20000−2i2i2i−2i000000000000
χ292-22-2-22-22-22-2-222000000002-2-22000000002-22-2-22-22-22-2-222000000002-2-2200000000
χ302-22-2-22-22-22-2-22200000000-222-2000000002-22-2-22-22-22-2-22200000000-222-200000000
χ314444-4-4-4-4440000000000000000000000004444-4-4-4-444000000000000000000000000
χ324-44-44-44-4-440000000000000000000000004-44-44-44-4-44000000000000000000000000
χ3388-8-800000000000000000000000000000088-8-8000000000000000000000000000000
χ348-8-880000000000000000000000000000008-8-88000000000000000000000000000000
χ351111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ37111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ38111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ3911111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ4011111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ4111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ4211111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ432222222222-2-2-2-222-2-20000000000000000-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000
χ442222222222-2-2-2-2-2-2220000000000000000-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000
χ45222222-2-2-2-200002-200i2i2−i2−i2i2i2−i2−i200000000-2-2-2-2-2-222220000-2200−i2−i2i2i2−i2−i2i2i200000000
χ46222222-2-2-2-200002-200−i2−i2i2i2−i2−i2i2i200000000-2-2-2-2-2-222220000-2200i2i2−i2−i2i2i2−i2−i200000000
χ47222222-2-2-2-20000-2200i2i2−i2−i2−i2−i2i2i200000000-2-2-2-2-2-2222200002-200−i2−i2i2i2i2i2−i2−i200000000
χ48222222-2-2-2-20000-2200−i2−i2i2i2i2i2−i2−i200000000-2-2-2-2-2-2222200002-200i2i2−i2−i2−i2−i2i2i200000000
χ492222-2-222-2-22-22-20000000000000000002i−2i-2-2-2-222-2-222-22-22000000000000000000−2i2i
χ502222-2-222-2-22-22-2000000000000000000−2i2i-2-2-2-222-2-222-22-220000000000000000002i−2i
χ512222-2-222-2-2-22-2200000000000000002i−2i00-2-2-2-222-2-2222-22-20000000000000000−2i2i00
χ522222-2-222-2-2-22-220000000000000000−2i2i00-2-2-2-222-2-2222-22-200000000000000002i−2i00
χ532-22-22-2-222-22-2-22000000000000002i−2i0000-22-22-222-2-22-222-200000000000000−2i2i0000
χ542-22-22-2-222-22-2-2200000000000000−2i2i0000-22-22-222-2-22-222-2000000000000002i−2i0000
χ552-22-22-2-222-2-222-20000000000002i−2i000000-22-22-222-2-222-2-22000000000000−2i2i000000
χ562-22-22-2-222-2-222-2000000000000−2i2i000000-22-22-222-2-222-2-220000000000002i−2i000000
χ572-22-2-222-22-20000002i−2i2−22−2i2−i2i2−i200000000-22-222-2-22-22000000−2i2i−22−22−i2i2−i2i200000000
χ582-22-2-222-22-20000002i−2i−22−22−i2i2−i2i200000000-22-222-2-22-22000000−2i2i2−22−2i2−i2i2−i200000000
χ592-22-2-222-22-2000000−2i2i2−22−2−i2i2−i2i200000000-22-222-2-22-220000002i−2i−22−22i2−i2i2−i200000000
χ602-22-2-222-22-2000000−2i2i−22−22i2−i2i2−i200000000-22-222-2-22-220000002i−2i2−22−2−i2i2−i2i200000000
χ612-22-2-22-22-2222-2-200002i−2i−2i2i000000000000-22-222-22-22-2-2-2220000−2i2i2i−2i000000000000
χ622-22-2-22-22-2222-2-20000−2i2i2i−2i000000000000-22-222-22-22-2-2-22200002i−2i−2i2i000000000000
χ632-22-2-22-22-22-2-222000000002-2-2200000000-22-222-22-22-222-2-200000000-222-200000000
χ642-22-2-22-22-22-2-22200000000-222-200000000-22-222-22-22-222-2-2000000002-2-2200000000
χ654444-4-4-4-444000000000000000000000000-4-4-4-44444-4-4000000000000000000000000
χ664-44-44-44-4-44000000000000000000000000-44-44-44-444-4000000000000000000000000
χ6788-8-8000000000000000000000000000000-8-888000000000000000000000000000000
χ688-8-88000000000000000000000000000000-888-8000000000000000000000000000000

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