Finite Group Databasebeta

← Group #147607

Character table — Group #147607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244444444444488888888888816161616161616161616161616161616161616161616
order12222222224444444444444444444444442244448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000000000
χ182222222222-2-2-2-222-2-222-2-2-2-222-2-22200000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-222-2-22222-2-200000000000000000000000000
χ212222-2-2-2-22222-2-22-22-22-22-2000000000000002-22-20000000000000000
χ222222-2-2-2-22222-2-22-22-22-22-200000000000000-22-220000000000000000
χ232222-2-2-2-22222-2-2-22-22-22-22000000000000002-2-220000000000000000
χ242222-2-2-2-22222-2-2-22-22-22-2200000000000000-222-20000000000000000
χ252222-2-2-2-222-2-2222-2-222-2-220000000022-2-22-200000000000000000000
χ262222-2-2-2-222-2-2222-2-222-2-2200000000-2-222-2200000000000000000000
χ272222-2-2-2-222-2-222-222-2-222-20000000022-2-2-2200000000000000000000
χ282222-2-2-2-222-2-222-222-2-222-200000000-2-2222-200000000000000000000
χ292-2-2222-2-2-222-22-2222-2-2-2-2200000000000000000000002i−2i2i−2i00000000
χ302-2-2222-2-2-222-22-2222-2-2-2-220000000000000000000000−2i2i−2i2i00000000
χ312-2-2222-2-2-222-22-2-2-2-22222-200000000000000000000002-2-2200000000
χ322-2-2222-2-2-222-22-2-2-2-22222-20000000000000000000000-222-200000000
χ332-2-2222-2-2-22-22-2222-22-2-22-20000000000000000002i−2i2i−2i000000000000
χ342-2-2222-2-2-22-22-2222-22-2-22-2000000000000000000−2i2i−2i2i000000000000
χ352-2-2222-2-2-22-22-22-2-22-222-220000000000000000002-2-22000000000000
χ362-2-2222-2-2-22-22-22-2-22-222-22000000000000000000-222-2000000000000
χ372-2-22-2-222-222-2-222-222-22-2-2000000000000000000000000002i−2i2i−2i0000
χ382-2-22-2-222-222-2-222-222-22-2-200000000000000000000000000−2i2i−2i2i0000
χ392-2-22-2-222-222-2-22-22-2-22-222000000000000000000000000002-2-220000
χ402-2-22-2-222-222-2-22-22-2-22-22200000000000000000000000000-222-20000
χ412-2-22-2-222-22-222-22-2-2-2-22220000000000000000000000000000002-22-2
χ422-2-22-2-222-22-222-22-2-2-2-2222000000000000000000000000000000-22-22
χ432-2-22-2-222-22-222-2-22222-2-2-20000000000000000000000000000002i−2i−2i2i
χ442-2-22-2-222-22-222-2-22222-2-2-2000000000000000000000000000000−2i2i2i−2i
χ4544444-44-4-4-4000000000000004i−4i000000000000000000000000000000
χ4644444-44-4-4-400000000000000−4i4i000000000000000000000000000000
χ474444-44-44-4-40000000000004i−4i00000000000000000000000000000000
χ484444-44-44-4-4000000000000−4i4i00000000000000000000000000000000
χ494-4-444-4-444-40000000000000000004i−4i00000000000000000000000000
χ504-4-444-4-444-4000000000000000000−4i4i00000000000000000000000000
χ514-4-44-444-44-400000000000000004i−4i0000000000000000000000000000
χ524-4-44-444-44-40000000000000000−4i4i0000000000000000000000000000
χ5388-8-800000000000000000000000000004i−4i0000000000000000000000
χ5488-8-80000000000000000000000000000−4i4i0000000000000000000000
χ558-88-8000000000000000000000000004i−4i000000000000000000000000
χ568-88-800000000000000000000000000−4i4i000000000000000000000000

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