Finite Group Databasebeta

← Group #242994

Character table — Group #242994

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222244444444224444444488888888224444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-111-1-1-1-111-1-1
χ10111111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-111
χ11111111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-111
χ12111111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1
χ13111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111-1-111
χ14111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-111-1-1
χ15111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ16111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-111-1-1-1-1-1-111
χ172222222222-2-2-2-2-2-22-22-2-222-200000000000000000000000000002i−2i2i−2i
χ182222222222-2-2-2-2-2-22-22-2-222-20000000000000000000000000000−2i2i−2i2i
χ1922222222-2-22222-2-2-2-2222-2-2-20000000000000000002-22-20000000000
χ2022222222-2-22222-2-2-2-2222-2-2-2000000000000000000-22-220000000000
χ2122222222-2-2-2-2-2-222-222-2-2-2-222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2222222222-2-2-2-2-2-222-222-2-2-2-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ23222222-2-222222222-2-2-2-2-22-2-20000000000000000002-2-220000000000
χ24222222-2-222222222-2-2-2-2-22-2-2000000000000000000-222-20000000000
χ25222222-2-222-2-2-2-2-2-2-22-2222-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ26222222-2-222-2-2-2-2-2-2-22-2222-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ27222222-2-2-2-2-2-2-2-2222-2-222-22-200000000000000000000000000002i−2i−2i2i
χ28222222-2-2-2-2-2-2-2-2222-2-222-22-20000000000000000000000000000−2i2i2i−2i
χ292222-2-2222222-2-22-2-22-22-2-22-200000000000000002i−2i000000002i−2i0000
χ302222-2-2222222-2-22-2-22-22-2-22-20000000000000000−2i2i00000000−2i2i0000
χ312222-2-22222-2-222-22-2-2-2-22-222000000002-22-200000000000000000000
χ322222-2-22222-2-222-22-2-2-2-22-22200000000-22-2200000000000000000000
χ332222-2-222-2-222-2-2-222-2-22-22-2200000000000000000000002i−2i2i−2i000000
χ342222-2-222-2-222-2-2-222-2-22-22-220000000000000000000000−2i2i−2i2i000000
χ352222-2-222-2-2-2-2222-222-2-222-2-20000000000002i−2i2i−2i0000000000000000
χ362222-2-222-2-2-2-2222-222-2-222-2-2000000000000−2i2i−2i2i0000000000000000
χ372222-2-2-2-22222-2-22-22-22-22-2-2200000000000000000000002i−2i−2i2i000000
χ382222-2-2-2-22222-2-22-22-22-22-2-220000000000000000000000−2i2i2i−2i000000
χ392222-2-2-2-222-2-222-222222-2-2-2-20000000000002i−2i−2i2i0000000000000000
χ402222-2-2-2-222-2-222-222222-2-2-2-2000000000000−2i2i2i−2i0000000000000000
χ412222-2-2-2-2-2-222-2-2-22-222-2222-200000000000000002i−2i00000000−2i2i0000
χ422222-2-2-2-2-2-222-2-2-22-222-2222-20000000000000000−2i2i000000002i−2i0000
χ432222-2-2-2-2-2-2-2-2222-2-2-222-2222000000002-2-2200000000000000000000
χ442222-2-2-2-2-2-2-2-2222-2-2-222-222200000000-222-200000000000000000000
χ454-4-444-400004-44-4000000000000002i2−2i22i2−2i2000000000000000000000000
χ464-4-444-400004-44-400000000000000−2i22i2−2i22i2000000000000000000000000
χ474-4-444-40000-44-440000000000000022−22−2222000000000000000000000000
χ484-4-444-40000-44-4400000000000000−222222−22000000000000000000000000
χ494-4-44-4400004-4-44000000000022−2222−220000000000000000000000000000
χ504-4-44-4400004-4-440000000000−2222−22220000000000000000000000000000
χ514-4-44-440000-444-400000000002i2−2i2−2i22i20000000000000000000000000000
χ524-4-44-440000-444-40000000000−2i22i22i2−2i20000000000000000000000000000
χ5388-8-800008i−8i0000000000000000000000000000000000000000000000
χ5488-8-80000−8i8i0000000000000000000000000000000000000000000000
χ558-88-8008i−8i000000000000000000000000000000000000000000000000
χ568-88-800−8i8i000000000000000000000000000000000000000000000000

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