Finite Group Databasebeta

← Group #288621

Character table — Group #288621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222224444444444444888888888881616161616161616161616161616161616163232
order12222244444444488888888884444888888822444488888888888824
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-111-1-111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-11-1-111-1-1111-1-1-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-11-1-11-11111-1-1-1-1-1-1-111
χ6111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1111-1-11111111-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-111-11111-1-1-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-111-11-1-1-1-11-1-1-1-11111
χ9111111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-11-111-1111-1-1-1111-1-1-1-11-1
χ10111111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-11-1-11-1-1-11-111-1-1-11111-11
χ11111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-111-111-1111-11-1-11-1-111-1-1-11
χ12111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-111-11-1-11-1-1-1111-111-1-1111-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-111-11-1-1-1-1-1-111111-1
χ14111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-11-1-11-111-111111-1-1-1-1-11
χ15111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111-111-11-1-11-1-1-111-1-111-11
χ16111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-11-1-11-11111-1-111-1-11-1
χ172222222-2222-2-2-2-222-2-2-2-20000000020022-2-20000000-2200000000000
χ182222222-2222-2-2-2-222-2-2-2-200000000200-2-22200000002-200000000000
χ192222222-2222-2-2-2-2-2-2222200000000-20022220000000-2-200000000000
χ202222222-2222-2-2-2-2-2-2222200000000-200-2-2-2-200000002200000000000
χ21222222-2-2-2-2-2-22-220000002i2i−2i−2i000002i−2i00000000000002i−2i000002-200
χ22222222-2-2-2-2-2-22-220000002i2i−2i−2i000002i−2i0000000000000−2i2i00000-2200
χ23222222-2-2-2-2-2-22-22000000−2i−2i2i2i00000−2i2i00000000000002i−2i00000-2200
χ24222222-2-2-2-2-2-22-22000000−2i−2i2i2i00000−2i2i0000000000000−2i2i000002-200
χ252222-2-222-22-22-2-222222-2-200000000-2000000220-2-2000000000000000
χ262222-2-222-22-22-2-222222-2-200000000-2000000-2-2022000000000000000
χ272222-2-222-22-22-2-22-2-2-2-2220000000020000002-20-22000000000000000
χ282222-2-222-22-22-2-22-2-2-2-222000000002000000-2202-2000000000000000
χ292222-2-22-2-22-2-222-222-2-2222i2i−2i−2i2i2i−2i−2i-2−2i2i000000000000000000000000
χ302222-2-22-2-22-2-222-222-2-222−2i−2i2i2i−2i−2i2i2i-22i−2i000000000000000000000000
χ312222-2-22-2-22-2-222-2-2-222-2-22i2i−2i−2i−2i−2i2i2i2−2i2i000000000000000000000000
χ322222-2-22-2-22-2-222-2-2-222-2-2−2i−2i2i2i2i2i−2i−2i22i−2i000000000000000000000000
χ332222-2-2-222-2222-2-2000000222200000-2-2000000200-220000-200000000
χ342222-2-2-222-2222-2-2000000222200000-2-2000000-2002-20000200000000
χ352222-2-2-222-2222-2-2000000-2-2-2-20000022000000200-2-20000200000000
χ362222-2-2-222-2222-2-2000000-2-2-2-20000022000000-200220000-200000000
χ37444444-44-4-4-44-44-400000000000000000000000000000000000000000
χ384444-4-4-4-44-44-4-44400000000000000000000000000000000000000000
χ394-44-44-440-4-440000000000000000000000000000000000000002i2−2i20000
χ404-44-44-440-4-44000000000000000000000000000000000000000−2i22i20000
χ414-44-44-4-4044-40000000000000000000004i−4i0000000000000000000000
χ424-44-44-4-4044-4000000000000000000000−4i4i0000000000000000000000
χ434-44-4-44404-4-400000000000000000000000000000000000002i2−2i2000000
χ444-44-4-44404-4-40000000000000000000000000000000000000−2i22i2000000
χ454-44-4-44-40-444000000000000000000000004-400000000000000000000
χ464-44-4-44-40-44400000000000000000000000-4400000000000000000000
χ474-4-440004000-400022−2222−22002i2−2i22i2−2i22i−2i2i−2i000000000000000000000000000
χ484-4-440004000-400022−2222−2200−2i22i2−2i22i2−2i2i−2i2i000000000000000000000000000
χ494-4-440004000-4000−2222−2222002i2−2i22i2−2i2−2i2i−2i2i000000000000000000000000000
χ504-4-440004000-4000−2222−222200−2i22i2−2i22i22i−2i2i−2i000000000000000000000000000
χ514-4-44000-4000400022−22−22220022−22−22222-2-22000000000000000000000000000
χ524-4-44000-4000400022−22−222200−222222−22-222-2000000000000000000000000000
χ534-4-44000-40004000−222222−220022−22−2222-222-2000000000000000000000000000
χ544-4-44000-40004000−222222−2200−222222−222-2-22000000000000000000000000000
χ5588-8-80000000000000004i2−4i200000000000000000000000000000000000
χ5688-8-8000000000000000−4i24i200000000000000000000000000000000000

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