Finite Group Databasebeta

← Group #288633

Character table — Group #288633

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222224444444444444888888888881616161616161616161616161616161616163232
order12222244444444488888888884444888888822444488888888888844
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-111-11-11-1-11-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1111-1-1-11-1-11-11-111-11-1-1-1-111-1-1
χ411111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111-1-1-1-1-1-1-1-1111-1-111-11-1-11-1-11111-1-1-1-1-1-1-111
χ6111111111111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-111-1-111111111-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-111-1-11111-1-1-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-111-111-1-1-1-11-1-1-1-11111
χ9111111111111111-1-1-1-1-1-11111-1-1-1-111-111-1-1-111-1111-1-1-11111-1-1-1-11-1
χ10111111111111111-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-11-1-11-1-1111-1-1-11111-11
χ11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-111-111-1-1-11-1-111-1-1-11
χ12111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-11-1-1-1111-1-111-1-1111-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-111-1-1-1-1-11-1-1-111111-1
χ14111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11-1-11-1111111-1-1-1-1-11
χ15111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111-111-11-1-1-1-111-1-111-11
χ16111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-11-1-111111-11-1-111-1-11-1
χ172222222-2222-2-2-2-22222-2-20000000022-200220000000-200-2000000000
χ182222222-2222-2-2-2-22222-2-200000000-2-2-200-2-200000002002000000000
χ192222222-2222-2-2-2-2-2-2-2-2220000000022200-2-20000000200-2000000000
χ202222222-2222-2-2-2-2-2-2-2-22200000000-2-2200220000000-2002000000000
χ21222222-2-2-2-2-2-22-220000002i2i−2i−2i00000002i−2i00000000002i−2i0000002-200
χ22222222-2-2-2-2-2-22-220000002i2i−2i−2i00000002i−2i0000000000−2i2i000000-2200
χ23222222-2-2-2-2-2-22-22000000−2i−2i2i2i0000000−2i2i00000000002i−2i000000-2200
χ24222222-2-2-2-2-2-22-22000000−2i−2i2i2i0000000−2i2i0000000000−2i2i0000002-200
χ252222-2-222-22-22-2-2222-2-2220000000000-2000020-2-20200000000000000
χ262222-2-222-22-22-2-2222-2-2220000000000-20000-20220-200000000000000
χ272222-2-222-22-22-2-22-2-222-2-2000000000020000202-20-200000000000000
χ282222-2-222-22-22-2-22-2-222-2-2000000000020000-20-220200000000000000
χ292222-2-22-2-22-2-222-222-2-2-2-22i2i−2i−2i2i2i−2i−2i002−2i2i0000000000000000000000
χ302222-2-22-2-22-2-222-222-2-2-2-2−2i−2i2i2i−2i−2i2i2i0022i−2i0000000000000000000000
χ312222-2-22-2-22-2-222-2-2-222222i2i−2i−2i−2i−2i2i2i00-2−2i2i0000000000000000000000
χ322222-2-22-2-22-2-222-2-2-22222−2i−2i2i2i2i2i−2i−2i00-22i−2i0000000000000000000000
χ332222-2-2-222-2222-2-200000022220000000-2-2000200-20-20000200000000
χ342222-2-2-222-2222-2-200000022220000000-2-2000-2002020000-200000000
χ352222-2-2-222-2222-2-2000000-2-2-2-2000000022000200-2020000-200000000
χ362222-2-2-222-2222-2-2000000-2-2-2-2000000022000-20020-20000200000000
χ37444444-44-4-4-44-44-400000000000000000000000000000000000000000
χ384444-4-4-4-44-44-4-44400000000000000000000000000000000000000000
χ394-44-44-4404-4-400000000000000000000000000000000000000022−220000
χ404-44-44-4404-4-4000000000000000000000000000000000000000−22220000
χ414-44-44-4-40-4440000000000000000004i−4i0000000000000000000000000
χ424-44-44-4-40-444000000000000000000−4i4i0000000000000000000000000
χ434-44-4-4440-4-4400000000000000000000000000000000000002i2−2i2000000
χ444-44-4-4440-4-440000000000000000000000000000000000000−2i22i2000000
χ454-44-4-44-4044-4000000000000000000000004i−4i00000000000000000000
χ464-44-4-44-4044-400000000000000000000000−4i4i00000000000000000000
χ474-4-440004000-400022−220022−222i2−2i22i2−2i22i−2i2i−2i000000000000000000000000000
χ484-4-440004000-400022−220022−22−2i22i2−2i22i2−2i2i−2i2i000000000000000000000000000
χ494-4-440004000-4000−222200−22222i2−2i22i2−2i2−2i2i−2i2i000000000000000000000000000
χ504-4-440004000-4000−222200−2222−2i22i2−2i22i22i−2i2i−2i000000000000000000000000000
χ514-4-44000-4000400022−2200−222222−22−22222-2-22000000000000000000000000000
χ524-4-44000-4000400022−2200−2222−222222−22-222-2000000000000000000000000000
χ534-4-44000-40004000−22220022−2222−22−2222-222-2000000000000000000000000000
χ544-4-44000-40004000−22220022−22−222222−222-2-22000000000000000000000000000
χ5588-8-8000000000000042−420000000000000000000000000000000000000
χ5688-8-80000000000000−42420000000000000000000000000000000000000

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