Finite Group Databasebeta

← Group #130708

Character table — Group #130708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222244444444444444488888888888881616161616161616161616161632323232
order12222244224444444444444244444444444424444444488888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i
χ41111111111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii
χ5111111111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11-1-111111111-1-1-1-1
χ6111111111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-111ii−i−iii−i−i−i−iii
χ8111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-111−i−iii−i−iiiii−i−i
χ91111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1111-1-1-11111-1-1-1-11-11-1
χ101111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-11111-11-11
χ111111111111-1-1-1-111111-1-1-1-1-11-1-111-1-1-1-111-1-1-1111ii−i−i−i−iiii−i−ii
χ121111111111-1-1-1-111111-1-1-1-1-11-1-111-1-1-1-111-1-1-1111−i−iiiii−i−i−iii−i
χ131111111111-1-1-1-11-1-1-1-1111111-1-1-1-11111-1-11-1-1-1111111-1-1-1-1-11-11
χ141111111111-1-1-1-11-1-1-1-1111111-1-1-1-11111-1-11-1-1-111-1-1-1-111111-11-1
χ151111111111-1-1-1-11-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1111-1-1ii−i−i−i−iii−iii−i
χ161111111111-1-1-1-11-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1111-1-1−i−iiiii−i−ii−i−ii
χ1722222222-2-200002222222-2-22-200-2-2000000-22-2000000000000000
χ1822222222-2-2000022222-2-222-2-200-2-20000002-22000000000000000
χ1922222222-2-200002-2-2-2-222-2-22-20022000000-2-22000000000000000
χ2022222222-2-200002-2-2-2-2-2-222-2-2002200000022-2000000000000000
χ21222222-2-2222222-200002222-2-2-2-200000022-200-200000000000000
χ22222222-2-2222222-20000-2-2-2-22-2-2-2000000-2-2200200000000000000
χ23222222-2-222-2-2-2-2-200002222-2-222000000-2-2-200200000000000000
χ24222222-2-222-2-2-2-2-20000-2-2-2-22-22200000022200-200000000000000
χ25222222-2-2-2-20000-2000022-2-2-22000022-2-20020002-2000000000000
χ26222222-2-2-2-20000-2000022-2-2-220000-2-222002000-22000000000000
χ27222222-2-2-2-20000-20000-2-22222000022-2-200-2000-22000000000000
χ28222222-2-2-2-20000-20000-2-222220000-2-22200-20002-2000000000000
χ2922-2-2-22002-222-2-2000002i−2i2i−2i00000000002i−2i0000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ3022-2-2-22002-222-2-2000002i−2i2i−2i00000000002i−2i000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ3122-2-2-22002-222-2-200000−2i2i−2i2i0000000000−2i2i0000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ3222-2-2-22002-222-2-200000−2i2i−2i2i0000000000−2i2i000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ3322-2-2-22002-2-2-222000002i−2i2i−2i0000000000−2i2i0000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ3422-2-2-22002-2-2-222000002i−2i2i−2i0000000000−2i2i000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ3522-2-2-22002-2-2-22200000−2i2i−2i2i00000000002i−2i0000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ3622-2-2-22002-2-2-22200000−2i2i−2i2i00000000002i−2i000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ374444-4-444000000-444-4-40000000000000000000000000000000000
χ384444-4-444000000-4-4-4440000000000000000000000000000000000
χ394444-4-4-4-400000040000000000004-4000000000000000000000000
χ404444-4-4-4-40000004000000000000-44000000000000000000000000
χ4144-4-4-4400-440000000004i−4i−4i4i000000000000000000000000000000
χ4244-4-4-4400-44000000000−4i4i4i−4i000000000000000000000000000000
χ434-44-4004-4002i−2i2i−2i0004-40000002i−2i002i−2i2i−2i00000000000000000000
χ444-44-4004-4002i−2i2i−2i000-440000002i−2i00−2i2i−2i2i00000000000000000000
χ454-44-4004-400−2i2i−2i2i0004-4000000−2i2i00−2i2i−2i2i00000000000000000000
χ464-44-4004-400−2i2i−2i2i000-44000000−2i2i002i−2i2i−2i00000000000000000000
χ474-44-400-44002i−2i2i−2i04-400000000−2i2i002i−2i−2i2i00000000000000000000
χ484-44-400-44002i−2i2i−2i0-4400000000−2i2i00−2i2i2i−2i00000000000000000000
χ494-44-400-4400−2i2i−2i2i04-4000000002i−2i00−2i2i2i−2i00000000000000000000
χ504-44-400-4400−2i2i−2i2i0-44000000002i−2i002i−2i−2i2i00000000000000000000
χ5188-8-88-800000000000000000000000000000000000000000000000
χ528-8-880000004i−4i−4i4i000000000000000000000000000000000000000
χ538-8-88000000−4i4i4i−4i000000000000000000000000000000000000000

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