Finite Group Databasebeta

← Group #130613

Character table — Group #130613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222244444444444444488888888888881616161616161616161616161632323232
order12222244444444444444444224444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1iiii−i−i−i−iii−i−i
χ41111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111-1-1-1-1111111111-1-1-1-111-1-11-1-1-1-111111111-1-1-1-1
χ6111111111111111-1-1-1-1111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-11111iiii−i−i−i−i−i−iii
χ8111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-11111−i−i−i−iiiiiii−i−i
χ911111111111-1-1-1-11111111111-1-11-1-1-1-1-1-111-111-1-111-1-111-1-11-11-1
χ1011111111111-1-1-1-11111111111-1-11-1-1-1-1-1-111-111-1-1-1-111-1-111-11-11
χ1111111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-111ii−i−i−i−iiii−i−ii
χ1211111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-111−i−iiiii−i−i−iii−i
χ1311111111111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-1-1-11111-1-111-1-1-11-11
χ1411111111111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-1-1-111-1-111-1-1111-11-1
χ1511111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1ii−i−i−i−iii−iii−i
χ1611111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1−i−iiiii−i−ii−i−ii
χ1722222222-2-220000222222-2-22-200-2000000-2-202-200000000000000
χ1822222222-2-2200002222-2-222-2200-2000000-2-20-2200000000000000
χ1922222222-2-220000-2-2-2-222-2-22-200-2000000220-2200000000000000
χ2022222222-2-220000-2-2-2-2-2-222-2200-20000002202-200000000000000
χ21222222-2-222-2222200002222-2-222-20000-2-200-20000000000000000
χ22222222-2-222-222220000-2-2-2-222-2-2-20000-2-20020000000000000000
χ23222222-2-222-2-2-2-2-200002222-2-2-2-2-20000220020000000000000000
χ24222222-2-222-2-2-2-2-20000-2-2-2-22222-200002200-20000000000000000
χ25222222-2-2-2-2-20000000022-2-2-2200222-2-200000002-2000000000000
χ26222222-2-2-2-2-20000000022-2-2-22002-2-2220000000-22000000000000
χ27222222-2-2-2-2-200000000-2-2222-200222-2-20000000-22000000000000
χ28222222-2-2-2-2-200000000-2-2222-2002-2-22200000002-2000000000000
χ2922-2-2-22002-202i2i−2i−2i00002i−2i2i−2i002-2000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ3022-2-2-22002-202i2i−2i−2i00002i−2i2i−2i002-200000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ3122-2-2-22002-202i2i−2i−2i0000−2i2i−2i2i00-22000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ3222-2-2-22002-202i2i−2i−2i0000−2i2i−2i2i00-2200000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ3322-2-2-22002-20−2i−2i2i2i00002i−2i2i−2i00-22000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ3422-2-2-22002-20−2i−2i2i2i00002i−2i2i−2i00-2200000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ3522-2-2-22002-20−2i−2i2i2i0000−2i2i−2i2i002-2000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ3622-2-2-22002-20−2i−2i2i2i0000−2i2i−2i2i002-200000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ374444-4-44400-4000000000000000000000004i−4i00000000000000000
χ384444-4-44400-400000000000000000000000−4i4i00000000000000000
χ394444-4-4-4-400400004i4i−4i−4i0000000000000000000000000000000000
χ404444-4-4-4-40040000−4i−4i4i4i0000000000000000000000000000000000
χ4144-4-4-4400-440000000004i−4i−4i4i000000000000000000000000000000
χ4244-4-4-4400-44000000000−4i4i4i−4i000000000000000000000000000000
χ434-44-4004i−4i0002-22-22+2i−2−2i2−2i−2+2i0000000002-22i−2i2i−2i0000000000000000000
χ444-44-4004i−4i0002-22-2−2−2i2+2i−2+2i2−2i000000000-22−2i2i2i−2i0000000000000000000
χ454-44-4004i−4i000-22-222+2i−2−2i2−2i−2+2i000000000-22−2i2i−2i2i0000000000000000000
χ464-44-4004i−4i000-22-22−2−2i2+2i−2+2i2−2i0000000002-22i−2i−2i2i0000000000000000000
χ474-44-400−4i4i0002-22-22−2i−2+2i2+2i−2−2i0000000002-2−2i2i−2i2i0000000000000000000
χ484-44-400−4i4i0002-22-2−2+2i2−2i−2−2i2+2i000000000-222i−2i−2i2i0000000000000000000
χ494-44-400−4i4i000-22-222−2i−2+2i2+2i−2−2i000000000-222i−2i2i−2i0000000000000000000
χ504-44-400−4i4i000-22-22−2+2i2−2i−2−2i2+2i0000000002-2−2i2i2i−2i0000000000000000000
χ5188-8-88-800000000000000000000000000000000000000000000000
χ528-8-8800000004i−4i−4i4i00000000000000000000000000000000000000
χ538-8-880000000−4i4i4i−4i00000000000000000000000000000000000000

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