Finite Group Databasebeta

← Group #136189

Character table — Group #136189

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order1222224444224444444488882244444444448888881616161616161616
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ51111111111111-1-1-1-11-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111-1-1-1-11-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ81111111111111-1-1-1-11-1-11111-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1
χ911-1-11-11-11-11-1-1ii−i−i1i−i1-11-11-1i−ii−ii−i1-1i−ii−i11-1-1ii−i−i11-1-1
χ1011-1-11-11-11-11-1-1ii−i−i1i−i1-11-11-1−iii−i−ii1-1i−ii−i-1-111−i−iii-1-111
χ1111-1-11-11-11-11-1-1ii−i−i1i−i1-11-1-11i−i−iii−i-11−iii−i11-1-1−i−iii-1-111
χ1211-1-11-11-11-11-1-1ii−i−i1i−i1-11-1-11−ii−ii−ii-11−iii−i-1-111ii−i−i11-1-1
χ1311-1-11-11-11-11-1-1−i−iii1−ii1-11-11-1i−i−iii−i1-1−ii−ii-1-111ii−i−i-1-111
χ1411-1-11-11-11-11-1-1−i−iii1−ii1-11-11-1−ii−ii−ii1-1−ii−ii11-1-1−i−iii11-1-1
χ1511-1-11-11-11-11-1-1−i−iii1−ii1-11-1-11i−ii−ii−i-11i−i−ii-1-111−i−iii11-1-1
χ1611-1-11-11-11-11-1-1−i−iii1−ii1-11-1-11−iii−i−ii-11i−i−ii11-1-1ii−i−i-1-111
χ1722222222222222222222-2-2-2-2000000000000-2-2000000000000
χ182222222222222-2-2-2-22-2-2-2-2-2-200000000000022000000000000
χ192222222222-2-2-20000-2002-2-2222000000-2-20000000000000000
χ202222222222-2-2-20000-2002-2-22-2-2000000220000000000000000
χ212222222222-2-2-20000-200-222-20000220000-2-200000000000000
χ222222222222-2-2-20000-200-222-20000-2-200002200000000000000
χ23222222-2-2-2-2-2-2222222-2-200000000000000000000002−22−22−22−2
χ24222222-2-2-2-2-2-2222222-2-20000000000000000000000−22−22−22−22
χ25222222-2-2-2-2-2-22-2-2-2-222200000000000000000000002−22−2−22−22
χ26222222-2-2-2-2-2-22-2-2-2-22220000000000000000000000−22−222−22−2
χ2722-2-22-22-22-22-2-22i2i−2i−2i22i−2i-22-22000000000000−2i2i000000000000
χ2822-2-22-22-22-22-2-2−2i−2i2i2i2−2i2i-22-220000000000002i−2i000000000000
χ2922-2-22-22-22-2-2220000-20022-2-22-2000000-220000000000000000
χ3022-2-22-22-22-2-2220000-20022-2-2-220000002-20000000000000000
χ3122-2-22-22-22-2-2220000-200-2-22200002i−2i0000−2i2i00000000000000
χ3222-2-22-22-22-2-2220000-200-2-2220000−2i2i00002i−2i00000000000000
χ3322-2-22-2-22-22-22-22i2i−2i−2i2−2i2i0000000000000000000000i2−i2−i2i22−2−22
χ3422-2-22-2-22-22-22-22i2i−2i−2i2−2i2i0000000000000000000000−i2i2i2−i2−222−2
χ3522-2-22-2-22-22-22-2−2i−2i2i2i22i−2i0000000000000000000000i2−i2−i2i2−222−2
χ3622-2-22-2-22-22-22-2−2i−2i2i2i22i−2i0000000000000000000000−i2i2i2−i22−2−22
χ37444444-4-4-4-444-40000-400000000000000000000000000000000
χ384444-4-444-4-400000000000000000000000000002i−2i2i−2i00000000
χ394444-4-444-4-40000000000000000000000000000−2i2i−2i2i00000000
χ404444-4-4-4-44400000000000000002200-2-2000000000000000000
χ414444-4-4-4-4440000000000000000-2-20022000000000000000000
χ4244-4-44-4-44-444-440000-400000000000000000000000000000000
χ4344-4-4-444-4-4400000000000000000000000000002i−2i−2i2i00000000
χ4444-4-4-444-4-440000000000000000000000000000−2i2i2i−2i00000000
χ4544-4-4-44-444-400000000000000002i−2i00−2i2i000000000000000000
χ4644-4-4-44-444-40000000000000000−2i2i002i−2i000000000000000000
χ478-88-80000000004i−4i4i−4i000000000000000000000000000000000
χ488-88-8000000000−4i4i−4i4i000000000000000000000000000000000
χ498-8-880000000004-4-44000000000000000000000000000000000
χ508-8-88000000000-444-4000000000000000000000000000000000

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