Finite Group Databasebeta

← Group #142201

Character table — Group #142201

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444444444888888881616161616161616161616161616161632323232
order1222224444224488888888444488884444444416161616161616164444
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1
χ61111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-11-11
χ81111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1
χ91111111111-1-1-1-1-1-11111-1-11-11-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-1
χ101111111111-1-1-1-1-1-11111-1-11-11-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111
χ111111111111-1-1-1-1-1-11111-1-11-11-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111
χ121111111111-1-1-1-1-1-11111-1-11-11-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111ii−i−i−i−iii−i−iiiii−i−i-111-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111−i−iiiii−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ1722222222222222-2-22222-2-2-2-2-2-2-2-22200000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000
χ192222222222-2-2-2-222222222-22-22-2-2-2-200000000000000000000
χ202222222222-2-2-2-222-2-2-2-2222-22-2-2-22200000000000000000000
χ21222222-2-2-2-222-2-2000000002-2-220000000000002−22−22−22−20000
χ22222222-2-2-2-222-2-2000000002-2-22000000000000−22−22−22−220000
χ23222222-2-2-2-222-2-200000000-222-20000000000002−22−2−22−220000
χ24222222-2-2-2-222-2-200000000-222-2000000000000−22−222−22−20000
χ25222222-2-2-2-2-2-2220000000022-2-2000000000000i2−i2−i2i2i2−i2−i2i20000
χ26222222-2-2-2-2-2-2220000000022-2-2000000000000−i2i2i2−i2−i2i2i2−i20000
χ27222222-2-2-2-2-2-22200000000-2-222000000000000i2−i2−i2i2−i2i2i2−i20000
χ28222222-2-2-2-2-2-22200000000-2-222000000000000−i2i2i2−i2i2−i2−i2i20000
χ2922-2-22-22-22-22-22-2220000-2-200002-20000002-22-2000000000000
χ3022-2-22-22-22-22-22-2220000-2-200002-2000000-22-22000000000000
χ3122-2-22-22-22-22-22-2-2-20000220000-22002i−2i2i−2i0000000000000000
χ3222-2-22-22-22-22-22-2-2-20000220000-2200−2i2i−2i2i0000000000000000
χ3322-2-22-22-22-2-22-22220000-2-20000-22002-2-220000000000000000
χ3422-2-22-22-22-2-22-22220000-2-20000-2200-222-20000000000000000
χ3522-2-22-22-22-2-22-22-2-200002200002-20000002i−2i−2i2i000000000000
χ3622-2-22-22-22-2-22-22-2-200002200002-2000000−2i2i2i−2i000000000000
χ374444-4-444-4-400004i−4i00004i−4i0000000000000000000000000000
χ384444-4-444-4-40000−4i4i0000−4i4i0000000000000000000000000000
χ394444-4-4-4-44400000044-4-4000000000000000000000000000000
χ404444-4-4-4-444000000-4-444000000000000000000000000000000
χ4144-4-44-4-44-444-4-44000000000000000000000000000000000000
χ4244-4-44-4-44-44-444-4000000000000000000000000000000000000
χ4344-4-4-444-4-4400004i−4i0000−4i4i0000000000000000000000000000
χ4444-4-4-444-4-440000−4i4i00004i−4i0000000000000000000000000000
χ4544-4-4-44-444-40000000000000000004i−4i00000000000000000000
χ4644-4-4-44-444-4000000000000000000−4i4i00000000000000000000
χ478-88-80000000000000042−42000000000000000000000000000000
χ488-88-800000000000000−4242000000000000000000000000000000
χ498-8-8800000000000042−4200000000000000000000000000000000
χ508-8-88000000000000−424200000000000000000000000000000000

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