Finite Group Databasebeta

← Group #72284727

Character table — Group #72284727

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11244488888816161616161616163232323232323232323232323232323264646464646464646464646464128128128128
order12222222224422224444224444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-11111-1-111-1-1-1-1111-1-1-1-111111111-1-1-1-1
χ411111111111111111111-1-11111-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ611111111111111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ711111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ811111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ9111111111111-1-111-1-1111-1-1-1-1-11-11111-1-111-111-1-111-1-111-1-11-11-1
χ10111111111111-1-111-1-1111-1-1-1-1-11-11111-1-111-111-1-1-1-111-1-111-11-11
χ11111111111111-1-111-1-111-11-1-1-1-1-1111-1-11111-1-1-11111-1-111-1-1-11-11
χ12111111111111-1-111-1-111-11-1-1-1-1-1111-1-11111-1-1-111-1-111-1-1111-11-1
χ13111111111111-1-1-1-1-1-1-1-11-1-1-1111-11111-1-1-1-11-1-111ii−i−i−i−iiii−i−ii
χ14111111111111-1-1-1-1-1-1-1-11-1-1-1111-11111-1-1-1-11-1-111−i−iiiii−i−i−iii−i
χ15111111111111-1-1-1-1-1-1-1-1-11-1-111-1111-1-111-1-1111-1-1ii−i−i−i−iii−iii−i
χ16111111111111-1-1-1-1-1-1-1-1-11-1-111-1111-1-111-1-1111-1-1−i−iiiii−i−ii−i−ii
χ172222222222222222222200-2-22200-2-20000-2-2-20000000000000000
χ1822222222222222-2-222-2-200-2-2-2-200-2-200002220000000000000000
χ19222222222222-2-222-2-2220022-2-200-2-20000-2-220000000000000000
χ20222222222222-2-2-2-2-2-2-2-200222200-2-2000022-20000000000000000
χ21222222-2-222-2-2002-2002-2020000022-200-2-22-20002-2000000000000
χ22222222-2-222-2-2002-2002-20-200000-22-200222-2000-22000000000000
χ23222222-2-222-2-2002-2002-220000020-22-2-200-2202-200000000000000
χ24222222-2-222-2-2002-2002-2-200000-20-222200-220-2200000000000000
χ25222222-2-222-2-200-2200-22020000022-200-2-2-22000-22000000000000
χ26222222-2-222-2-200-2200-220-200000-22-20022-220002-2000000000000
χ27222222-2-222-2-200-2200-2220000020-22-2-2002-20-2200000000000000
χ28222222-2-222-2-200-2200-22-200000-20-2222002-202-200000000000000
χ2944444444-4-4-4-400000000004-400000000000000000000000000000
χ3044444444-4-4-4-40000000000-4400000000000000000000000000000
χ31444444-4-4-4-4444-4004-400000000000000000000000000000000000
χ32444444-4-4-4-444-4400-4400000000000000000000000000000000000
χ334444-4-4004-4000004000-40000000000000000000002-2002-2000000
χ344444-4-4004-4000004000-4000000000000000000000-2200-22000000
χ354444-4-4004-400000-400040000000000000000000002i−2i00−2i2i000000
χ364444-4-4004-400000-40004000000000000000000000−2i2i002i−2i000000
χ374444-4-400-4400004000-40000000000000000000000002-2002-20000
χ384444-4-400-4400004000-4000000000000000000000000-2200-220000
χ394444-4-400-440000-400040000000000000000000000002i−2i00−2i2i0000
χ404444-4-400-440000-40004000000000000000000000000−2i2i002i−2i0000
χ41444-4-4400004-404000-4002-20000-22002-22-20000000000000000000
χ42444-4-4400004-404000-400-2200002-200-22-220000000000000000000
χ43444-4-4400004-40-4000400220000-2-2002-2-220000000000000000000
χ44444-4-4400004-40-4000400-2-200002200-222-20000000000000000000
χ45444-4-440000-444000-40002-20000-2200-22-220000000000000000000
χ46444-4-440000-444000-4000-2200002-2002-22-20000000000000000000
χ47444-4-440000-44-40004000220000-2-200-222-20000000000000000000
χ48444-4-440000-44-40004000-2-2000022002-2-220000000000000000000
χ49888-88-80000000000000000004-4000000000000000000000000000
χ50888-88-8000000000000000000-44000000000000000000000000000
χ511616-160008-8000000000000000000000000000000000000000000000
χ521616-16000-88000000000000000000000000000000000000000000000
χ5332-32000000000000000000000000000000000000000000000000000

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