Finite Group Databasebeta

← Group #72283606

Character table — Group #72283606

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222444444444444888888888888888888888888161616163232323232326464646464646464
order1222222222444444444444888888888888888888888888224422222444448888
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1ii−i−i−i−iii
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1−i−iiiii−i−i
χ911111-1-1-1-111-1-111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11-11-11-11-1
χ1011111-1-1-1-111-1-111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-1-11-11-11-11
χ1111111-1-1-1-111-1-111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111i−i−iii−i−ii
χ1211111-1-1-1-111-1-111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111−iii−i−iii−i
χ1311111-1-1-1-111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-11-11-1-11-11
χ1411111-1-1-1-111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1-11-111-11-1
χ1511111-1-1-1-111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-11i−i−ii−iii−i
χ1611111-1-1-1-111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-11−iii−ii−i−ii
χ172222222222222222222222-2-2-2-2-2-2-2-2000000000000000022-2-220000-200000000
χ182222222222222222222222-2-2-2-2-2-2-2-20000000000000000-2-222-20000200000000
χ1922222-2-2-2-222-2-222-2-2-2-2222-2-2-2-22222000000000000000022-2-2-20000200000000
χ2022222-2-2-2-222-2-222-2-2-2-2222-2-2-2-222220000000000000000-2-22220000-200000000
χ212-2-22-200002-200-2-2000022222-2-20000000000002222-2-2-2-22-22-20002-2000000000
χ222-2-22-200002-200-2-2000022222-2-20000000000002222-2-2-2-2-22-22000-22000000000
χ232-2-22-200002-200-2-2000022222-2-2000000000000-2-2-2-222222-22-2000-22000000000
χ242-2-22-200002-200-2-2000022222-2-2000000000000-2-2-2-22222-22-220002-2000000000
χ252-2-22-200002-200-2-20000222-2-22200002222-2-2-2-2000000002-2-2202-200000000000
χ262-2-22-200002-200-2-20000222-2-22200002222-2-2-2-200000000-222-20-2200000000000
χ272-2-22-200002-200-2-20000222-2-2220000-2-2-2-22222000000002-2-220-2200000000000
χ282-2-22-200002-200-2-20000222-2-2220000-2-2-2-2222200000000-222-202-200000000000
χ294444444444444-4-4-4-4-4-44-4-4000000000000000000000000000000000000000000
χ304444444444-4-4-4000000-4000000000022-2-222-2-222-2-222-2-2000000000000000000
χ314444444444-4-4-4000000-40000000000-2-222-2-222-2-222-2-222000000000000000000
χ3244444-4-4-4-444-4-4-4-444444-4-4000000000000000000000000000000000000000000
χ3344444-4-4-4-44-444000000-4000000000022-2-222-2-2-2-222-2-222000000000000000000
χ3444444-4-4-4-44-444000000-40000000000-2-222-2-22222-2-222-2-2000000000000000000
χ354444-444-4-4-40000000000002-22-222-2-20022−220022−220022−220022−22000000000000000000
χ364444-444-4-4-40000000000002-22-222-2-200−222200−222200−222200−2222000000000000000000
χ374444-444-4-4-4000000000000-22-22-2-22222−220022−220022−220022−2200000000000000000000
χ384444-444-4-4-4000000000000-22-22-2-222−222200−222200−222200−222200000000000000000000
χ394444-4-4-444-40000000000002-22-2-2-2220022−220022−2200−222200−2222000000000000000000
χ404444-4-4-444-40000000000002-22-2-2-22200−222200−22220022−220022−22000000000000000000
χ414444-4-4-444-4000000000000-22-2222-2-222−220022−2200−222200−222200000000000000000000
χ424444-4-4-444-4000000000000-22-2222-2-2−222200−22220022−220022−2200000000000000000000
χ434-4-4440000-404-40000000002-2-222-22-222−2200−2222000022−2200−2222000000000000000000
χ444-4-4440000-404-40000000002-2-222-22-2−22220022−220000−22220022−22000000000000000000
χ454-4-4440000-404-4000000000-222-2-22-220022−2200−222222−2200−222200000000000000000000
χ464-4-4440000-404-4000000000-222-2-22-2200−22220022−22−22220022−2200000000000000000000
χ474-4-4440000-40-440000000002-2-22-22-2222−2200−22220000−22220022−22000000000000000000
χ484-4-4440000-40-440000000002-2-22-22-22−22220022−22000022−2200−2222000000000000000000
χ494-4-4440000-40-44000000000-222-22-22-20022−2200−2222−22220022−2200000000000000000000
χ504-4-4440000-40-44000000000-222-22-22-200−22220022−2222−2200−222200000000000000000000
χ514-4-44-4000044000044-4-4-4000000000022-2-2-2-22222-2-2-2-222000000000000000000
χ524-4-44-4000044000044-4-4-40000000000-2-22222-2-2-2-22222-2-2000000000000000000
χ534-4-44-40000440000-4-444-4000000000022-2-2-2-222-2-22222-2-2000000000000000000
χ544-4-44-40000440000-4-444-40000000000-2-22222-2-222-2-2-2-222000000000000000000
χ554-4-44-400004-4004400004-4-400004-4-440000000000000000000000000000000000
χ564-4-44-400004-4004400004-4-40000-444-40000000000000000000000000000000000
χ5788-8-80008-800004-44-44-404-4000000000000000000000000000000000000000000
χ5888-8-80008-80000-44-44-440-44000000000000000000000000000000000000000000
χ5988-8-8000-8800004-4-44-4404-4000000000000000000000000000000000000000000
χ6088-8-8000-880000-444-44-40-44000000000000000000000000000000000000000000
χ618-88-808-80000004-44-4-440-44000000000000000000000000000000000000000000
χ628-88-808-8000000-44-444-404-4000000000000000000000000000000000000000000
χ638-88-80-880000004-4-444-40-44000000000000000000000000000000000000000000
χ648-88-80-88000000-444-4-4404-4000000000000000000000000000000000000000000

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