Finite Group Databasebeta

← Group #150458

Character table — Group #150458

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order12222222224444444444444448888888888888888244444888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-111-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111
χ51111111111-1-1-1-1-1-1-111-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-11-1-1ii−i−i
χ61111111111-1-1-1-1-1-1-111-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-11-1-111−i−iii
χ71111111111-1-1-1-1-1-1-111-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-11-1-1−i−iii
χ81111111111-1-1-1-1-1-1-111-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-11-1-111ii−i−i
χ911111-1-1-1-111111-1-1-111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1111-11-1i−ii−i
χ1011111-1-1-1-111111-1-1-111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1111-11−ii−ii
χ1111111-1-1-1-111111-1-1-111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1111-11-1−ii−ii
χ1211111-1-1-1-111111-1-1-111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1111-11i−ii−i
χ1311111-1-1-1-11-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-111111-111-1-1-111-1-11
χ1411111-1-1-1-11-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-11111-11-11-111-1-111-1
χ1511111-1-1-1-11-1-1-1-1111111-1-1-111-1-1-1-111111111-1-1-1-11-111-1-1-11-111-1
χ1611111-1-1-1-11-1-1-1-1111111-1-1-111-1-1-1-111111111-1-1-1-1-11-11-111-11-1-11
χ17222222222222222222222-2-2-2-20000000000000000000-2-20000000
χ182222222222-2-2-2-2-2-2-222-22-2-2220000000000000000000-220000000
χ1922222-2-2-2-222222-2-2-222-2-222220000000000000000000-2-20000000
χ2022222-2-2-2-22-2-2-2-2222222-222-2-20000000000000000000-220000000
χ212-22-2-20000222-2-20002-2002i−2i2i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ222-22-2-20000222-2-20002-2002i−2i2i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ232-22-2-20000222-2-20002-200−2i2i−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ242-22-2-20000222-2-20002-200−2i2i−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ252-22-2-200002-2-2220002-2002i−2i−2i2i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i000000000000
χ262-22-2-200002-2-2220002-2002i−2i−2i2i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i000000000000
χ272-22-2-200002-2-2220002-200−2i2i2i−2i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i000000000000
χ282-22-2-200002-2-2220002-200−2i2i2i−2i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i000000000000
χ2944444444440000000-4-40-400000000000000000000000000000000
χ3044444-4-4-4-440000000-4-40400000000000000000000000000000000
χ314444-444-4-4-4000000000000000000000000000000022-200-2000000
χ324444-444-4-4-40000000000000000000000000000000-2-22002000000
χ334444-4-4-444-400000000000000000000000000000002-2-2002000000
χ344444-4-4-444-40000000000000000000000000000000-22200-2000000
χ3544-4-404-40002-22-222-200-2000002−22−22−22−22−22−22−22−2000000000000
χ3644-4-404-40002-22-222-200-200000−22−22−22−22−22−22−22−22000000000000
χ3744-4-404-4000-22-22-2-2200200000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3844-4-404-4000-22-22-2-2200200000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3944-4-40-440002-22-2-2-2200200000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4044-4-40-440002-22-2-2-2200200000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4144-4-40-44000-22-2222-200-2000002−22−2−22−22−22−222−22−2000000000000
χ4244-4-40-44000-22-2222-200-200000−22−222−22−22−22−2−22−22000000000000
χ434-44-4-40000400004-44-44-4000000000000000000000000000000000
χ444-44-4-4000040000-44-4-444000000000000000000000000000000000
χ454-4-440004-402-2-222-2-2002000002−2−222−2−222−2−222−2−22000000000000
χ464-4-440004-402-2-222-2-200200000−222−2−222−2−222−2−222−2000000000000
χ474-4-440004-40-222-2-22200-200000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ484-4-440004-40-222-2-22200-200000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ494-4-44000-4402-2-22-22200-200000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ504-4-44000-4402-2-22-22200-200000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ514-4-44000-440-222-22-2-2002000002−2−22−222−2−222−22−2−22000000000000
χ524-4-44000-440-222-22-2-200200000−222−22−2−222−2−22−222−2000000000000
χ538-88-880000-80000000000000000000000000000000000000000000

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