Finite Group Databasebeta

← Group #152659

Character table — Group #152659

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order12222244444444444444222228888888888888888244444444488
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-111-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1
χ51111111111-1-1-1-1-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-11ii−i−i-1-1
χ61111111111-1-1-1-1-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-11-1-1−i−iii11
χ71111111111-1-1-1-1-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-11−i−iii-1-1
χ81111111111-1-1-1-1-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-11-1-1ii−i−i11
χ9111111-1-1-1-11111-1-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1-111i−ii−i1-1
χ10111111-1-1-1-11111-1-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i-111-11-1−ii−ii-11
χ11111111-1-1-1-11111-1-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1-111−ii−ii1-1
χ12111111-1-1-1-11111-1-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii-111-11-1i−ii−i-11
χ13111111-1-1-1-1-1-1-1-111111111-1111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-11-11
χ14111111-1-1-1-1-1-1-1-111111111-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-111-11-1
χ15111111-1-1-1-1-1-1-1-111111111-111-1-1-1-111111111-1-1-1-11-1-1-1-11-111-1-11
χ16111111-1-1-1-1-1-1-1-111111111-111-1-1-1-111111111-1-1-1-1-111-1-1-11-1-111-1
χ1722222222222222222222-2-22-2-20000000000000000000-2-20000000
χ182222222222-2-2-2-2-2-222-2-2-2-22220000000000000000000-220000000
χ19222222-2-2-2-22222-2-222-2-2-2-2-22200000000000000000002-20000000
χ20222222-2-2-2-2-2-2-2-2222222-2-2-2-2-20000000000000000000220000000
χ212-2-22-2200000000222-2-2-22-202-200002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222-2-22-2200000000222-2-2-22-202-20000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ232-2-22-2200000000222-2-2-2-220-222i2i−2i−2i000000002i2i−2i−2i000000000000
χ242-2-22-2200000000222-2-2-2-220-22−2i−2i2i2i00000000−2i−2i2i2i000000000000
χ252-2-22-2200000000-2-22-2222-20-22000022-2-2-2-2220000000000000000
χ262-2-22-2200000000-2-22-2222-20-220000-2-22222-2-20000000000000000
χ272-2-22-2200000000-2-22-222-2202-222-2-200000000-2-222000000000000
χ282-2-22-2200000000-2-22-222-2202-2-2-2220000000022-2-2000000000000
χ294444444444000000-4-40000-4000000000000000000000000000000
χ30444444-4-4-4-4000000-4-400004000000000000000000000000000000
χ314444-4-444-4-4000000000000000000000000000000022-200-2000000
χ324444-4-444-4-40000000000000000000000000000000-2-22002000000
χ334444-4-4-4-44400000000000000000000000000000002-2200-2000000
χ344444-4-4-4-4440000000000000000000000000000000-22-2002000000
χ3544-4-400004i−4i2i2i−2i−2i2-2002-200000i2−i2i2−i22−22−22−22−2i2−i2i2−i2000000000000
χ3644-4-400004i−4i2i2i−2i−2i2-2002-200000−i2i2−i2i2−22−22−22−22−i2i2−i2i2000000000000
χ3744-4-400004i−4i−2i−2i2i2i-2200-22000002−22−2−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ3844-4-400004i−4i−2i−2i2i2i-2200-2200000−22−22i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ3944-4-40000−4i4i2i2i−2i−2i-2200-22000002−22−2i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ4044-4-40000−4i4i2i2i−2i−2i-2200-2200000−22−22−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ4144-4-40000−4i4i−2i−2i2i2i2-2002-200000i2−i2i2−i2−22−22−22−22i2−i2i2−i2000000000000
χ4244-4-40000−4i4i−2i−2i2i2i2-2002-200000−i2i2−i2i22−22−22−22−2−i2i2−i2i2000000000000
χ434-44-4004i−4i002i−2i2i−2i2-200-22000002−2−22i2−i2−i2i2i2−i2−i2i22−2−22000000000000
χ444-44-4004i−4i002i−2i2i−2i2-200-2200000−222−2−i2i2i2−i2−i2i2i2−i2−222−2000000000000
χ454-44-4004i−4i00−2i2i−2i2i-22002-200000i2−i2−i2i2−222−22−2−22−i2i2i2−i2000000000000
χ464-44-4004i−4i00−2i2i−2i2i-22002-200000−i2i2i2−i22−2−22−222−2i2−i2−i2i2000000000000
χ474-44-400−4i4i002i−2i2i−2i-22002-200000i2−i2−i2i22−2−22−222−2−i2i2i2−i2000000000000
χ484-44-400−4i4i002i−2i2i−2i-22002-200000−i2i2i2−i2−222−22−2−22i2−i2−i2i2000000000000
χ494-44-400−4i4i00−2i2i−2i2i2-200-22000002−2−22−i2i2i2−i2−i2i2i2−i22−2−22000000000000
χ504-44-400−4i4i00−2i2i−2i2i2-200-2200000−222−2i2−i2−i2i2i2−i2−i2i2−222−2000000000000
χ514-4-44-4400004-4-4400-4400000000000000000000000000000000000
χ524-4-44-440000-444-400-4400000000000000000000000000000000000
χ538-8-888-800000000000000000000000000000000000000000000000

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