Finite Group Databasebeta

← Group #149779

Character table — Group #149779

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444444444444444488881616161616163232323232323232
order12222244442244444444448888888888888888444422444488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ9111111-1-1-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11-11-11-1
χ10111111-1-1-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-11-11-11
χ11111111-1-1-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ12111111-1-1-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ13111111-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-111-1-11
χ14111111-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-111-111-1-111-1
χ15111111-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1i−i−ii−iii−i
χ16111111-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1−iii−ii−i−ii
χ172222222222222-2-2-2-2-2-2-2-22000000000000000022-2-2002-20000000000
χ182222222222222-2-2-2-2-2-2-2-220000000000000000-2-22200-220000000000
χ19222222-2-2-2-2-2-22-2-2-2-222222000000000000000022-2-200-220000000000
χ20222222-2-2-2-2-2-22-2-2-2-2222220000000000000000-2-222002-20000000000
χ212-2-22-22000000222-2-20000-2000000002i2i2i2i−2i−2i−2i−2i2i−2i2i−2i00002-200000000
χ222-2-22-22000000222-2-20000-2000000002i2i2i2i−2i−2i−2i−2i−2i2i−2i2i0000-2200000000
χ232-2-22-22000000222-2-20000-200000000−2i−2i−2i−2i2i2i2i2i2i−2i2i−2i0000-2200000000
χ242-2-22-22000000222-2-20000-200000000−2i−2i−2i−2i2i2i2i2i−2i2i−2i2i00002-200000000
χ252-2-22-220000002-2-2220000-22i2i2i2i−2i−2i−2i−2i000000002i−2i−2i2i2-2000000000000
χ262-2-22-220000002-2-2220000-22i2i2i2i−2i−2i−2i−2i00000000−2i2i2i−2i-22000000000000
χ272-2-22-220000002-2-2220000-2−2i−2i−2i−2i2i2i2i2i000000002i−2i−2i2i-22000000000000
χ282-2-22-220000002-2-2220000-2−2i−2i−2i−2i2i2i2i2i00000000−2i2i2i−2i2-2000000000000
χ294444444444-4-4-400000000-40000000000000000000000000000000000
χ30444444-4-4-4-444-400000000-40000000000000000000000000000000000
χ314444-4-444-4-400000000000022-2-222-2-222-2-222-2-2000000000000000000
χ324444-4-444-4-4000000000000-2-222-2-222-2-222-2-222000000000000000000
χ334444-4-4-4-44400000000000022-2-222-2-2-2-222-2-222000000000000000000
χ344444-4-4-4-444000000000000-2-222-2-22222-2-222-2-2000000000000000000
χ3544-4-400004i−4i0002-22-22i2i−2i−2i0002i2−2i2002i2−2i222−220022−2200000000000000000000
χ3644-4-400004i−4i0002-22-22i2i−2i−2i000−2i22i200−2i22i2−222200−222200000000000000000000
χ3744-4-400004i−4i000-22-22−2i−2i2i2i02i2−2i2002i2−2i2000022−220022−22000000000000000000
χ3844-4-400004i−4i000-22-22−2i−2i2i2i0−2i22i200−2i22i20000−222200−2222000000000000000000
χ3944-4-40000−4i4i0002-22-2−2i−2i2i2i0002i2−2i2002i2−2i2−222200−222200000000000000000000
χ4044-4-40000−4i4i0002-22-2−2i−2i2i2i000−2i22i200−2i22i222−220022−2200000000000000000000
χ4144-4-40000−4i4i000-22-222i2i−2i−2i02i2−2i2002i2−2i20000−222200−2222000000000000000000
χ4244-4-40000−4i4i000-22-222i2i−2i−2i0−2i22i200−2i22i2000022−220022−22000000000000000000
χ434-44-4004i−4i000002-2-222i−2i2i−2i022−2200−2222002i2−2i200−2i22i200000000000000000000
χ444-44-4004i−4i000002-2-222i−2i2i−2i0−22220022−2200−2i22i2002i2−2i200000000000000000000
χ454-44-4004i−4i00000-222-2−2i2i−2i2i00022−2200−2222002i2−2i200−2i22i2000000000000000000
χ464-44-4004i−4i00000-222-2−2i2i−2i2i000−22220022−2200−2i22i2002i2−2i2000000000000000000
χ474-44-400−4i4i000002-2-22−2i2i−2i2i022−2200−222200−2i22i2002i2−2i200000000000000000000
χ484-44-400−4i4i000002-2-22−2i2i−2i2i0−22220022−22002i2−2i200−2i22i200000000000000000000
χ494-44-400−4i4i00000-222-22i−2i2i−2i00022−2200−222200−2i22i2002i2−2i2000000000000000000
χ504-44-400−4i4i00000-222-22i−2i2i−2i000−22220022−22002i2−2i200−2i22i2000000000000000000
χ514-4-444-400004-400000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000
χ524-4-444-400004-40000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000
χ534-4-444-40000-4400000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000
χ544-4-444-40000-440000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000
χ554-4-44-44000000-400004-4-4440000000000000000000000000000000000
χ564-4-44-44000000-40000-444-440000000000000000000000000000000000

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