Finite Group Databasebeta

← Group #150182

Character table — Group #150182

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12224444224422442244444444448888888822444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ101111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111
χ121111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
χ131111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-222-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-2220000000000000000000000000000
χ192222-2-2-2-222-2-2-2-2222222-2-2-2-222-2-20000000000000000000000000000
χ202222-2-2-2-222-2-2-2-222-2-2-2-222-2-222220000000000000000000000000000
χ212-2-2222-2-22-22-22-22-2002i−2i0000002i−2i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ222-2-2222-2-22-22-22-22-2002i−2i0000002i−2i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ232-2-2222-2-22-22-22-22-200−2i2i000000−2i2i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ242-2-2222-2-22-22-22-22-200−2i2i000000−2i2i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ252-2-2222-2-22-22-2-22-222-2002-200000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ262-2-2222-2-22-22-2-22-222-2002-200000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ272-2-2222-2-22-22-2-22-22-2200-22000000000000000000000000002−22−2−22−22
χ282-2-2222-2-22-22-2-22-22-2200-2200000000000000000000000000−22−222−22−2
χ292-2-22-2-2222-2-222-2-222-200-2200000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ302-2-22-2-2222-2-222-2-222-200-2200000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ312-2-22-2-2222-2-222-2-22-22002-2000000000000000000000000002−2−22−222−2
χ322-2-22-2-2222-2-222-2-22-22002-200000000000000000000000000−222−22−2−22
χ332-2-22-2-2222-2-22-222-2002i−2i000000−2i2i0000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ342-2-22-2-2222-2-22-222-2002i−2i000000−2i2i000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ352-2-22-2-2222-2-22-222-200−2i2i0000002i−2i0000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ362-2-22-2-2222-2-22-222-200−2i2i0000002i−2i000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ37444444444444-4-4-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-4000000000000000022-2-222-2-200000000000000000000
χ3944444444-4-4-4-40000000000000000-2-222-2-22200000000000000000000
χ404444-4-4-4-444-4-444-4-40000000000000000000000000000000000000000
χ414444-4-4-4-4-4-444000000000000000022-2-2-2-22200000000000000000000
χ424444-4-4-4-4-4-4440000000000000000-2-22222-2-200000000000000000000
χ4344-4-44i−4i4i−4i000000000000002-22i−2i000022−22002i2−2i200000000000000000000
χ4444-4-44i−4i4i−4i000000000000002-22i−2i0000−222200−2i22i200000000000000000000
χ4544-4-44i−4i4i−4i00000000000000-22−2i2i0022−22002i2−2i20000000000000000000000
χ4644-4-44i−4i4i−4i00000000000000-22−2i2i00−222200−2i22i20000000000000000000000
χ4744-4-4−4i4i−4i4i000000000000002-2−2i2i000022−2200−2i22i200000000000000000000
χ4844-4-4−4i4i−4i4i000000000000002-2−2i2i0000−2222002i2−2i200000000000000000000
χ4944-4-4−4i4i−4i4i00000000000000-222i−2i0022−2200−2i22i20000000000000000000000
χ5044-4-4−4i4i−4i4i00000000000000-222i−2i00−2222002i2−2i20000000000000000000000
χ514-4-4444-4-4-44-440000000000000000000000002-22-20000000000000000
χ524-4-4444-4-4-44-44000000000000000000000000-22-220000000000000000
χ534-4-44-4-444-444-40000000000000000000000002-2-220000000000000000
χ544-4-44-4-444-444-4000000000000000000000000-222-20000000000000000
χ558-88-88i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000

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