Finite Group Databasebeta

← Group #152239

Character table — Group #152239

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444444444444444488881616161616163232323232323232
order12442488882444444444444488888888888888224424888888888888
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
χ5111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ6111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ7111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ8111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ9111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-11-11-11-1
χ10111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11-11-11-11
χ11111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1i−ii−i−ii−ii
χ12111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−ii−iii−ii−i
χ13111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111111111-1-1-1-11-1-111-1-11
χ14111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111111111-1-1-1-1-111-1-111-1
χ15111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-11111i−i−ii−iii−i
χ16111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-11111−iii−ii−i−ii
χ1722222222222-2-2-2-2000000002-2-2-2-222000000002-22-2002-20000000000
χ1822222222222-2-2-2-2000000002-2-2-2-22200000000-22-2200-220000000000
χ19222222-2-2-2-22-2-2-2-20000000022222-2-2000000002-22-200-220000000000
χ20222222-2-2-2-22-2-2-2-20000000022222-2-200000000-22-22002-20000000000
χ2122-2-22-20000-222-2-20000000020000002222-2-2-2-222-2-22-2000000000000
χ2222-2-22-20000-222-2-20000000020000002222-2-2-2-2-2-222-22000000000000
χ2322-2-22-20000-222-2-2000000002000000-2-2-2-2222222-2-2-22000000000000
χ2422-2-22-20000-222-2-2000000002000000-2-2-2-22222-2-2222-2000000000000
χ2522-2-22-20000-2-2-2222i2i2i2i−2i−2i−2i−2i2000000000000002-2-2200002i−2i00000000
χ2622-2-22-20000-2-2-2222i2i2i2i−2i−2i−2i−2i200000000000000-222-20000−2i2i00000000
χ2722-2-22-20000-2-2-222−2i−2i−2i−2i2i2i2i2i2000000000000002-2-220000−2i2i00000000
χ2822-2-22-20000-2-2-222−2i−2i−2i−2i2i2i2i2i200000000000000-222-200002i−2i00000000
χ294444444444-4000000000000-40000-4-400000000000000000000000000
χ30444444-4-4-4-4-4000000000000-400004400000000000000000000000000
χ314444-4-40000000002i2i−2i−2i2i2i−2i−2i000004i−4i22-2-222-2-2000000000000000000
χ324444-4-40000000002i2i−2i−2i2i2i−2i−2i00000−4i4i-2-222-2-222000000000000000000
χ334444-4-4000000000−2i−2i2i2i−2i−2i2i2i000004i−4i-2-222-2-222000000000000000000
χ344444-4-4000000000−2i−2i2i2i−2i−2i2i2i00000−4i4i22-2-222-2-2000000000000000000
χ3544-4-44-400004000000000000-44i4i−4i−4i0000000000000000000000000000
χ3644-4-44-400004000000000000-4−4i−4i4i4i0000000000000000000000000000
χ3744-4-4-4444-4-40000022-2-2-2-222000000022-2-2-2-222000000000000000000
χ3844-4-4-4444-4-400000-2-22222-2-20000000-2-22222-2-2000000000000000000
χ3944-4-4-44-4-4440000022-2-2-2-2220000000-2-22222-2-2000000000000000000
χ4044-4-4-44-4-44400000-2-22222-2-2000000022-2-2-2-222000000000000000000
χ414-44i−4i002i2−2i222−2202-22i−2i2-22i−2i2i−2i2-202ζ−2ζ2ζ3−2ζ3000022−22002i2−2i2000000000000000000
χ424-44i−4i002i2−2i222−2202-22i−2i-22−2i2i−2i2i-2202ζ−2ζ2ζ3−2ζ30000−222200−2i22i2000000000000000000
χ434-44i−4i002i2−2i222−220-22−2i2i2i−2i2-2-22−2i2i0−2ζ2ζ−2ζ32ζ30022−22002i2−2i200000000000000000000
χ444-44i−4i002i2−2i222−220-22−2i2i−2i2i-222-22i−2i0−2ζ2ζ−2ζ32ζ300−222200−2i22i200000000000000000000
χ454-44i−4i00−2i22i2−222202-22i−2i2-22i−2i2i−2i2-20−2ζ2ζ−2ζ32ζ30000−222200−2i22i2000000000000000000
χ464-44i−4i00−2i22i2−222202-22i−2i-22−2i2i−2i2i-220−2ζ2ζ−2ζ32ζ3000022−22002i2−2i2000000000000000000
χ474-44i−4i00−2i22i2−22220-22−2i2i2i−2i2-2-22−2i2i02ζ−2ζ2ζ3−2ζ300−222200−2i22i200000000000000000000
χ484-44i−4i00−2i22i2−22220-22−2i2i−2i2i-222-22i−2i02ζ−2ζ2ζ3−2ζ30022−22002i2−2i200000000000000000000
χ494-4−4i4i002i2−2i2−222202-2−2i2i2-2−2i2i−2i2i2-202ζ3−2ζ32ζ−2ζ0000−2222002i2−2i2000000000000000000
χ504-4−4i4i002i2−2i2−222202-2−2i2i-222i−2i2i−2i-2202ζ3−2ζ32ζ−2ζ000022−2200−2i22i2000000000000000000
χ514-4−4i4i002i2−2i2−22220-222i−2i2i−2i-222-2−2i2i0−2ζ32ζ3−2ζ2ζ0022−2200−2i22i200000000000000000000
χ524-4−4i4i002i2−2i2−22220-222i−2i−2i2i2-2-222i−2i0−2ζ32ζ3−2ζ2ζ00−2222002i2−2i200000000000000000000
χ534-4−4i4i00−2i22i222−2202-2−2i2i2-2−2i2i−2i2i2-20−2ζ32ζ3−2ζ2ζ000022−2200−2i22i2000000000000000000
χ544-4−4i4i00−2i22i222−2202-2−2i2i-222i−2i2i−2i-220−2ζ32ζ3−2ζ2ζ0000−2222002i2−2i2000000000000000000
χ554-4−4i4i00−2i22i222−220-222i−2i2i−2i-222-2−2i2i02ζ3−2ζ32ζ−2ζ00−2222002i2−2i200000000000000000000
χ564-4−4i4i00−2i22i222−220-222i−2i−2i2i2-2-222i−2i02ζ3−2ζ32ζ−2ζ0022−2200−2i22i200000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.