Finite Group Databasebeta

← Group #152208

Character table — Group #152208

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222244444444444222222444444444448888888888884444
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-11-1-1-1-111-1-1111-1-1-1-111111111-1-1-1-1
χ411111111111111111111-1-11-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-111-1-111-111-111111111-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ611111111111-1-111-1-111-111-111111111-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ711111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ811111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ9111111-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-11-1
χ10111111-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-11-11
χ11111111-1-1-1-1-1111111111-1-11-1-111-1-111-1-1-1-1-11111-1-111-1-1-11-11
χ12111111-1-1-1-1-1111111111-1-11-1-111-1-111-1-1-1-1-111-1-111-1-1111-11-1
χ13111111-1-1-1-1-1-1-111-1-111-111-111-1-1-1-1-1-1111-1-111ii−i−i−i−iiii−i−ii
χ14111111-1-1-1-1-1-1-111-1-111-111-111-1-1-1-1-1-1111-1-111−i−iiiii−i−i−iii−i
χ15111111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-11111111-1-1ii−i−i−i−iii−iii−i
χ16111111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-11111111-1-1−i−iiiii−i−ii−i−ii
χ1722222222222222222-2-2-200-20000-2-20022-20000000000000000
χ1822222222222-2-222-2-2-2-220020000-2-200-2-220000000000000000
χ19222222-2-2-2-2-2222222-2-2-200-200002200-2-220000000000000000
χ20222222-2-2-2-2-2-2-222-2-2-2-220020000220022-20000000000000000
χ2122-2-22-200000222-2-2-22-222-2-22-20000000002-200000000000000
χ2222-2-22-200000222-2-2-22-22-22-2-22000000000-2200000000000000
χ2322-2-22-200000222-2-2-2-22-2002002i−2i002i−2i000002i−2i000000000000
χ2422-2-22-200000222-2-2-2-22-200200−2i2i00−2i2i00000−2i2i000000000000
χ2522-2-22-200000-2-22-2222-2-22-222-2000000000-2200000000000000
χ2622-2-22-200000-2-22-2222-2-2-222-220000000002-200000000000000
χ2722-2-22-200000-2-22-222-22200-2002i−2i002i−2i00000−2i2i000000000000
χ2822-2-22-200000-2-22-222-22200-200−2i2i00−2i2i000002i−2i000000000000
χ2944444444-4-4400-4-400000000000000000000000000000000000
χ30444444-4-444-400-4-400000000000000000000000000000000000
χ314444-4-44400-4000000000220-2-2-2-200220000000000000000000
χ324444-4-44400-4000000000-2-20222200-2-20000000000000000000
χ334444-4-4-4-4004000000000220-2-22200-2-20000000000000000000
χ344444-4-4-4-4004000000000-2-2022-2-200220000000000000000000
χ3544-4-44-40000000-440000000000004i−4i000000000000000000000
χ3644-4-44-40000000-44000000000000−4i4i000000000000000000000
χ3744-4-4-44004i−4i00000000002-20-222i−2i00−2i2i0000000000000000000
χ3844-4-4-44004i−4i0000000000-2202-2−2i2i002i−2i0000000000000000000
χ3944-4-4-4400−4i4i00000000002-20-22−2i2i002i−2i0000000000000000000
χ4044-4-4-4400−4i4i0000000000-2202-22i−2i00−2i2i0000000000000000000
χ414-44-4004i−4i0002-2002-2000000000000002i−2i00000i2−i22−2i2−i22−20000
χ424-44-4004i−4i0002-2002-2000000000000002i−2i00000−i2i2−22−i2i2−220000
χ434-44-4004i−4i000-2200-2200000000000000−2i2i000002−2−i2i2−22i2−i20000
χ444-44-4004i−4i000-2200-2200000000000000−2i2i00000−22i2−i22−2−i2i20000
χ454-44-400−4i4i0002-2002-200000000000000−2i2i00000i2−i2−22i2−i2−220000
χ464-44-400−4i4i0002-2002-200000000000000−2i2i00000−i2i22−2−i2i22−20000
χ474-44-400−4i4i000-2200-22000000000000002i−2i000002−2i2−i2−22−i2i20000
χ484-44-400−4i4i000-2200-22000000000000002i−2i00000−22−i2i22−2i2−i20000
χ498-8-8800000004-400-44000000000000000000000000000000000
χ508-8-880000000-44004-4000000000000000000000000000000000

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