Finite Group Databasebeta

← Group #251021

Character table — Group #251021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444448888888888888888888881616161616161616161616161616161632
order12222244444444444444422244448888888888888822244444444888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-1-1111-1-1-1
χ311111111111111111111111111-1-111-1-1111111-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-11-1-1-111-1-1-1111
χ511111111111111-1-11-1-11111-11-11111-1-111-1-1-1-1-1-1-1-11-1-1-11-1111-1-1-1-1-1111
χ611111111111111-1-11-1-11111-11-111-1-1-1-1-1-111111111111-1-1-111-111-1-1-1-1-1-1
χ711111111111111-1-11-1-11111-11-1-1-1111111-1-1-1-11111-1-1-1-11-1-1-1111111-1-1-1
χ811111111111111-1-11-1-11111-11-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ9111111111111-1-11111111-1-11-1111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1
χ10111111111111-1-11111111-1-11-1111-1-111-1-1-1-1-1-1-1-1-1-1111-11-1-1-11111-1-1-1-11
χ11111111111111-1-11111111-1-11-11-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-111-111-1-11
χ12111111111111-1-11111111-1-11-11-1-1-1-1-1-1-1-1-1-1-1-11111-111-11-1111-1-1-11111-1
χ13111111111111-1-1-1-11-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-1-111-11111-1
χ14111111111111-1-1-1-11-1-111-1-1-1-1-111-1-1-1-1-1-1111111111-1-1111-1-11-1-1-111-1-11
χ15111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1111111-1-1-1-11111-1111-1111-1-1-11-1-1-1-11
χ16111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1111111111-1-111-1
χ1722222222-222-20022-222-2-200-20-22200220000000000-20000000000-200000
χ1822222222-222-20022-222-2-200-20-2-2-200-2-2000000000020000000000200000
χ1922222222-222-200-2-2-2-2-2-2-2002022200-2-20000000000-20000000000200000
χ2022222222-222-200-2-2-2-2-2-2-200202-2-20022000000000020000000000-200000
χ21222222-2-22-2-222200-2002-2-2-20200000000022-2-2000002-200000000000000
χ22222222-2-22-2-222200-2002-2-2-202000000000-2-22200000-2200000000000000
χ23222222-2-22-2-22-2-200-2002-2220-200000000022-2-200000-2200000000000000
χ24222222-2-22-2-22-2-200-2002-2220-2000000000-2-222000002-200000000000000
χ252222-2-22-222-222200-200-222-20-20002200-2-2000000000000-2000200000000
χ262222-2-22-222-222200-200-222-20-2000-2-200220000000000002000-200000000
χ272222-2-22-222-22-2-200-200-22-22020002200-2-20000000000002000-200000000
χ282222-2-22-222-22-2-200-200-22-2202000-2-20022000000000000-2000200000000
χ292222-2-2-222-22222222-2-2-2-2-222-2-20000000000000000000-20200000000000
χ302222-2-2-222-22222-2-2222-2-2-22-2-22000000000000000000020-200000000000
χ312222-2-2-222-222-2-2222-2-2-2-22-222-2000000000000000000020-200000000000
χ322222-2-2-222-222-2-2-2-2222-2-22-2-2220000000000000000000-20200000000000
χ332222-2-2-22-2-22-20022-2-2-22200-20200000000000000000000002-200002-2000
χ342222-2-2-22-2-22-20022-2-2-22200-2020000000000000000000000-220000-22000
χ352222-2-2-22-2-22-200-2-2-222220020-200000000000000000000002-20000-22000
χ362222-2-2-22-2-22-200-2-2-222220020-20000000000000000000000-2200002-2000
χ3722-2-22-2-2-20220002i−2i02i−2i00000002i−2ii2−i22-2i2−i22−22−2i2i2−i2−i2000000000000002−20
χ3822-2-22-2-2-20220002i−2i02i−2i00000002i−2i−i2i22-2−i2i2−22−22−i2−i2i2i200000000000000−220
χ3922-2-22-2-2-20220002i−2i02i−2i0000000−2i2ii2−i2-22i2−i22−22−2−i2−i2i2i200000000000000−220
χ4022-2-22-2-2-20220002i−2i02i−2i0000000−2i2i−i2i2-22−i2i2−22−22i2i2−i2−i2000000000000002−20
χ4122-2-22-2-2-2022000−2i2i0−2i2i00000002i−2ii2−i2-22i2−i2−22−22−i2−i2i2i2000000000000002−20
χ4222-2-22-2-2-2022000−2i2i0−2i2i00000002i−2i−i2i2-22−i2i22−22−2i2i2−i2−i200000000000000−220
χ4322-2-22-2-2-2022000−2i2i0−2i2i0000000−2i2ii2−i22-2i2−i2−22−22i2i2−i2−i200000000000000−220
χ4422-2-22-2-2-2022000−2i2i0−2i2i0000000−2i2i−i2i22-2−i2i22−22−2−i2−i2i2i2000000000000002−20
χ45444444-4-4-4-4-4-40000400-4400000000000000000000000000000000000000
χ464444-4-44-4-44-4-400004004-400000000000000000000000000000000000000
χ4744-4-44-4440-4-40000000000000000000000022−22−2222000000000000000000000
χ4844-4-44-4440-4-400000000000000000000000−222222−22000000000000000000000
χ4944-4-4-444-40-440004i−4i0−4i4i0000000000000000000000000000000000000000
χ5044-4-4-444-40-44000−4i4i04i−4i0000000000000000000000000000000000000000
χ5144-4-4-44-4404-4000000000000000002i2−2i200−2i22i20000000000000000000000000
χ5244-4-4-44-4404-400000000000000000−2i22i2002i2−2i20000000000000000000000000
χ534-44-40000400-44i−4i0000000000000000000000002i−2i2i−2i0000000002-2000000
χ544-44-40000400-44i−4i000000000000000000000000−2i2i−2i2i000000000-22000000
χ554-44-40000400-4−4i4i0000000000000000000000002i−2i2i−2i000000000-22000000
χ564-44-40000400-4−4i4i000000000000000000000000−2i2i−2i2i0000000002-2000000
χ578-88-80000-800800000000000000000000000000000000000000000000000
χ588-8-88000000000000000000000000000000000022−22−222200000000000000000
χ598-8-880000000000000000000000000000000000−222222−2200000000000000000

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