Finite Group Databasebeta

← Group #288608

Character table — Group #288608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884448888888844448888888888888882444448888888824
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-1111-11-11-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111-1-11111111-1-11111-1-1-11-11-111-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ511111111111111111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-11-1-111111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-11-11111-1-1-1-1111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111111-11-1-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1111111-1-1-1
χ9111111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-111-1-111-1
χ10111111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-11111-1-11-11-1-111-1-1111-11
χ11111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-111-11-111-1-1-1-111-1-11
χ12111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111-1-1-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-11-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-11-11-1-1-1-1-11111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-11111-1-111-1-1-1-1-1-11-11-1111-1-111-11-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-111111-1-111-1-1-1-11
χ17222222222-2-222222-2-2-222-2-20000000022-2000000220000000000-2000000-200
χ18222222222-2-222222-2-2-222-2-200000000-2-2-2000000-2-200000000002000000200
χ19222222222-2-22-2-2-2-2-2-2-2-2-22200000000222000000-2-200000000002000000-200
χ20222222222-2-22-2-2-2-2-2-2-2-2-22200000000-2-22000000220000000000-2000000200
χ21222222-2-2-2-2-2-20000-22200002i2i−2i−2i000000000002i−2i0022-2-200000002i−2i0000000
χ22222222-2-2-2-2-2-20000-22200002i2i−2i−2i000000000002i−2i00-2-2220000000−2i2i0000000
χ23222222-2-2-2-2-2-20000-2220000−2i−2i2i2i00000000000−2i2i0022-2-20000000−2i2i0000000
χ24222222-2-2-2-2-2-20000-2220000−2i−2i2i2i00000000000−2i2i00-2-22200000002i−2i0000000
χ252222-2-22-2222-22222-2-22-2-2220000000000-20000000000002-2-20200000000000
χ262222-2-22-2222-22222-2-22-2-2220000000000-2000000000000-2220-200000000000
χ272222-2-22-2222-2-2-2-2-2-2-2222-2-2000000000020000000000002-220-200000000000
χ282222-2-22-2222-2-2-2-2-2-2-2222-2-200000000002000000000000-22-20200000000000
χ292222-2-22-22-2-2-2222222-2-2-2-2-22i2i−2i−2i2i2i−2i−2i0020000−2i2i0000000000000000000000
χ302222-2-22-22-2-2-2222222-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i00200002i−2i0000000000000000000000
χ312222-2-22-22-2-2-2-2-2-2-222-222222i2i−2i−2i−2i−2i2i2i00-20000−2i2i0000000000000000000000
χ322222-2-22-22-2-2-2-2-2-2-222-22222−2i−2i2i2i2i2i−2i−2i00-200002i−2i0000000000000000000000
χ332222-2-2-22-22220000-22-200002222000000022-2-2-2-200000000020-20000000000
χ342222-2-2-22-22220000-22-2000022220000000-2-222-2-2000000000-2020000000000
χ352222-2-2-22-22220000-22-20000-2-2-2-2000000022-2-222000000000-2020000000000
χ362222-2-2-22-22220000-22-20000-2-2-2-20000000-2-2222200000000020-20000000000
χ3722-2-22-2-2-220022i2i−2i−2i0002i−2i00000000002i−2i0i2−i2i2−i2002-22−22−20000000002−2i2−i2000
χ3822-2-22-2-2-220022i2i−2i−2i0002i−2i00000000002i−2i0−i2i2−i2i2002-2−22−22000000000−22−i2i2000
χ3922-2-22-2-2-220022i2i−2i−2i0002i−2i0000000000−2i2i0i2−i2i2−i200-222−22−2000000000−22−i2i2000
χ4022-2-22-2-2-220022i2i−2i−2i0002i−2i0000000000−2i2i0−i2i2−i2i200-22−22−220000000002−2i2−i2000
χ4122-2-22-2-2-22002−2i−2i2i2i000−2i2i00000000002i−2i0i2−i2i2−i200-22−22−220000000002−2−i2i2000
χ4222-2-22-2-2-22002−2i−2i2i2i000−2i2i00000000002i−2i0−i2i2−i2i200-222−22−2000000000−22i2−i2000
χ4322-2-22-2-2-22002−2i−2i2i2i000−2i2i0000000000−2i2i0i2−i2i2−i2002-2−22−22000000000−22i2−i2000
χ4422-2-22-2-2-22002−2i−2i2i2i000−2i2i0000000000−2i2i0−i2i2−i2i2002-22−22−20000000002−2−i2i2000
χ45444444-4-4-444-400004-4-40000000000000000000000000000000000000000000
χ464444-4-4-44-4-4-4400004-440000000000000000000000000000000000000000000
χ4744-4-44-444-400-400000000000000000000000000000022−22−22220000000000000000
χ4844-4-44-444-400-4000000000000000000000000000000−222222−220000000000000000
χ4944-4-4-444-4-400400000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ5044-4-4-444-4-40040000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ5144-4-4-44-44400-44i4i−4i−4i000−4i4i00000000000000000000000000000000000000000
χ5244-4-4-44-44400-4−4i−4i4i4i0004i−4i00000000000000000000000000000000000000000
χ534-44-4000004-402i2−2i22i2−2i2000002i2−2i22i2−2i22i2−2i22-22-20000000000000000000000000000000
χ544-44-4000004-402i2−2i22i2−2i2000002i2−2i2−2i22i2−2i22i2-22-220000000000000000000000000000000
χ554-44-4000004-40−2i22i2−2i22i200000−2i22i22i2−2i22i2−2i2-22-220000000000000000000000000000000
χ564-44-4000004-40−2i22i2−2i22i200000−2i22i2−2i22i2−2i22i22-22-20000000000000000000000000000000
χ574-44-400000-4402i2−2i22i2−2i200000−2i22i222−22−2222−2i2i2i−2i0000000000000000000000000000000
χ584-44-400000-4402i2−2i22i2−2i200000−2i22i2−222222−222i−2i−2i2i0000000000000000000000000000000
χ594-44-400000-440−2i22i2−2i22i2000002i2−2i222−22−22222i−2i−2i2i0000000000000000000000000000000
χ604-44-400000-440−2i22i2−2i22i2000002i2−2i2−222222−22−2i2i2i−2i0000000000000000000000000000000
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

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