Finite Group Databasebeta

← Group #352526

Character table — Group #352526

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444444444448888888888888888224444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111111111-111-1-1-1-1-111-1-1-1-1-1-111-1-111-1-11-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-11-11
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1111111-1-111-1-1-11-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11111-1-111-1-1111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-111-1-1-1-111-1-1-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-111111111-1-1-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1111111-1-11111-1-11-1-11
χ172222222222-2-22-2-22-2-222-2-20000000000000000222-2-222-2-2-200000000000000000000
χ182222222222-2-22-2-22-2-222-2-20000000000000000-2-2222-2-222-200000000000000000000
χ192222222222-2-22-2-22-2-2-2-222000000000000000022-2-2-2-2-222200000000000000000000
χ202222222222-2-22-2-22-2-2-2-2220000000000000000-2-2-22222-2-2200000000000000000000
χ2122222222-2-222-222-2-2-22222222222220000000000-2000000-2-2-2-2-20000000000000000
χ2222222222-2-222-222-2-2-22222-2-2-2-2-2-2-2-20000000000-2000000-222220000000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-22222-2-2-2-2000000000020000002-2-2220000000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-2-2-2-2-2222200000000002000000222-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000002i2i2i2i−2i−2i−2i−2i00-2000000200002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000−2i−2i−2i−2i2i2i2i2i00-200000020000−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-222000000002i2i2i2i−2i−2i−2i−2i002000000-20000−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000−2i−2i−2i−2i2i2i2i2i002000000-200002i2i−2i−2i000000000000
χ29222-22-2-2-2222-2-22-2-22-20000000022-2-2000000002-202-200000002-22-22-2000000000000
χ30222-22-2-2-2222-2-22-2-22-20000000022-2-200000000-220-2200000002-2-22-22000000000000
χ31222-22-2-2-2222-2-22-2-22-200000000-2-222000000002-202-20000000-22-22-22000000000000
χ32222-22-2-2-2222-2-22-2-22-200000000-2-22200000000-220-220000000-222-22-2000000000000
χ33222-22-2-2-222-22-2-22-2-22000022-2-2000022-2-222-2-22-20-22000002-2000000000000000000
χ34222-22-2-2-222-22-2-22-2-22000022-2-20000-2-222-2-222-2202-2000002-2000000000000000000
χ35222-22-2-2-222-22-2-22-2-220000-2-222000022-2-222-2-2-2202-200000-22000000000000000000
χ36222-22-2-2-222-22-2-22-2-220000-2-2220000-2-222-2-2222-20-2200000-22000000000000000000
χ37222-22-2-2-2-2-22-222-22-220000000022-2-22i2i−2i−2i−2i−2i2i2i000002i−2i2i−2i000-220000000000000000
χ38222-22-2-2-2-2-22-222-22-220000000022-2-2−2i−2i2i2i2i2i−2i−2i00000−2i2i−2i2i000-220000000000000000
χ39222-22-2-2-2-2-22-222-22-2200000000-2-2222i2i−2i−2i−2i−2i2i2i00000−2i2i−2i2i0002-20000000000000000
χ40222-22-2-2-2-2-22-222-22-2200000000-2-222−2i−2i2i2i2i2i−2i−2i000002i−2i2i−2i0002-20000000000000000
χ41222-22-2-2-2-2-2-222-2222-2000022-2-2000000000000000002i−2i−2i2i0-2200−2i2i2i−2i000000000000
χ42222-22-2-2-2-2-2-222-2222-2000022-2-200000000000000000−2i2i2i−2i0-22002i−2i−2i2i000000000000
χ43222-22-2-2-2-2-2-222-2222-20000-2-222000000000000000002i−2i−2i2i02-2002i−2i−2i2i000000000000
χ44222-22-2-2-2-2-2-222-2222-20000-2-22200000000000000000−2i2i2i−2i02-200−2i2i2i−2i000000000000
χ452-2-2-2222-200220-2-20002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000i2−i2i2−i22−22−20000
χ462-2-2-2222-200220-2-20002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000−i2i2−i2i2−22−220000
χ472-2-2-2222-200220-2-20002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000i2−i2i2−i2−22−220000
χ482-2-2-2222-200220-2-20002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−i2i2−i2i22−22−20000
χ492-2-2-2222-200220-2-2000-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000i2−i2−i2i22−2−220000
χ502-2-2-2222-200220-2-2000-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000−i2i2i2−i2−222−20000
χ512-2-2-2222-200220-2-2000-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000i2−i2−i2i2−222−20000
χ522-2-2-2222-200220-2-2000-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000−i2i2i2−i22−2−220000
χ5344-44-44-4-44-400400-40000000000000022−2222−2222−2222−22000000000000000000000000000000
χ5444-44-44-4-44-400400-400000000000000−2222−2222−2222−2222000000000000000000000000000000
χ5544-44-44-4-4-4400-4004000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ5644-44-44-4-4-4400-400400000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ5744-4-4-4-4444-400-40040000000000000022−22−222222−22−2222000000000000000000000000000000
χ5844-4-4-4-4444-400-400400000000000000−222222−22−222222−22000000000000000000000000000000
χ5944-4-4-4-444-4400400-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ6044-4-4-4-444-4400400-400000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ614-4-444-4-44004-40-44000000000004i−4i−4i4i00000000000000000000000000000000000000
χ624-4-444-4-44004-40-4400000000000−4i4i4i−4i00000000000000000000000000000000000000
χ634-4-444-4-4400-4404-400000004i−4i−4i4i000000000000000000000000000000000000000000
χ644-4-444-4-4400-4404-40000000−4i4i4i−4i000000000000000000000000000000000000000000
χ654-4-4-4444-400-4-40440004-4-440000000000000000000000000000000000000000000000
χ664-4-4-4444-400-4-4044000-444-40000000000000000000000000000000000000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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