Finite Group Databasebeta

← Group #258362

Character table — Group #258362

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422444444444888888888888888824444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ41111111111111111111111111111111111-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ91111111111-1-1-1-1111111-1-11111-1-111-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-111-1-1
χ101111111111-1-1-1-1111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-11111-1-111
χ111111111111-1-1-1-1111111-1-11111-1-111-1-111-1-1-1-111-11111-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-111
χ121111111111-1-1-1-1111111-1-11111-1-111-1-111-1-1-1-111-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-11111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-111-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11111-1-1-1-111111-11111-1-1-1-111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-11-1-1-1-1111111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-111
χ1722222222222222-2-2-222-2-2-2222222-2-2-2-2-2-2002200-2000000000000000000000000000000
χ1822222222222222-2-2-222-2-2-2-2-2-2-222-2-2222200-2-200-2000000000000000000000000000000
χ192222222222-2-2-2-2-2-2-222-2222222-2-2-2-222-2-200-2-2002000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-222-222-2-2-2-2-2-2-2-2-2-2220022002000000000000000000000000000000
χ2122222222-2-22222222-2-22220000-2-2-2-20000220022-20000000000000000-2-2000000000000
χ2222222222-2-22222222-2-22220000-2-2-2-20000-2-200-2-2-2000000000000000022000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-20000-2-222000000000020000000000000000002-2002-2000000
χ2422222222-2-22222-2-2-2-2-2-2-2-20000-2-22200000000002000000000000000000-2200-22000000
χ2522222222-2-2-2-2-2-2222-2-22-2-2000022-2-200002200-2-220000000000000000-22000000000000
χ2622222222-2-2-2-2-2-2222-2-22-2-2000022-2-20000-2-20022200000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222000022220000000000-20000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222000022220000000000-2000000000000000000-22002-2000000
χ29222-22-2-2-20022-2-22-2-20022-20000000000002i−2i002i−2i0i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000
χ30222-22-2-2-20022-2-22-2-20022-20000000000002i−2i002i−2i0−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000
χ31222-22-2-2-20022-2-22-2-20022-2000000000000−2i2i00−2i2i0i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000
χ32222-22-2-2-20022-2-22-2-20022-2000000000000−2i2i00−2i2i0−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000
χ33222-22-2-2-200-2-2222-2-2002-220000000000002i−2i00−2i2i0i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000
χ34222-22-2-2-200-2-2222-2-2002-220000000000002i−2i00−2i2i0−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000
χ35222-22-2-2-200-2-2222-2-2002-22000000000000−2i2i002i−2i0i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000
χ36222-22-2-2-200-2-2222-2-2002-22000000000000−2i2i002i−2i0−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000
χ3722-22-2-2-222-22i−2i2i−2i0002-200022-2-22i−2i000000002i−2i00000000000i2−i2i2−i22−22−20000000000i2−i22−2
χ3822-22-2-2-222-22i−2i2i−2i0002-200022-2-22i−2i000000002i−2i00000000000−i2i2−i2i2−22−220000000000−i2i2−22
χ3922-22-2-2-222-22i−2i2i−2i0002-2000-2-2222i−2i00000000−2i2i00000000000i2−i2i2−i22−22−20000000000−i2i2−22
χ4022-22-2-2-222-22i−2i2i−2i0002-2000-2-2222i−2i00000000−2i2i00000000000−i2i2−i2i2−22−220000000000i2−i22−2
χ4122-22-2-2-222-2−2i2i−2i2i0002-200022-2-2−2i2i00000000−2i2i00000000000i2−i2i2−i2−22−220000000000i2−i2−22
χ4222-22-2-2-222-2−2i2i−2i2i0002-200022-2-2−2i2i00000000−2i2i00000000000−i2i2−i2i22−22−20000000000−i2i22−2
χ4322-22-2-2-222-2−2i2i−2i2i0002-2000-2-222−2i2i000000002i−2i00000000000i2−i2i2−i2−22−220000000000−i2i22−2
χ4422-22-2-2-222-2−2i2i−2i2i0002-2000-2-222−2i2i000000002i−2i00000000000−i2i2−i2i22−22−20000000000i2−i2−22
χ452-2-222-22-2-22000022-22-2-2002i−2i2i−2i00-22002i−2i000000000002-22-200000000000000002i−2i0000
χ462-2-222-22-2-22000022-22-2-2002i−2i2i−2i00-22002i−2i00000000000-22-220000000000000000−2i2i0000
χ472-2-222-22-2-22000022-22-2-200−2i2i−2i2i00-2200−2i2i000000000002-22-20000000000000000−2i2i0000
χ482-2-222-22-2-22000022-22-2-200−2i2i−2i2i00-2200−2i2i00000000000-22-2200000000000000002i−2i0000
χ492-2-222-22-2-220000-2-222-22002i−2i2i−2i002-200−2i2i00000002i−2i2i−2i00000000000000002-200000000
χ502-2-222-22-2-220000-2-222-22002i−2i2i−2i002-200−2i2i0000000−2i2i−2i2i0000000000000000-2200000000
χ512-2-222-22-2-220000-2-222-2200−2i2i−2i2i002-2002i−2i00000002i−2i2i−2i0000000000000000-2200000000
χ522-2-222-22-2-220000-2-222-2200−2i2i−2i2i002-2002i−2i0000000−2i2i−2i2i00000000000000002-200000000
χ53444-44-4-4-40044-4-4-44400-4-440000000000000000000000000000000000000000000000000
χ54444-44-4-4-400-4-444-44400-44-40000000000000000000000000000000000000000000000000
χ5544-44-4-4-44-444i−4i4i−4i000-440000000−4i4i0000000000000000000000000000000000000000000
χ5644-44-4-4-44-44−4i4i−4i4i000-4400000004i−4i0000000000000000000000000000000000000000000
χ5744-4-4-444-4004i−4i−4i4i000000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ5844-4-4-444-4004i−4i−4i4i00000000000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ5944-4-4-444-400−4i4i4i−4i000000000000000000000000000000000002i−2i−2i2i-222-200000000000000
χ6044-4-4-444-400−4i4i4i−4i00000000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ614-444-44-4-4440000000-4-4000000000004-4000000000000000000000000000000000000000
χ624-444-44-4-4440000000-4-400000000000-44000000000000000000000000000000000000000
χ634-444-44-4-4-4-40000000440004i−4i−4i4i000000000000000000000000000000000000000000000
χ644-444-44-4-4-4-4000000044000−4i4i4i−4i000000000000000000000000000000000000000000000
χ654-4-444-44-44-4000044-4-44-4000000004-400000000000000000000000000000000000000000
χ664-4-444-44-44-40000-4-44-44400000000-4400000000000000000000000000000000000000000
χ674-4-4-444-440000004-4400-400000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ684-4-4-444-440000004-4400-40000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ694-4-4-444-44000000-44-400400000000000000000000022−22−222200000000000000000000000000
χ704-4-4-444-44000000-44-4004000000000000000000000−222222−2200000000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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