Finite Group Databasebeta

← Group #350165

Character table — Group #350165

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442244444444444444444444444444444444444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-22222-2-222222222-2-20000-200000000-2-2-2-20000000000000000000000
χ182222222222-2-222-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000-20000000022220000000000000000000000
χ192222222222-2-222-2-2-2-2-2-2222222-2-2-2-2-2-20000200000000-2-2220000000000000000000000
χ202222222222-2-222-2-2-2-2-2-222-2-2-2-22222-2-2000020000000022-2-20000000000000000000000
χ2122222222-2-222-2-22222-2-22200000000-2-222-2-2-2000000000000-2-222000000000000000000
χ2222222222-2-222-2-22222-2-22200000000-2-2-2-222-200000000000022-2-2000000000000000000
χ2322222222-2-222-2-222-2-222-2-200000000-2-222222000000000000-2-2-2-2000000000000000000
χ2422222222-2-222-2-222-2-222-2-200000000-2-2-2-2-2-220000000000002222000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-200000000220000222-2-222-2-200000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-2000000002200002-2-222-2-22200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200000000220000-222-2-2-2-22200000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200000000220000-2-2-22222-2-200000000000000000000000000
χ29222-2-2-22-2-2-20022002-22-20022-2-222-2-200000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ30222-2-2-22-2-2-20022002-22-20022-2-222-2-200000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ31222-2-2-22-2-2-20022002-22-200-2-222-2-22200000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ32222-2-2-22-2-2-20022002-22-200-2-222-2-22200000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ33222-2-2-22-2-2-2002200-22-220022-2-2-2-22200000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ34222-2-2-22-2-2-2002200-22-220022-2-2-2-22200000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ35222-2-2-22-2-2-2002200-22-2200-2-22222-2-200000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ36222-2-2-22-2-2-2002200-22-2200-2-22222-2-200000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ372-22-222-2-22-22-22-22-200000000002i−2i2i−2i2-2002i−2i02-22-20000002i−2i002i−2i000000000000000000
χ382-22-222-2-22-22-22-22-200000000002i−2i2i−2i2-200−2i2i0-22-220000002i−2i00−2i2i000000000000000000
χ392-22-222-2-22-22-22-22-20000000000−2i2i−2i2i2-2002i−2i0-22-22000000−2i2i002i−2i000000000000000000
χ402-22-222-2-22-22-22-22-20000000000−2i2i−2i2i2-200−2i2i02-22-2000000−2i2i00−2i2i000000000000000000
χ412-22-222-2-22-2-222-2-2200000000002i−2i2i−2i-222i−2i00000002-22-200−2i2i2i−2i00000000000000000000
χ422-22-222-2-22-2-222-2-2200000000002i−2i2i−2i-22−2i2i0000000-22-2200−2i2i−2i2i00000000000000000000
χ432-22-222-2-22-2-222-2-220000000000−2i2i−2i2i-222i−2i0000000-22-22002i−2i2i−2i00000000000000000000
χ442-22-222-2-22-2-222-2-220000000000−2i2i−2i2i-22−2i2i00000002-22-2002i−2i−2i2i00000000000000000000
χ452-22-222-2-2-222-2-222-20000002i−2i2i−2i0000-22002i−2i000002-2-222i−2i0000−2i2i000000000000000000
χ462-22-222-2-2-222-2-222-20000002i−2i2i−2i0000-2200−2i2i00000-222-22i−2i00002i−2i000000000000000000
χ472-22-222-2-2-222-2-222-2000000−2i2i−2i2i0000-22002i−2i00000-222-2−2i2i0000−2i2i000000000000000000
χ482-22-222-2-2-222-2-222-2000000−2i2i−2i2i0000-2200−2i2i000002-2-22−2i2i00002i−2i000000000000000000
χ492-22-222-2-2-22-22-22-220000002i−2i2i−2i00002-22i−2i000-222-20000−2i2i00−2i2i00000000000000000000
χ502-22-222-2-2-22-22-22-220000002i−2i2i−2i00002-2−2i2i0002-2-220000−2i2i002i−2i00000000000000000000
χ512-22-222-2-2-22-22-22-22000000−2i2i−2i2i00002-22i−2i0002-2-2200002i−2i00−2i2i00000000000000000000
χ522-22-222-2-2-22-22-22-22000000−2i2i−2i2i00002-2−2i2i000-222-200002i−2i002i−2i00000000000000000000
χ53444-4-4-44-44400-4-4004-4-44000000000000000000000000000000000000000000000000000
χ54444-4-4-44-44400-4-400-444-4000000000000000000000000000000000000000000000000000
χ5544-444-4-4-4004400-4-4000000000000000000000000000000000000022−2222−2200000000000000
χ5644-444-4-4-4004400-4-40000000000000000000000000000000000000−2222−222200000000000000
χ5744-444-4-4-400-4-40044000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ5844-444-4-4-400-4-4004400000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ5944-4-4-44-440000000000004i−4i00000000000000000000000000000002i−2i−2i2i2-2-220000000000
χ6044-4-4-44-440000000000004i−4i0000000000000000000000000000000−2i2i2i−2i-222-20000000000
χ6144-4-4-44-44000000000000−4i4i00000000000000000000000000000002i−2i−2i2i-222-20000000000
χ6244-4-4-44-44000000000000−4i4i0000000000000000000000000000000−2i2i2i−2i2-2-220000000000
χ634-444-4-4-444-400-44000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ644-444-4-4-444-400-4400000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ654-444-4-4-44-44004-40000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ664-444-4-4-44-44004-4000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ674-4-4-44-444004-400-4400000000000000000000000000000000000000000000000000022−2200
χ684-4-4-44-444004-400-44000000000000000000000000000000000000000000000000000−222200
χ694-4-4-44-44400-44004-4000000000000000000000000000000000000000000000000022−220000
χ704-4-4-44-44400-44004-40000000000000000000000000000000000000000000000000−22220000
χ718-8-88-888-8000000000000000000000000000000000000000000000000000000000000000

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