Finite Group Databasebeta

← Group #258418

Character table — Group #258418

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888824444444448888
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
χ311111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ411111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111111-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-11111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111
χ711111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ811111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111-1-1-1-11111111111111-1-1-1-11-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-111-1-1
χ1011111111-1-1-1-11111111111111-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-11111-1-111
χ1111111111-1-1-1-11111111111111-1-1-1-11-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-111
χ1211111111-1-1-1-11111111111111-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-11-1-1-1-11-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-11-1-1-1-11-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11111-1-1-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-11-1-1-1-11-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-1-1111111-1-1
χ1611111111-1-1-1-111111111-1-1-1-11-1-1-1-11-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-111
χ1722222222222222-2-222-2-22222-222-2-2-2-222-2-200-2-200000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-222-2-2-2-2-2-222002200000000000000000000000000000000
χ19222222222222-2-222-2-2220000-2-2-222-2-200002200220000000000000000-2-2000000000000
χ20222222222222-2-222-2-2220000-2-2-222-2-20000-2-200-2-2000000000000000022000000000000
χ21222222222222-2-2-2-2-2-2-2-200002-2-2-2-22200000000000000000000000000002-2002-2000000
χ22222222222222-2-2-2-2-2-2-2-200002-2-2-2-2220000000000000000000000000000-2200-22000000
χ2322222222-2-2-2-222-2-222-2-22222-2-2-222-22-2-22200-2-200000000000000000000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-2-2-2-2-2-222-2222-2-2002200000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-2220000-222-2-2-2200002200-2-20000000000000000-22000000000000
χ2622222222-2-2-2-2-2-222-2-2220000-222-2-2-220000-2-2002200000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000222222-200000000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000222222-20000000000000000000000000000-22002-2000000
χ292-222-2-2-222i2i−2i−2i2-2002-20022-2-202i−2i00002i−2i0000000000000000i2i2−i2−i222−2−20000000000i2−i22−2
χ302-222-2-2-222i2i−2i−2i2-2002-20022-2-202i−2i00002i−2i0000000000000000−i2−i2i2i2−2−2220000000000−i2i2−22
χ312-222-2-2-222i2i−2i−2i2-2002-200-2-22202i−2i0000−2i2i0000000000000000i2i2−i2−i222−2−20000000000−i2i2−22
χ322-222-2-2-222i2i−2i−2i2-2002-200-2-22202i−2i0000−2i2i0000000000000000−i2−i2i2i2−2−2220000000000i2−i22−2
χ332-222-2-2-22−2i−2i2i2i2-2002-20022-2-20−2i2i0000−2i2i0000000000000000i2i2−i2−i2−2−2220000000000i2−i2−22
χ342-222-2-2-22−2i−2i2i2i2-2002-20022-2-20−2i2i0000−2i2i0000000000000000−i2−i2i2i222−2−20000000000−i2i22−2
χ352-222-2-2-22−2i−2i2i2i2-2002-200-2-2220−2i2i00002i−2i0000000000000000i2i2−i2−i2−2−2220000000000−i2i22−2
χ362-222-2-2-22−2i−2i2i2i2-2002-200-2-2220−2i2i00002i−2i0000000000000000−i2−i2i2i222−2−20000000000i2−i2−22
χ372-22-2-222-22i−2i2i−2i002-2002-200000002i−2i0000002i−2i002-222−2−2i2i2−i2−i2i2−i2i2−i22−22−200000000000000
χ382-22-2-222-22i−2i2i−2i002-2002-200000002i−2i0000002i−2i002-2−2−222−i2−i2i2i2−i2i2−i2i2−22−2200000000000000
χ392-22-2-222-22i−2i2i−2i002-2002-200000002i−2i000000−2i2i00-2222−2−2i2i2−i2−i2−i2i2−i2i2−22−2200000000000000
χ402-22-2-222-22i−2i2i−2i002-2002-200000002i−2i000000−2i2i00-22−2−222−i2−i2i2i2i2−i2i2−i22−22−200000000000000
χ412-22-2-222-2−2i2i−2i2i002-2002-20000000−2i2i0000002i−2i00-2222−2−2−i2−i2i2i2i2−i2i2−i2−22−2200000000000000
χ422-22-2-222-2−2i2i−2i2i002-2002-20000000−2i2i0000002i−2i00-22−2−222i2i2−i2−i2−i2i2−i2i22−22−200000000000000
χ432-22-2-222-2−2i2i−2i2i002-2002-20000000−2i2i000000−2i2i002-222−2−2−i2−i2i2i2−i2i2−i2i22−22−200000000000000
χ442-22-2-222-2−2i2i−2i2i002-2002-20000000−2i2i000000−2i2i002-2−2−222i2i2−i2−i2i2−i2i2−i2−22−2200000000000000
χ452-2-2222-2-20000-22222-2-2-22i−2i2i−2i-20000200000002i−2i0000002-22-200000000000000002i−2i0000
χ462-2-2222-2-20000-22222-2-2-22i−2i2i−2i-20000200000002i−2i000000-22-220000000000000000−2i2i0000
χ472-2-2222-2-20000-22222-2-2-2−2i2i−2i2i-2000020000000−2i2i0000002-22-20000000000000000−2i2i0000
χ482-2-2222-2-20000-22222-2-2-2−2i2i−2i2i-2000020000000−2i2i000000-22-2200000000000000002i−2i0000
χ492-2-2222-2-20000-22-2-22-2222i−2i2i−2i20000-20000000−2i2i002i−2i2i−2i00000000000000002-200000000
χ502-2-2222-2-20000-22-2-22-2222i−2i2i−2i20000-20000000−2i2i00−2i2i−2i2i0000000000000000-2200000000
χ512-2-2222-2-20000-22-2-22-222−2i2i−2i2i20000-200000002i−2i002i−2i2i−2i0000000000000000-2200000000
χ522-2-2222-2-20000-22-2-22-222−2i2i−2i2i20000-200000002i−2i00−2i2i−2i2i00000000000000002-200000000
χ53444-44-4-4-44-4-4400000000000000000000000000000000000002-2-222-2-2200000000000000
χ54444-44-4-4-44-4-440000000000000000000000000000000000000-222-2-222-200000000000000
χ55444-44-4-4-4-444-400000000000000000000000000000000000002-2-22-222-200000000000000
χ56444-44-4-4-4-444-40000000000000000000000000000000000000-222-22-2-2200000000000000
χ5744-44-4-44-400004400-4-40000000000000004-4000000000000000000000000000000000000
χ5844-44-4-44-400004400-4-4000000000000000-44000000000000000000000000000000000000
χ5944-44-4-44-40000-4-40044004i−4i−4i4i00000000000000000000000000000000000000000000000
χ6044-44-4-44-40000-4-4004400−4i4i4i−4i00000000000000000000000000000000000000000000000
χ6144-4-4-44-440000004-400-4400000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ6244-4-4-44-440000004-400-440000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ6344-4-4-44-44000000-44004-40000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ6444-4-4-44-44000000-44004-4000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ654-444-4-4-444i4i−4i−4i-4400-440000000−4i4i00000000000000000000000000000000000000000000
χ664-444-4-4-44−4i−4i4i4i-4400-4400000004i−4i00000000000000000000000000000000000000000000
χ674-44-4-444-44i−4i4i−4i00-4400-440000000−4i4i000000000000000000000000000000000000000000
χ684-44-4-444-4−4i4i−4i4i00-4400-4400000004i−4i000000000000000000000000000000000000000000
χ694-4-4444-4-400004-444-44-4-4000040000-400000000000000000000000000000000000000000
χ704-4-4444-4-400004-4-4-4-44440000-40000400000000000000000000000000000000000000000
χ718-8-8-88-888000000000000000000000000000000000000000000000000000000000000000

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