Finite Group Databasebeta

← Group #252689

Character table — Group #252689

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444444444444444888888888888888822224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111-1-111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111111-1-1-1-111-1-11111111111111111-1-1-1-11-1-11-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111
χ7111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ8111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-111111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-111111-1-1
χ1011111111-1-1-1-111111111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1111-1-111
χ1111111111-1-1-1-111111111-1-1-1-1111111-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-1-111
χ1211111111-1-1-1-111111111-1-1-1-1111111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-1-111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1111-1-1-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1111-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1111-1-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-11-1-1-111-1-111
χ1722222222222222-2-2-222-222-2-20000-2-222-20000220000000000000000000000-200-2000000
χ1822222222222222-2-2-222-222-2-20000-2-2-2-2-20000-2-200000000000000000000002002000000
χ19222222222222-2-2222-2-22-2-2222222-2-200-2-2-2-2-20022000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-222-2-2-2-2-2-200-2222200-2-2000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2000022002000000000000000000000000000002-202-20000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-200002200200000000000000000000000000000-220-220000
χ2322222222-2-2-2-222-2-2-222-2-2-2220000-2-22220000-2-20000000000000000000000200-2000000
χ2422222222-2-2-2-222-2-2-222-2-2-2220000-2-2-2-220000220000000000000000000000-2002000000
χ2522222222-2-2-2-2-2-2222-2-2222-2-22222-2-2002-2-22200-2-2000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2222-2-2-2-2-2-2-2-200222-2-20022000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-2000000000000000000000000000002-20-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-200000000000000000000000000000-2202-20000
χ292-222-2-22-200002-222-22-2-200002i2i−2i−2i2-20002i−2i00000000002i2i−2i−2i00000000002-20000000000
χ302-222-2-22-200002-222-22-2-200002i2i−2i−2i2-20002i−2i0000000000−2i−2i2i2i0000000000-220000000000
χ312-222-2-22-200002-222-22-2-20000−2i−2i2i2i2-2000−2i2i00000000002i2i−2i−2i0000000000-220000000000
χ322-222-2-22-200002-222-22-2-20000−2i−2i2i2i2-2000−2i2i0000000000−2i−2i2i2i00000000002-20000000000
χ332-222-2-22-20000-2222-2-22-200002i2i−2i−2i-22000−2i2i0000002i2i−2i−2i0000000000002-2000000000000
χ342-222-2-22-20000-2222-2-22-200002i2i−2i−2i-22000−2i2i000000−2i−2i2i2i000000000000-22000000000000
χ352-222-2-22-20000-2222-2-22-20000−2i−2i2i2i-220002i−2i0000002i2i−2i−2i000000000000-22000000000000
χ362-222-2-22-20000-2222-2-22-20000−2i−2i2i2i-220002i−2i000000−2i−2i2i2i0000000000002-2000000000000
χ372-22-22-2-2222-2-222000-2-202-2000000002i−2i000002i−2i002−22−22−22−2i2i2−i2−i2i2i2−i2−i200000000000000
χ382-22-22-2-2222-2-222000-2-202-2000000002i−2i000002i−2i00−22−22−22−22−i2−i2i2i2−i2−i2i2i200000000000000
χ392-22-22-2-2222-2-222000-2-202-200000000−2i2i00000−2i2i002−22−22−22−2−i2−i2i2i2−i2−i2i2i200000000000000
χ402-22-22-2-2222-2-222000-2-202-200000000−2i2i00000−2i2i00−22−22−22−22i2i2−i2−i2i2i2−i2−i200000000000000
χ412-22-22-2-22-2-22222000-2-20-22000000002i−2i00000−2i2i002−22−2−22−22i2i2−i2−i2−i2−i2i2i200000000000000
χ422-22-22-2-22-2-22222000-2-20-22000000002i−2i00000−2i2i00−22−222−22−2−i2−i2i2i2i2i2−i2−i200000000000000
χ432-22-22-2-22-2-22222000-2-20-2200000000−2i2i000002i−2i002−22−2−22−22−i2−i2i2i2i2i2−i2−i200000000000000
χ442-22-22-2-22-2-22222000-2-20-2200000000−2i2i000002i−2i00−22−222−22−2i2i2−i2−i2−i2−i2i2i200000000000000
χ452-2-2-2222-22-22-2002-2200-2002-22i−2i2i−2i000000000002i−2i000000002−22−22−22−20000000000i2−i2i2−i2
χ462-2-2-2222-22-22-2002-2200-2002-22i−2i2i−2i000000000002i−2i00000000−22−22−22−220000000000−i2i2−i2i2
χ472-2-2-2222-22-22-2002-2200-2002-2−2i2i−2i2i00000000000−2i2i000000002−22−22−22−20000000000−i2i2−i2i2
χ482-2-2-2222-22-22-2002-2200-2002-2−2i2i−2i2i00000000000−2i2i00000000−22−22−22−220000000000i2−i2i2−i2
χ492-2-2-2222-2-22-22002-2200-200-222i−2i2i−2i00000000000−2i2i000000002−22−2−22−220000000000i2−i2−i2i2
χ502-2-2-2222-2-22-22002-2200-200-222i−2i2i−2i00000000000−2i2i00000000−22−222−22−20000000000−i2i2i2−i2
χ512-2-2-2222-2-22-22002-2200-200-22−2i2i−2i2i000000000002i−2i000000002−22−2−22−220000000000−i2i2i2−i2
χ522-2-2-2222-2-22-22002-2200-200-22−2i2i−2i2i000000000002i−2i00000000−22−222−22−20000000000i2−i2−i2i2
χ53444-4-44-4-400004-4000-44000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ54444-4-44-4-400004-4000-4400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ55444-4-44-4-40000-440004-400000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ56444-4-44-4-40000-440004-40000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ5744-444-4-4-44-4-4400000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5844-444-4-4-44-4-440000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5944-444-4-4-4-444-400000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ6044-444-4-4-4-444-40000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ6144-4-4-4-4440000004-4-400400004-4-440000000000000000000000000000000000000000000
χ6244-4-4-4-4440000004-4-40040000-444-40000000000000000000000000000000000000000000
χ6344-4-4-4-444000000-44400-40000000000000004i−4i0000000000000000000000000000000000
χ6444-4-4-4-444000000-44400-4000000000000000−4i4i0000000000000000000000000000000000
χ654-444-4-44-400004-4-4-444-4400000000-4400000000000000000000000000000000000000000
χ664-444-4-44-40000-44-4-44-444000000004-400000000000000000000000000000000000000000
χ674-44-44-4-4444-4-4-4-4000440-440000000000000000000000000000000000000000000000000
χ684-44-44-4-44-4-444-4-40004404-40000000000000000000000000000000000000000000000000
χ694-4-4-4444-44-44-400-44-400400-4400000000000000000000000000000000000000000000000
χ704-4-4-4444-4-44-4400-44-4004004-400000000000000000000000000000000000000000000000
χ718-8-88-88-88000000000000000000000000000000000000000000000000000000000000000

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