Finite Group Databasebeta

← Group #284062

Character table — Group #284062

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-111-1-11-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111
χ1011111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-1-11-1-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1111-1-1-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1111-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111111-1-1-11111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-11-1-1-111-1-1111-1
χ172222222222-2-2-222-2-20000-22222-2-2-2-222220000000000000000000000-200-200000000
χ182222222222-2-2-222-2-20000-22222-2-2-2-2-2-2-2-20000000000000000000000200200000000
χ192222222222-2-2-222-2-20000-2-2-2-2-2222222-2-20000000000000000000000200-200000000
χ202222222222-2-2-222-2-20000-2-2-2-2-22222-2-2220000000000000000000000-200200000000
χ2122222222-2-2222-2-22-22222-2000000000000-2-222-2-2220000-2-200000000000000000000
χ2222222222-2-2222-2-22-22222-2000000000000-2-2-2-222-2-200002200000000000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-20000000000002222-2-2-2-200002200000000000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-200000000000022-2-222220000-2-200000000000000000000
χ2522-2-2-2-222222-22-2-2-2-2000022i2i−2i−2i2i2i−2i−2i0000000000000000000000000002i−2i02-2000000
χ2622-2-2-2-222222-22-2-2-2-2000022i2i−2i−2i2i2i−2i−2i000000000000000000000000000−2i2i0-22000000
χ2722-2-2-2-222222-22-2-2-2-200002−2i−2i2i2i−2i−2i2i2i0000000000000000000000000002i−2i0-22000000
χ2822-2-2-2-222222-22-2-2-2-200002−2i−2i2i2i−2i−2i2i2i000000000000000000000000000−2i2i02-2000000
χ2922-2-2-2-22222-22-2-2-22222-2-2-22i2i−2i−2i−2i−2i2i2i00002-20000002i2i−2i−2i0000000000000000000000
χ3022-2-2-2-22222-22-2-2-22222-2-2-2−2i−2i2i2i2i2i−2i−2i00002-2000000−2i−2i2i2i0000000000000000000000
χ3122-2-2-2-22222-22-2-2-222-2-222-22i2i−2i−2i−2i−2i2i2i0000-22000000−2i−2i2i2i0000000000000000000000
χ3222-2-2-2-22222-22-2-2-222-2-222-2−2i−2i2i2i2i2i−2i−2i0000-220000002i2i−2i−2i0000000000000000000000
χ3322-2-2-2-222-2-2-22-2222-222-2-22000000000000-2200000000000022-2-222-2-2000000000000
χ3422-2-2-2-222-2-2-22-2222-222-2-22000000000000-22000000000000-2-222-2-222000000000000
χ3522-2-2-2-222-2-2-22-2222-2-2-22220000000000002-200000000000022-2-2-2-222000000000000
χ3622-2-2-2-222-2-2-22-2222-2-2-22220000000000002-2000000000000-2-22222-2-2000000000000
χ372-222-2-22-200-2-2200202i−2i2i−2i02−22−22−22−2000000002i−2i00i2−i2i2−i22-2i2−i2i2−i22−22−2000000000000
χ382-222-2-22-200-2-2200202i−2i2i−2i02−22−22−22−200000000−2i2i00i2−i2i2−i2-22−i2i2−i2i2−22−22000000000000
χ392-222-2-22-200-2-2200202i−2i2i−2i0−22−22−22−22000000002i−2i00−i2i2−i2i22-2−i2i2−i2i2−22−22000000000000
χ402-222-2-22-200-2-2200202i−2i2i−2i0−22−22−22−2200000000−2i2i00−i2i2−i2i2-22i2−i2i2−i22−22−2000000000000
χ412-222-2-22-200-2-220020−2i2i−2i2i02−22−22−22−2000000002i−2i00−i2i2−i2i2-22i2−i2i2−i2−22−22000000000000
χ422-222-2-22-200-2-220020−2i2i−2i2i02−22−22−22−200000000−2i2i00−i2i2−i2i22-2−i2i2−i2i22−22−2000000000000
χ432-222-2-22-200-2-220020−2i2i−2i2i0−22−22−22−22000000002i−2i00i2−i2i2−i2-22−i2i2−i2i22−22−2000000000000
χ442-222-2-22-200-2-220020−2i2i−2i2i0−22−22−22−2200000000−2i2i00i2−i2i2−i22-2i2−i2i2−i2−22−22000000000000
χ452-2-2-2222-2002-2-200202i−2i−2i2i0i2−i2−i2i2−i2i2i2−i20000002-2002i−2i−222−200i2−i2−i2i22−2−22000000000000
χ462-2-2-2222-2002-2-200202i−2i−2i2i0i2−i2−i2i2−i2i2i2−i2000000-2200−2i2i−222−200−i2i2i2−i2−222−2000000000000
χ472-2-2-2222-2002-2-200202i−2i−2i2i0−i2i2i2−i2i2−i2−i2i20000002-2002i−2i2−2−2200−i2i2i2−i2−222−2000000000000
χ482-2-2-2222-2002-2-200202i−2i−2i2i0−i2i2i2−i2i2−i2−i2i2000000-2200−2i2i2−2−2200i2−i2−i2i22−2−22000000000000
χ492-2-2-2222-2002-2-20020−2i2i2i−2i0i2−i2−i2i2−i2i2i2−i20000002-200−2i2i2−2−2200i2−i2−i2i2−222−2000000000000
χ502-2-2-2222-2002-2-20020−2i2i2i−2i0i2−i2−i2i2−i2i2i2−i2000000-22002i−2i2−2−2200−i2i2i2−i22−2−22000000000000
χ512-2-2-2222-2002-2-20020−2i2i2i−2i0−i2i2i2−i2i2−i2−i2i20000002-200−2i2i−222−200−i2i2i2−i22−2−22000000000000
χ522-2-2-2222-2002-2-20020−2i2i2i−2i0−i2i2i2−i2i2−i2−i2i2000000-22002i−2i−222−200i2−i2−i2i2−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-44-4-4-44-40004-40000000000000000000000000000000000000000000000022−220000
χ55444-44-4-4-44-40004-400000000000000000000000000000000000000000000000−22220000
χ56444-44-4-4-4-44000-440000000000000004-4000000000000000000000000000000000000
χ57444-44-4-4-4-44000-44000000000000000-44000000000000000000000000000000000000
χ5844-44-44-4-44-4000-44000000000000000000000000000000000000000000000000022−2200
χ5944-44-44-4-44-4000-440000000000000000000000000000000000000000000000000−222200
χ6044-44-44-4-4-440004-4000000000000000004-40000000000000000000000000000000000
χ6144-44-44-4-4-440004-400000000000000000-440000000000000000000000000000000000
χ6244-4-4-4-444-4-44-4444-440000-40000000000000000000000000000000000000000000000
χ634-444-4-44-40044-400-400000022−2222−22−2222−222200000000000000000000000000000000000000
χ644-444-4-44-40044-400-4000000−2222−222222−2222−2200000000000000000000000000000000000000
χ654-4-4-4444-400-44400-40000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ664-4-4-4444-400-44400-4000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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