Finite Group Databasebeta

← Group #283985

Character table — Group #283985

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822224444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11-1-111-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111-111-1-11-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1111-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-111-1-1-111-11
χ911111111111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-111
χ1011111111111111111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111-1-1-1-111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-1-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-111111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111-1-1-111-1-1-11
χ172222222222-2-2-222-2-20000-22222-2-2-2-200002200220000000000000000-20000-2000000
χ182222222222-2-2-222-2-20000-22222-2-2-2-20000-2-200-2-20000000000000000200002000000
χ192222222222-2-2-222-2-20000-2-2-2-2-2222200002200-2-2000000000000000020000-2000000
χ202222222222-2-2-222-2-20000-2-2-2-2-222220000-2-200220000000000000000-200002000000
χ2122222222-2-2222-2-22-22222-200000000-2-22200-2-200-2-200002200000000000000000000
χ2222222222-2-2222-2-22-22222-200000000-2-2-2-2002200220000-2-200000000000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-200000000222200-2-200220000-2-200000000000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-20000000022-2-2002200-2-200002200000000000000000000
χ2522-22-2-2-2200-22200-202i2i−2i−2i0i2i2−i2−i2i2i2−i2−i20000002i−2i002-222−2−20022−2−2i2i2−i2−i2000000000000
χ2622-22-2-2-2200-22200-202i2i−2i−2i0i2i2−i2−i2i2i2−i2−i2000000−2i2i00-2222−2−200−2−222−i2−i2i2i2000000000000
χ2722-22-2-2-2200-22200-202i2i−2i−2i0−i2−i2i2i2−i2−i2i2i20000002i−2i002-2−2−22200−2−222−i2−i2i2i2000000000000
χ2822-22-2-2-2200-22200-202i2i−2i−2i0−i2−i2i2i2−i2−i2i2i2000000−2i2i00-22−2−2220022−2−2i2i2−i2−i2000000000000
χ2922-22-2-2-2200-22200-20−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i20000002i−2i00-22−2−2220022−2−2−i2−i2i2i2000000000000
χ3022-22-2-2-2200-22200-20−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i2000000−2i2i002-2−2−22200−2−222i2i2−i2−i2000000000000
χ3122-22-2-2-2200-22200-20−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i20000002i−2i00-2222−2−200−2−222i2i2−i2−i2000000000000
χ3222-22-2-2-2200-22200-20−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i2000000−2i2i002-222−2−20022−2−2−i2−i2i2i2000000000000
χ332-22-2-2-2220022-200-202i−2i2i−2i02−22−22−22−2002-200000000i2−i2i2−i22i−2i2−22−2i2−i2i2−i2000000000000
χ342-22-2-2-2220022-200-202i−2i2i−2i02−22−22−22−200-2200000000i2−i2i2−i2−2i2i−22−22−i2i2−i2i2000000000000
χ352-22-2-2-2220022-200-202i−2i2i−2i0−22−22−22−22002-200000000−i2i2−i2i22i−2i−22−22−i2i2−i2i2000000000000
χ362-22-2-2-2220022-200-202i−2i2i−2i0−22−22−22−2200-2200000000−i2i2−i2i2−2i2i2−22−2i2−i2i2−i2000000000000
χ372-22-2-2-2220022-200-20−2i2i−2i2i02−22−22−22−2002-200000000−i2i2−i2i2−2i2i2−22−2−i2i2−i2i2000000000000
χ382-22-2-2-2220022-200-20−2i2i−2i2i02−22−22−22−200-2200000000−i2i2−i2i22i−2i−22−22i2−i2i2−i2000000000000
χ392-22-2-2-2220022-200-20−2i2i−2i2i0−22−22−22−22002-200000000i2−i2i2−i2−2i2i−22−22i2−i2i2−i2000000000000
χ402-22-2-2-2220022-200-20−2i2i−2i2i0−22−22−22−2200-2200000000i2−i2i2−i22i−2i2−22−2−i2i2−i2i2000000000000
χ412-2-2-222-22222-22-2-2-2-2000022i−2i−2i2i−2i2i2i−2i0000000000000000000000000002i−2i2-20000000
χ422-2-2-222-22222-22-2-2-2-2000022i−2i−2i2i−2i2i2i−2i000000000000000000000000000−2i2i-220000000
χ432-2-2-222-22222-22-2-2-2-200002−2i2i2i−2i2i−2i−2i2i0000000000000000000000000002i−2i-220000000
χ442-2-2-222-22222-22-2-2-2-200002−2i2i2i−2i2i−2i−2i2i000000000000000000000000000−2i2i2-20000000
χ452-2-2-222-2222-22-2-2-2222-2-22-22i−2i−2i2i2i−2i−2i2i2-20000000000−2i2i2i−2i0000000000000000000000
χ462-2-2-222-2222-22-2-2-2222-2-22-2−2i2i2i−2i−2i2i2i−2i2-200000000002i−2i−2i2i0000000000000000000000
χ472-2-2-222-2222-22-2-2-222-222-2-22i−2i−2i2i2i−2i−2i2i-2200000000002i−2i−2i2i0000000000000000000000
χ482-2-2-222-2222-22-2-2-222-222-2-2−2i2i2i−2i−2i2i2i−2i-220000000000−2i2i2i−2i0000000000000000000000
χ492-2-2-222-22-2-2-22-2222-22-2-22200000000-2200000000000000002-2-222-2-22000000000000
χ502-2-2-222-22-2-2-22-2222-22-2-22200000000-220000000000000000-222-2-222-2000000000000
χ512-2-2-222-22-2-2-22-2222-2-222-22000000002-200000000000000002-2-22-222-2000000000000
χ522-2-2-222-22-2-2-22-2222-2-222-22000000002-20000000000000000-222-22-2-22000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ5444-44-4-4-44004-4-40040000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ5544-44-4-4-44004-4-4004000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-4-44-44-44-40004-400000000000000000004i−4i00000000000000000000000000000000
χ5744-4-44-44-44-40004-40000000000000000000−4i4i00000000000000000000000000000000
χ5844-4-44-44-4-44000-4400000000000000000000000000000000000000000000000002i2−2i200
χ5944-4-44-44-4-44000-440000000000000000000000000000000000000000000000000−2i22i200
χ604-4444-4-4-44-4000-44000000000000000000000004i−4i0000000000000000000000000000
χ614-4444-4-4-44-4000-4400000000000000000000000−4i4i0000000000000000000000000000
χ624-4444-4-4-4-440004-4000000000000000000000000000000000000000000000002i2−2i20000
χ634-4444-4-4-4-440004-400000000000000000000000000000000000000000000000−2i22i20000
χ644-44-4-4-44400-4-4400400000022−2222−22−2222−222200000000000000000000000000000000000000
χ654-44-4-4-44400-4-44004000000−2222−222222−2222−2200000000000000000000000000000000000000
χ664-4-4-444-44-4-44-4444-440000-40000000000000000000000000000000000000000000000
χ67888-8-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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