Finite Group Databasebeta

← Group #270084

Character table — Group #270084

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-111-1
χ71111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11
χ911111111111111111-1-1-1-1111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11
χ1011111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111111-1-1111-1-1-1-1-1-1111
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-111111111-1-1-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1111-1-111-1-111-1-1-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-111-1-1-1-1-111-1-1111
χ172222222222-22-2-2-22-22222-200000000-2-2220022000000-2-20000000-200000000000
χ182222222222-22-2-2-22-22222-200000000-2-2-2-200-2-2000000220000000200000000000
χ192222222222-22-2-2-22-2-2-2-2-2-200000000222200-2-2000000220000000-200000000000
χ202222222222-22-2-2-22-2-2-2-2-2-20000000022-2-20022000000-2-20000000200000000000
χ2122222222-2-22-2222-2-20000-2222222-2-200002200-2-20000000000-200000000000000
χ2222222222-2-22-2222-2-20000-22222-2-2220000-2-200-2-20000000000200000000000000
χ2322222222-2-22-2222-2-20000-2-2-2-2-222220000-2-200220000000000-200000000000000
χ2422222222-2-22-2222-2-20000-2-2-2-2-2-2-2-2-200002200220000000000200000000000000
χ2522-2-22-22-22-20-2000202i2i−2i−2i022−2−20000002-2002i−2i2−2i2i2−i2−i200i2i2−i2−i2000000002−200000
χ2622-2-22-22-22-20-2000202i2i−2i−2i022−2−2000000-2200−2i2i2−2i2i2−i2−i200−i2−i2i2i200000000−2200000
χ2722-2-22-22-22-20-2000202i2i−2i−2i0−2−2220000002-2002i−2i−22−i2−i2i2i200−i2−i2i2i200000000−2200000
χ2822-2-22-22-22-20-2000202i2i−2i−2i0−2−222000000-2200−2i2i−22−i2−i2i2i200i2i2−i2−i2000000002−200000
χ2922-2-22-22-22-20-200020−2i−2i2i2i022−2−20000002-200−2i2i2−2−i2−i2i2i200−i2−i2i2i2000000002−200000
χ3022-2-22-22-22-20-200020−2i−2i2i2i022−2−2000000-22002i−2i2−2−i2−i2i2i200i2i2−i2−i200000000−2200000
χ3122-2-22-22-22-20-200020−2i−2i2i2i0−2−2220000002-200−2i2i−22i2i2−i2−i200i2i2−i2−i200000000−2200000
χ3222-2-22-22-22-20-200020−2i−2i2i2i0−2−222000000-22002i−2i−22i2i2−i2−i200−i2−i2i2i2000000002−200000
χ332-2-2-2-2222222-2-22-2-220000-20000002-200002-200002i−2i2i−2i00000002i−2i000000000000
χ342-2-2-2-2222222-2-22-2-220000-20000002-200002-20000−2i2i−2i2i0000000−2i2i000000000000
χ352-2-2-2-2222222-2-22-2-220000-2000000-220000-2200002i−2i2i−2i0000000−2i2i000000000000
χ362-2-2-2-2222222-2-22-2-220000-2000000-220000-220000−2i2i−2i2i00000002i−2i000000000000
χ372-2-2-2-2222-2-222-22-22-22-22-220000002-22-200-220000000000000000002-2000000000
χ382-2-2-2-2222-2-222-22-22-22-22-22000000-222-2002-2000000000000000000-22000000000
χ392-2-2-2-2222-2-222-22-22-2-22-2220000002-2-2200-22000000000000000000-22000000000
χ402-2-2-2-2222-2-222-22-22-2-22-222000000-22-22002-20000000000000000002-2000000000
χ412-2-2-2-2222-2-2-222-22222-22-2-200000000-220000000000000000000000002-200002-20
χ422-2-2-2-2222-2-2-222-22222-22-2-200000000-22000000000000000000000000-220000-220
χ432-2-2-2-2222-2-2-222-2222-22-22-2000000002-20000000000000000000000002-20000-220
χ442-2-2-2-2222-2-2-222-2222-22-22-2000000002-2000000000000000000000000-2200002-20
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-44-4-40000000000000022−2222−2200000000000000000022−222-22-2000000000000000
χ47444-4-44-4-40000000000000022−2222−22000000000000000000−2222-22-22000000000000000
χ48444-4-44-4-400000000000000−2222−222200000000000000000022−22-22-22000000000000000
χ49444-4-44-4-400000000000000−2222−2222000000000000000000−22222-22-2000000000000000
χ5044-44-4-4-4400404-4-400000004-4-44000000000000000000000000000000000000000
χ5144-44-4-4-4400404-4-40000000-444-4000000000000000000000000000000000000000
χ5244-44-4-4-4400-40-44400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ5344-44-4-4-4400-40-4440000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ5444-4-44-44-4-4404000-40000002222−22−22000000000000−22220000000000000000000000000
χ5544-4-44-44-4-4404000-4000000−22−22222200000000000022−220000000000000000000000000
χ564-444-4-44-44-404000-400000000000000000000000022−22−2222000000000000000000000
χ574-444-4-44-44-404000-4000000000000000000000000−222222−22000000000000000000000
χ584-444-4-44-4-440-4000404i−4i−4i4i00000000000000000000000000000000000000000000
χ594-444-4-44-4-440-400040−4i4i4i−4i00000000000000000000000000000000000000000000
χ604-44-44-4-440040-4-44000000000004i−4i0000000000000000000000000000000000000
χ614-44-44-4-440040-4-4400000000000−4i4i0000000000000000000000000000000000000
χ624-44-44-4-4400-4044-40000000000000000000000000000000000000000000002i2−2i2000
χ634-44-44-4-4400-4044-4000000000000000000000000000000000000000000000−2i22i2000
χ644-4-4-4-444444-4-44-44-4-4000040000000000000000000000000000000000000000000
χ658-8-8888-8-8000000000000000000000000000000000000000000000000000000000

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