Finite Group Databasebeta

← Group #269751

Character table — Group #269751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-111111-1-1-1-111-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-1111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111-1-11-1-111-1-1-1-11
χ172222222222-22-2-2-220000-22222-200002222-2-200002200-2-2000000000000000-2000000000
χ182222222222-22-2-2-220000-22222-20000-2-2-2-2-2-20000-2-200220000000000000002000000000
χ192222222222-22-2-2-220000-2-2-2-2-2-200002222220000-2-200-2-20000000000000002000000000
χ202222222222-22-2-2-220000-2-2-2-2-2-20000-2-2-2-2220000220022000000000000000-2000000000
χ2122222222-2-22-2222-22222-20000-2222200000022-2-200-2-200000000000000-2000000000000
χ2222222222-2-22-2222-22222-20000-2-2-2-2-2000000-2-2-2-20022000000000000002000000000000
χ2322222222-2-22-2222-2-2-2-2-2-20000-22222000000-2-22200-2-2000000000000002000000000000
χ2422222222-2-22-2222-2-2-2-2-2-20000-2-2-2-2-20000002222002200000000000000-2000000000000
χ25222-2-2-2-2200-2022-2022-2-20000002i2i−2i−2ii2i2−i2−i2002i−2i000000i2−i20000i2i2−i2−i222−2−200000000002−20
χ26222-2-2-2-2200-2022-2022-2-20000002i2i−2i−2i−i2−i2i2i2002i−2i000000−i2i20000−i2−i2i2i2−2−2220000000000−220
χ27222-2-2-2-2200-2022-2022-2-2000000−2i−2i2i2ii2i2−i2−i200−2i2i000000i2−i20000i2i2−i2−i2−2−2220000000000−220
χ28222-2-2-2-2200-2022-2022-2-2000000−2i−2i2i2i−i2−i2i2i200−2i2i000000−i2i20000−i2−i2i2i222−2−200000000002−20
χ29222-2-2-2-2200-2022-20-2-2220000002i2i−2i−2ii2i2−i2−i200−2i2i000000i2−i20000−i2−i2i2i222−2−20000000000−220
χ30222-2-2-2-2200-2022-20-2-2220000002i2i−2i−2i−i2−i2i2i200−2i2i000000−i2i20000i2i2−i2−i2−2−22200000000002−20
χ31222-2-2-2-2200-2022-20-2-222000000−2i−2i2i2ii2i2−i2−i2002i−2i000000i2−i20000−i2−i2i2i2−2−22200000000002−20
χ32222-2-2-2-2200-2022-20-2-222000000−2i−2i2i2i−i2−i2i2i2002i−2i000000−i2i20000i2i2−i2−i222−2−20000000000−220
χ332-222-22-2-22-20-20002000002i2i−2i−2i02−22−22-22-20000002i−2i2−200i2i2−i2−i200002−22−200000000i2−i2000
χ342-222-22-2-22-20-20002000002i2i−2i−2i02−22−2-22-22000000−2i2i2−200i2i2−i2−i20000−22−2200000000−i2i2000
χ352-222-22-2-22-20-20002000002i2i−2i−2i0−22−222-22-20000002i−2i−2200−i2−i2i2i20000−22−2200000000−i2i2000
χ362-222-22-2-22-20-20002000002i2i−2i−2i0−22−22-22-22000000−2i2i−2200−i2−i2i2i200002−22−200000000i2−i2000
χ372-222-22-2-22-20-2000200000−2i−2i2i2i02−22−22-22-2000000−2i2i2−200−i2−i2i2i200002−22−200000000−i2i2000
χ382-222-22-2-22-20-2000200000−2i−2i2i2i02−22−2-22-220000002i−2i2−200−i2−i2i2i20000−22−2200000000i2−i2000
χ392-222-22-2-22-20-2000200000−2i−2i2i2i0−22−222-22-2000000−2i2i−2200i2i2−i2−i20000−22−2200000000i2−i2000
χ402-222-22-2-22-20-2000200000−2i−2i2i2i0−22−22-22-220000002i−2i−2200i2i2−i2−i200002−22−200000000−i2i2000
χ412-2-2-2-2222222-2-22-2-22-22-220000-20000000000002-20000002i−2i2i−2i0000000002i−2i0000000000
χ422-2-2-2-2222222-2-22-2-22-22-220000-20000000000002-2000000−2i2i−2i2i000000000−2i2i0000000000
χ432-2-2-2-2222222-2-22-2-2-22-2220000-2000000000000-220000002i−2i2i−2i000000000−2i2i0000000000
χ442-2-2-2-2222222-2-22-2-2-22-2220000-2000000000000-22000000−2i2i−2i2i0000000002i−2i0000000000
χ452-2-2-2-2222-2-222-22-222-22-2-22-22-22000000002-200-220000000000000000000000002-200000
χ462-2-2-2-2222-2-222-22-222-22-2-2-22-22200000000-2200-22000000000000000000000000-2200000
χ472-2-2-2-2222-2-222-22-22-22-22-22-22-22000000002-2002-2000000000000000000000000-2200000
χ482-2-2-2-2222-2-222-22-22-22-22-2-22-22200000000-22002-20000000000000000000000002-200000
χ492-2-2-2-2222-2-2-222-222000022-22-2-200000000-22000000000000002-22-2000000002-20000000
χ502-2-2-2-2222-2-2-222-222000022-22-2-200000000-2200000000000000-22-2200000000-220000000
χ512-2-2-2-2222-2-2-222-22200002-22-22-2000000002-2000000000000002-22-200000000-220000000
χ522-2-2-2-2222-2-2-222-22200002-22-22-2000000002-200000000000000-22-22000000002-20000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-440040-4-440000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ55444-4-4-4-440040-4-44000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ5644-4-444-4-44-404000-400000000000000000000000000000022−22−2222000000000000000000000
χ5744-4-444-4-44-404000-4000000000000000000000000000000−222222−22000000000000000000000
χ5844-4-444-4-4-440-40004000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5944-4-444-4-4-440-4000400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ604-444-44-4-4-4404000-4000000000022−2222−22000000000000−2222000000000000000000000000000
χ614-444-44-4-4-4404000-40000000000−2222−222200000000000022−22000000000000000000000000000
χ624-44-44-44-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ634-44-44-44-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ644-44-44-44-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ654-44-44-44-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ664-4-444-4-4400404-4-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ674-4-444-4-4400404-4-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ684-4-444-4-4400-40-44404-4-44000000000000000000000000000000000000000000000000000
χ694-4-444-4-4400-40-4440-444-4000000000000000000000000000000000000000000000000000
χ704-4-4-4-444444-4-44-44-40000-400004000000000000000000000000000000000000000000000
χ7188-88-8-88-8000000000000000000000000000000000000000000000000000000000000000

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