Finite Group Databasebeta

← Group #305261

Character table — Group #305261

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-111111111-1-1-11-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11-1111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-11111-1-11-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-111111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111-111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-11-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ172222222222-2-22-22-2-222220000-222220000-2-200220000-2-2000000000000000-2000000000
χ182222222222-2-22-22-2-222220000-2-2-2-2-20000-2-200-2-20000220000000000000002000000000
χ192222222222-2-22-22-2-2-2-2-2-20000-2222200002200-2-20000-2-20000000000000002000000000
χ202222222222-2-22-22-2-2-2-2-2-20000-2-2-2-2-20000220022000022000000000000000-2000000000
χ2122222222-2-222-22-22-200002222-20000222200-2-20022-2-20000000000000000-20000000000
χ2222222222-2-222-22-22-200002222-20000-2-2-2-200-2-200-2-222000000000000000020000000000
χ2322222222-2-222-22-22-20000-2-2-2-2-200002222002200-2-2-2-2000000000000000020000000000
χ2422222222-2-222-22-22-20000-2-2-2-2-20000-2-2-2-200220022220000000000000000-20000000000
χ25222-2-2-2-222-20020-2002i2i−2i−2i0000022-2-222−2−200002i−2i002−2000000i2i2−i2−i222−2−200000000i2−i2000
χ26222-2-2-2-222-20020-2002i2i−2i−2i0000022-2-2−2−22200002i−2i00−22000000−i2−i2i2i2−2−22200000000−i2i2000
χ27222-2-2-2-222-20020-2002i2i−2i−2i00000-2-22222−2−20000−2i2i002−2000000i2i2−i2−i2−2−22200000000−i2i2000
χ28222-2-2-2-222-20020-2002i2i−2i−2i00000-2-222−2−2220000−2i2i00−22000000−i2−i2i2i222−2−200000000i2−i2000
χ29222-2-2-2-222-20020-200−2i−2i2i2i0000022-2-222−2−20000−2i2i002−2000000−i2−i2i2i222−2−200000000−i2i2000
χ30222-2-2-2-222-20020-200−2i−2i2i2i0000022-2-2−2−2220000−2i2i00−22000000i2i2−i2−i2−2−22200000000i2−i2000
χ31222-2-2-2-222-20020-200−2i−2i2i2i00000-2-22222−2−200002i−2i002−2000000−i2−i2i2i2−2−22200000000i2−i2000
χ32222-2-2-2-222-20020-200−2i−2i2i2i00000-2-222−2−22200002i−2i00−22000000i2i2−i2−i222−2−200000000−i2i2000
χ332-22-22-22-22222-2-2-2-222-22-222-2-2-2000000002-22-2000000000000000000002-200000000000
χ342-22-22-22-22222-2-2-2-222-22-2-2-222-2000000002-2-2200000000000000000000-2200000000000
χ352-22-22-22-22222-2-2-2-22-22-2222-2-2-200000000-222-200000000000000000000-2200000000000
χ362-22-22-22-22222-2-2-2-22-22-22-2-222-200000000-22-22000000000000000000002-200000000000
χ372-22-22-22-222-2-2-22-22-22-22-20000200000000-2200000000002i2i−2i−2i0000000000002i−2i0000000
χ382-22-22-22-222-2-2-22-22-22-22-20000200000000-220000000000−2i−2i2i2i000000000000−2i2i0000000
χ392-22-22-22-222-2-2-22-22-2-22-2200002000000002-200000000002i2i−2i−2i000000000000−2i2i0000000
χ402-22-22-22-222-2-2-22-22-2-22-2200002000000002-20000000000−2i−2i2i2i0000000000002i−2i0000000
χ412-22-22-22-2-2-2222-22-2-2000022-2-220000000000-220000000000002i−2i2i−2i00000000002i−2i00000
χ422-22-22-22-2-2-2222-22-2-2000022-2-220000000000-22000000000000−2i2i−2i2i0000000000−2i2i00000
χ432-22-22-22-2-2-2222-22-2-20000-2-222200000000002-20000000000002i−2i2i−2i0000000000−2i2i00000
χ442-22-22-22-2-2-2222-22-2-20000-2-222200000000002-2000000000000−2i2i−2i2i00000000002i−2i00000
χ452-2-2-2-2222002-20-202000002-22-202−22−22-22-20000002-2002−22−22−200002−22−200000000002−20
χ462-2-2-2-2222002-20-202000002-22-202−22−2-22-22000000-22002−22−22−20000−22−220000000000−220
χ472-2-2-2-2222002-20-202000002-22-20−22−222-22-20000002-200−22−22−220000−22−220000000000−220
χ482-2-2-2-2222002-20-202000002-22-20−22−22-22-22000000-2200−22−22−2200002−22−200000000002−20
χ492-2-2-2-2222002-20-20200000-22-2202−22−22-22-2000000-22002−2−22−2200002−22−20000000000−220
χ502-2-2-2-2222002-20-20200000-22-2202−22−2-22-220000002-2002−2−22−220000−22−2200000000002−20
χ512-2-2-2-2222002-20-20200000-22-220−22−222-22-2000000-2200−222−22−20000−22−2200000000002−20
χ522-2-2-2-2222002-20-20200000-22-220−22−22-22-220000002-200−222−22−200002−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4400-4040000000000000002222−22−2200000000−2222000000000000000000000000000
χ55444-4-4-4-44-4400-404000000000000000−22−2222220000000022−22000000000000000000000000000
χ5644-44-4-44-4004-4040-4000004-4-440000000000000000000000000000000000000000000000
χ5744-44-4-44-4004-4040-400000-444-40000000000000000000000000000000000000000000000
χ5844-44-4-44-400-440-4040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5944-44-4-44-400-440-404000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ604-444-44-4-44-400-404004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ614-444-44-4-44-400-40400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ624-444-44-4-4-440040-40000000000000000000000000000000000022−22−222200000000000000000
χ634-444-44-4-4-440040-400000000000000000000000000000000000−222222−2200000000000000000
χ644-44-44-44-4-4-4-4-44444400000000-4000000000000000000000000000000000000000000000
χ654-4-444-4-4400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ664-4-444-4-4400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ674-4-444-4-44000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ684-4-444-4-44000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ694-4-4-4-444400-44040-4000000000022−2222−2200000000000000−22220000000000000000000000000
χ704-4-4-4-444400-44040-40000000000−2222−22220000000000000022−220000000000000000000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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