Finite Group Databasebeta

← Group #309524

Character table — Group #309524

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-111111111-11-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-111-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-111111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11
χ17222222222-222-2-22-20000-22222-200002222002200-2-200-2-2000000000000-2000000000000
χ18222222222-222-2-22-20000-22222-20000-2-2-2-200-2-200-2-200220000000000002000000000000
χ19222222222-222-2-22-20000-2-2-2-2-2-20000222200-2-2002200-2-20000000000002000000000000
χ20222222222-222-2-22-20000-2-2-2-2-2-20000-2-2-2-2002200220022000000000000-2000000000000
χ2122222222-22-2-222-222222-20000-2222200002200-2-200-2-2000000000000000-200000000000
χ2222222222-22-2-222-222222-20000-2-2-2-2-20000-2-200-2-20022000000000000000200000000000
χ2322222222-22-2-222-22-2-2-2-2-20000-222220000-2-2002200-2-2000000000000000200000000000
χ2422222222-22-2-222-22-2-2-2-2-20000-2-2-2-2-200002200220022000000000000000-200000000000
χ25222-22-2-2-2-202-20020000002i2i−2i−2i022−2−222-2-2002i−2i00002−200i2i2−i2−i2000022−2−20000000000i2−i20
χ26222-22-2-2-2-202-20020000002i2i−2i−2i022−2−2-2-22200−2i2i00002−200i2i2−i2−i20000−2−2220000000000−i2i20
χ27222-22-2-2-2-202-20020000002i2i−2i−2i0−2−22222-2-2002i−2i0000−2200−i2−i2i2i20000−2−2220000000000−i2i20
χ28222-22-2-2-2-202-20020000002i2i−2i−2i0−2−222-2-22200−2i2i0000−2200−i2−i2i2i2000022−2−20000000000i2−i20
χ29222-22-2-2-2-202-2002000000−2i−2i2i2i022−2−222-2-200−2i2i00002−200−i2−i2i2i2000022−2−20000000000−i2i20
χ30222-22-2-2-2-202-2002000000−2i−2i2i2i022−2−2-2-222002i−2i00002−200−i2−i2i2i20000−2−2220000000000i2−i20
χ31222-22-2-2-2-202-2002000000−2i−2i2i2i0−2−22222-2-200−2i2i0000−2200i2i2−i2−i20000−2−2220000000000i2−i20
χ32222-22-2-2-2-202-2002000000−2i−2i2i2i0−2−222-2-222002i−2i0000−2200i2i2−i2−i2000022−2−20000000000−i2i20
χ332-222-2-22-222-2-2-2-2222i2i−2i−2i22i−2i2i−2i-20000000000002i−2i2i−2i000000000000000000002-20000000
χ342-222-2-22-222-2-2-2-2222i2i−2i−2i2−2i2i−2i2i-20000000000002i−2i−2i2i00000000000000000000-220000000
χ352-222-2-22-222-2-2-2-222−2i−2i2i2i22i−2i2i−2i-2000000000000−2i2i2i−2i00000000000000000000-220000000
χ362-222-2-22-222-2-2-2-222−2i−2i2i2i2−2i2i−2i2i-2000000000000−2i2i−2i2i000000000000000000002-20000000
χ372-222-2-22-22-2-2-2222-20000-22i−2i2i−2i200000000000000−2i2i0000000022-2-20000002i−2i000000000
χ382-222-2-22-22-2-2-2222-20000-22i−2i2i−2i200000000000000−2i2i00000000-2-222000000−2i2i000000000
χ392-222-2-22-22-2-2-2222-20000-2−2i2i−2i2i2000000000000002i−2i0000000022-2-2000000−2i2i000000000
χ402-222-2-22-22-2-2-2222-20000-2−2i2i−2i2i2000000000000002i−2i00000000-2-2220000002i−2i000000000
χ412-222-2-22-2-2222-2-2-222i2i−2i−2i-200002000000000000−2i2i0000002-22-2000000000000002i−2i00000
χ422-222-2-22-2-2222-2-2-222i2i−2i−2i-200002000000000000−2i2i000000-22-2200000000000000−2i2i00000
χ432-222-2-22-2-2222-2-2-22−2i−2i2i2i-2000020000000000002i−2i0000002-22-200000000000000−2i2i00000
χ442-222-2-22-2-2222-2-2-22−2i−2i2i2i-2000020000000000002i−2i000000-22-22000000000000002i−2i00000
χ452-2-222-2-2202002-20-22i−2i2i−2i0000002i−2i2i−2i2−22−22-2000000002−20000i2−i2i2−i2i2−i2i2−i2000000002−2000
χ462-2-222-2-2202002-20-22i−2i2i−2i0000002i−2i2i−2i−22−222-200000000−220000−i2i2−i2i2−i2i2−i2i200000000−22000
χ472-2-222-2-2202002-20-22i−2i2i−2i000000−2i2i−2i2i2−22−2-22000000002−20000i2−i2i2−i2−i2i2−i2i200000000−22000
χ482-2-222-2-2202002-20-22i−2i2i−2i000000−2i2i−2i2i−22−22-2200000000−220000−i2i2−i2i2i2−i2i2−i2000000002−2000
χ492-2-222-2-2202002-20-2−2i2i−2i2i0000002i−2i2i−2i2−22−2-22000000002−20000−i2i2−i2i2i2−i2i2−i200000000−22000
χ502-2-222-2-2202002-20-2−2i2i−2i2i0000002i−2i2i−2i−22−22-2200000000−220000i2−i2i2−i2−i2i2−i2i2000000002−2000
χ512-2-222-2-2202002-20-2−2i2i−2i2i000000−2i2i−2i2i2−22−22-2000000002−20000−i2i2−i2i2−i2i2−i2i2000000002−2000
χ522-2-222-2-2202002-20-2−2i2i−2i2i000000−2i2i−2i2i−22−222-200000000−220000i2−i2i2−i2i2−i2i2−i200000000−22000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-440-4400-4000000000002222−22−22000000000000−2222000000000000000000000000000
χ55444-44-4-4-440-4400-400000000000−22−22222200000000000022−22000000000000000000000000000
χ5644-44-44-4-40400-440-44-4-44000000000000000000000000000000000000000000000000000
χ5744-44-44-4-40400-440-4-444-4000000000000000000000000000000000000000000000000000
χ5844-44-44-4-40-4004-40400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5944-44-44-4-40-4004-4040000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ604-444-4-44-4-4-44444-4-4000040000-4000000000000000000000000000000000000000000000
χ614-44-4-44-44404-400-400000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ624-44-4-44-44404-400-40000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ634-44-4-44-44-40-440040000004-4-440000000000000000000000000000000000000000000000
χ644-44-4-44-44-40-44004000000-444-40000000000000000000000000000000000000000000000
χ654-4-444-4-440-400-44040000000000000022−2222−220000000000−22220000000000000000000000000
χ664-4-444-4-440-400-440400000000000000−2222−2222000000000022−220000000000000000000000000
χ674-4-4-4444-40000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ684-4-4-4444-40000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ694-4-4-4444-4000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ704-4-4-4444-4000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ7188-8-8-8-888000000000000000000000000000000000000000000000000000000000000000

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