Finite Group Databasebeta

← Group #333313

Character table — Group #333313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444222444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11-1-1111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1111-1-11-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1111-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-11-1-11-1-111-1-1-1-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-111-1-11111-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1111111-1-11-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-11111-1-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-11-1-1-1-1-11111111-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1111111-11111-1-1-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-1-11-1-1-111-1-1-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-11-1-1-11-1-11111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111-1-1111-1-1-1-11111-1-1
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-200000000002200-2-2200-200000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-20000000000-2-20022-200200000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-2000022220000000000220022-200-200000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2000022220000000000-2-200-2-2200200000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-2000000000000220022000000-200-20000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-2000000000000-2-200-2-200000020020000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000022220000000000002200-2-2000000-20020000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200002222000000000000-2-20022000000200-20000000000
χ25222-2-2-2-220-202020-20022-2-2i2i2−i2−i20000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i22-2002-20000000000i2−i200i2−i20000
χ26222-2-2-2-220-202020-20022-2-2i2i2−i2−i20000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2-2200-220000000000−i2i200−i2i20000
χ27222-2-2-2-220-202020-20022-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22-2002-20000000000−i2i200−i2i20000
χ28222-2-2-2-220-202020-20022-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2-2200-220000000000i2−i200i2−i20000
χ29222-2-2-2-220-202020-200-2-222i2i2−i2−i20000i2i2−i2−i2−i2−i2−i2−i2i2i2i2i22-200-220000000000−i2i200i2−i20000
χ30222-2-2-2-220-202020-200-2-222i2i2−i2−i20000i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2-22002-20000000000i2−i200−i2i20000
χ31222-2-2-2-220-202020-200-2-222−i2−i2i2i20000−i2−i2i2i2i2i2i2i2−i2−i2−i2−i22-200-220000000000i2−i200−i2i20000
χ32222-2-2-2-220-202020-200-2-222−i2−i2i2i20000−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2-22002-20000000000−i2i200i2−i20000
χ332-22-222-2-2-202020-2000i2−i2i2−i20000i2i2−i2−i22i−2i2i−2i22−2−222−2−2002-2002i−2i00000000002−200i2−i200
χ342-22-222-2-2-202020-2000i2−i2i2−i20000i2i2−i2−i22i−2i2i−2i22−2−222−2−200-2200−2i2i0000000000−2200−i2i200
χ352-22-222-2-2-202020-2000i2−i2i2−i20000i2i2−i2−i2−2i2i−2i2i−2−222−2−222002-200−2i2i0000000000−2200i2−i200
χ362-22-222-2-2-202020-2000i2−i2i2−i20000i2i2−i2−i2−2i2i−2i2i−2−222−2−22200-22002i−2i00000000002−200−i2i200
χ372-22-222-2-2-202020-2000−i2i2−i2i20000−i2−i2i2i22i−2i2i−2i−2−222−2−222002-2002i−2i0000000000−2200−i2i200
χ382-22-222-2-2-202020-2000−i2i2−i2i20000−i2−i2i2i22i−2i2i−2i−2−222−2−22200-2200−2i2i00000000002−200i2−i200
χ392-22-222-2-2-202020-2000−i2i2−i2i20000−i2−i2i2i2−2i2i−2i2i22−2−222−2−2002-200−2i2i00000000002−200−i2i200
χ402-22-222-2-2-202020-2000−i2i2−i2i20000−i2−i2i2i2−2i2i−2i2i22−2−222−2−200-22002i−2i0000000000−2200i2−i200
χ412-2-2-2-2222-2-222-2-222-2200000000000000002-22-22-22-20000000002-2002-200000000000
χ422-2-2-2-2222-2-222-2-222-2200000000000000002-22-22-22-2000000000-2200-2200000000000
χ432-2-2-2-2222-2-222-2-222-220000000000000000-22-22-22-220000000002-200-2200000000000
χ442-2-2-2-2222-2-222-2-222-220000000000000000-22-22-22-22000000000-22002-200000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-4-44040-40-4040000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ47444-4-4-4-44040-40-404000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ4844-44-44-4-44040-40-4000000000000000000022−22−222222−22−222200000000000000000000000000
χ4944-44-44-4-44040-40-40000000000000000000−222222−22−222222−2200000000000000000000000000
χ5044-44-44-4-4-40-4040400000004i−4i4i−4i000000000000000000000000000000000000000000
χ5144-44-44-4-4-40-404040000000−4i4i−4i4i000000000000000000000000000000000000000000
χ5244-4-44-44-40000000000000022−22−22222i2−2i22i2−2i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5344-4-44-44-40000000000000022−22−2222−2i22i2−2i22i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5444-4-44-44-400000000000000−222222−222i2−2i22i2−2i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5544-4-44-44-400000000000000−222222−22−2i22i2−2i22i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ564-444-4-44-400000000002i2−2i2−2i22i20000000022−22−2222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ574-444-4-44-400000000002i2−2i2−2i22i200000000−222222−222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ584-444-4-44-40000000000−2i22i22i2−2i20000000022−22−22222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ594-444-4-44-40000000000−2i22i22i2−2i200000000−222222−22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ604-44-444-4-440-40-4040002i2−2i22i2−2i20000−2i2−2i22i22i200000000000000000000000000000000000000
χ614-44-444-4-440-40-404000−2i22i2−2i22i200002i22i2−2i2−2i200000000000000000000000000000000000000
χ624-4-444-4-4404040-40-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ634-4-444-4-4404040-40-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ644-4-444-4-440-40-4040400000000004-4-4400000000000000000000000000000000000000
χ654-4-444-4-440-40-404040000000000-444-400000000000000000000000000000000000000
χ664-4-4-4-444444-4-444-4-4-4400000000000000000000000000000000000000000000000000
χ674-4-4-4-44444-4-444-4-444-400000000000000000000000000000000000000000000000000
χ684-4-4-4-4444-444-4-444-44-400000000000000000000000000000000000000000000000000

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