Finite Group Databasebeta

← Group #301091

Character table — Group #301091

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-111-1-1-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-11-1-1-1-1-1-11-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11111-1-11-1-111-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-111-1-1-1-1-111-1-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111111-1-111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-111-1-111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-1-1-111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1111-1-1-1-1-1-111
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111111-1-1-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-111-1-1111-1-111-1-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111-1-1-1-111-11111-1-1-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-111-1-1111-1-1-1-111111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-1-1-1-111-1-111-11
χ17222222222-2-22-2-222-2-2000000002222-2-2-2-2000000000022-2-2002000000-20000000000
χ18222222222-2-22-2-222-2-2000000002222-2-2-2-20000000000-2-22200-200000020000000000
χ19222222222-2-22-2-222-2-200000000-2-2-2-222220000000000222200-2000000-20000000000
χ20222222222-2-22-2-222-2-200000000-2-2-2-222220000000000-2-2-2-200200000020000000000
χ2122222222-222-222-2-2-2-22222-2-2-2-20000000000000000220000-2-202-2000000000000000
χ2222222222-222-222-2-2-2-22222-2-2-2-20000000000000000-2-20000220-22000000000000000
χ2322222222-222-222-2-2-2-2-2-2-2-222220000000000000000220000-2-20-22000000000000000
χ2422222222-222-222-2-2-2-2-2-2-2-222220000000000000000-2-200002202-2000000000000000
χ25222-2-2-2-22200-200-2200i2i2−i2−i2i2i2−i2−i2000022-2-2i2i2i2i2−i2−i2−i2−i2002i−2i2i−2i0000000000002−22−20000
χ26222-2-2-2-22200-200-2200i2i2−i2−i2i2i2−i2−i2000022-2-2i2i2i2i2−i2−i2−i2−i200−2i2i−2i2i000000000000−22−220000
χ27222-2-2-2-22200-200-2200i2i2−i2−i2i2i2−i2−i20000-2-222−i2−i2−i2−i2i2i2i2i2002i−2i−2i2i0000000000002−2−220000
χ28222-2-2-2-22200-200-2200i2i2−i2−i2i2i2−i2−i20000-2-222−i2−i2−i2−i2i2i2i2i200−2i2i2i−2i000000000000−222−20000
χ29222-2-2-2-22200-200-2200−i2−i2i2i2−i2−i2i2i2000022-2-2−i2−i2−i2−i2i2i2i2i2002i−2i2i−2i000000000000−22−220000
χ30222-2-2-2-22200-200-2200−i2−i2i2i2−i2−i2i2i2000022-2-2−i2−i2−i2−i2i2i2i2i200−2i2i−2i2i0000000000002−22−20000
χ31222-2-2-2-22200-200-2200−i2−i2i2i2−i2−i2i2i20000-2-222i2i2i2i2−i2−i2−i2−i2002i−2i−2i2i000000000000−222−20000
χ32222-2-2-2-22200-200-2200−i2−i2i2i2−i2−i2i2i20000-2-222i2i2i2i2−i2−i2−i2−i200−2i2i2i−2i0000000000002−2−220000
χ332-2-2-2-22222-2-2-2222-2-22000000000000000022-2-222-2-22-200002-2000000002-200000000
χ342-2-2-2-22222-2-2-2222-2-22000000000000000022-2-222-2-2-220000-2200000000-2200000000
χ352-2-2-2-22222-2-2-2222-2-220000000000000000-2-222-2-2222-200002-200000000-2200000000
χ362-2-2-2-22222-2-2-2222-2-220000000000000000-2-222-2-222-220000-22000000002-200000000
χ372-2-2-2-2222-2222-2-2-22-220000000022-2-22-22-200000000000000000002-22-200000000000
χ382-2-2-2-2222-2222-2-2-22-220000000022-2-22-22-20000000000000000000-22-2200000000000
χ392-2-2-2-2222-2222-2-2-22-2200000000-2-222-22-2200000000000000000002-2-2200000000000
χ402-2-2-2-2222-2222-2-2-22-2200000000-2-222-22-220000000000000000000-222-200000000000
χ412-2-2-2-2222-2-2-2222-222-20000000022-2-2-22-22000000002-20000-22000000000000002-200
χ422-2-2-2-2222-2-2-2222-222-20000000022-2-2-22-2200000000-2200002-200000000000000-2200
χ432-2-2-2-2222-2-2-2222-222-200000000-2-2222-22-2000000002-20000-2200000000000000-2200
χ442-2-2-2-2222-2-2-2222-222-200000000-2-2222-22-200000000-2200002-2000000000000002-200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-4-44-4004004-4002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ47444-4-4-4-44-4004004-400−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ4844-44-44-4-40000000000000022−2222−2222−2222−2200002-22-22-22-200000000000000000000000000
χ4944-44-44-4-40000000000000022−2222−22−2222−22220000-22-22-22-2200000000000000000000000000
χ5044-44-44-4-400000000000000−2222−222222−2222−220000-22-22-22-2200000000000000000000000000
χ5144-44-44-4-400000000000000−2222−2222−2222−222200002-22-22-22-200000000000000000000000000
χ5244-4-44-44-404-404-4000000004i−4i−4i4i000000000000000000000000000000000000000000
χ5344-4-44-44-404-404-400000000−4i4i4i−4i000000000000000000000000000000000000000000
χ5444-4-44-44-40-440-44000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ5544-4-44-44-40-440-4400000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ564-444-4-44-404-40-44000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000
χ574-444-4-44-404-40-4400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000
χ584-444-4-44-40-4404-400004i−4i4i−4i0000000000000000000000000000000000000000000000
χ594-444-4-44-40-4404-40000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ604-44-444-4-4000000000022−22−2222000022−22−222200002-2-222-2-2200000000000000000000000000
χ614-44-444-4-4000000000022−22−22220000−222222−220000-222-2-222-200000000000000000000000000
χ624-44-444-4-40000000000−222222−22000022−22−22220000-222-2-222-200000000000000000000000000
χ634-44-444-4-40000000000−222222−220000−222222−2200002-2-222-2-2200000000000000000000000000
χ644-4-444-4-44400400-4-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ654-4-444-4-44400400-4-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ664-4-444-4-44-400-40044000000000000004-4-440000000000000000000000000000000000
χ674-4-444-4-44-400-4004400000000000000-444-40000000000000000000000000000000000
χ684-4-4-4-4444444-4-4-44-44-400000000000000000000000000000000000000000000000000

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