Finite Group Databasebeta

← Group #307696

Character table — Group #307696

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-11-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-11-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1111111-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-11-1-1-111-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-11-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1111-111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1111-1-111-1-1-11
χ17222222222-222-2-22-2-2-2000000002222-2-2-2-20000000022-2-200002-20000000000000000
χ18222222222-222-2-22-2-2-2000000002222-2-2-2-200000000-2-2220000-220000000000000000
χ19222222222-222-2-22-2-2-200000000-2-2-2-222220000000022-2-20000-220000000000000000
χ20222222222-222-2-22-2-2-200000000-2-2-2-2222200000000-2-22200002-20000000000000000
χ2122222222-22-2-222-22-2-22222-2-2-2-2000000000000000000002222000000-2-20000000000
χ2222222222-22-2-222-22-2-22222-2-2-2-200000000000000000000-2-2-2-2000000220000000000
χ2322222222-22-2-222-22-2-2-2-2-2-222220000000000000000000022-2-2000000-220000000000
χ2422222222-22-2-222-22-2-2-2-2-2-2222200000000000000000000-2-2220000002-20000000000
χ25222-2-22-2-20-2002-2020022-2-2000022−2−222−2−22222−2−2−2−200002i−2i2i−2i000000000000i2−i2i2−i200
χ26222-2-22-2-20-2002-2020022-2-2000022−2−222−2−22222−2−2−2−20000−2i2i−2i2i000000000000−i2i2−i2i200
χ27222-2-22-2-20-2002-2020022-2-20000−2−222−2−222−2−2−2−2222200002i−2i2i−2i000000000000−i2i2−i2i200
χ28222-2-22-2-20-2002-2020022-2-20000−2−222−2−222−2−2−2−222220000−2i2i−2i2i000000000000i2−i2i2−i200
χ29222-2-22-2-20-2002-20200-2-222000022−2−222−2−2−2−2−2−2222200002i−2i−2i2i000000000000i2−i2−i2i200
χ30222-2-22-2-20-2002-20200-2-222000022−2−222−2−2−2−2−2−222220000−2i2i2i−2i000000000000−i2i2i2−i200
χ31222-2-22-2-20-2002-20200-2-2220000−2−222−2−2222222−2−2−2−200002i−2i−2i2i000000000000−i2i2i2−i200
χ32222-2-22-2-20-2002-20200-2-2220000−2−222−2−2222222−2−2−2−20000−2i2i2i−2i000000000000i2−i2−i2i200
χ332-2-2-2-22222-2-2-2222-22-22-22-222-2-2000000000000000000000000002i−2i2i−2i000000000000
χ342-2-2-2-22222-2-2-2222-22-22-22-222-2-200000000000000000000000000−2i2i−2i2i000000000000
χ352-2-2-2-22222-2-2-2222-22-2-22-22-2-222000000000000000000000000002i−2i−2i2i000000000000
χ362-2-2-2-22222-2-2-2222-22-2-22-22-2-22200000000000000000000000000−2i2i2i−2i000000000000
χ372-2-2-2-2222-2222-2-2-222-200000000000000002i2i−2i−2i2i2i−2i−2i2i−2i2i−2i000000000000002-2000000
χ382-2-2-2-2222-2222-2-2-222-200000000000000002i2i−2i−2i2i2i−2i−2i−2i2i−2i2i00000000000000-22000000
χ392-2-2-2-2222-2222-2-2-222-20000000000000000−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i00000000000000-22000000
χ402-2-2-2-2222-2222-2-2-222-20000000000000000−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i000000000000002-2000000
χ412-2-2-2-2222-2-22222-2-2-222-22-2-2-22200000000000000002i−2i−2i2i0000000000002i−2i00000000
χ422-2-2-2-2222-2-22222-2-2-222-22-2-2-2220000000000000000−2i2i2i−2i000000000000−2i2i00000000
χ432-2-2-2-2222-2-22222-2-2-22-22-2222-2-200000000000000002i−2i−2i2i000000000000−2i2i00000000
χ442-2-2-2-2222-2-22222-2-2-22-22-2222-2-20000000000000000−2i2i2i−2i0000000000002i−2i00000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-40400-440-400000000002222−22−22−22−2222220000000000000000000000000000000000
χ47444-4-44-4-40400-440-40000000000−22−2222222222−22−220000000000000000000000000000000000
χ4844-44-4-44-4404-400-4000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ4944-44-4-44-4404-400-40000000000000000000−2222−2222−2222−222200000000000000000000000000
χ5044-44-4-44-4-40-44004000000000004i−4i4i−4i00000000000000000000000000000000000000
χ5144-44-4-44-4-40-4400400000000000−4i4i−4i4i00000000000000000000000000000000000000
χ5244-4-44-4-44000000000000002i2−2i22i2−2i22i2−2i2−2i22i200002-22-2-22-2200000000000000000000000000
χ5344-4-44-4-44000000000000002i2−2i22i2−2i2−2i22i22i2−2i20000-22-222-22-200000000000000000000000000
χ5444-4-44-4-4400000000000000−2i22i2−2i22i22i2−2i2−2i22i20000-22-222-22-200000000000000000000000000
χ5544-4-44-4-4400000000000000−2i22i2−2i22i2−2i22i22i2−2i200002-22-2-22-2200000000000000000000000000
χ564-444-4-4-44000000000000002i2−2i2−2i22i2000022−2222−222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ574-444-4-4-44000000000000002i2−2i2−2i22i20000−2222−2222−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ584-444-4-4-4400000000000000−2i22i22i2−2i2000022−2222−22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ594-444-4-4-4400000000000000−2i22i22i2−2i20000−2222−22222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ604-44-44-44-440-4400-40000000000000004-4-440000000000000000000000000000000000
χ614-44-44-44-440-4400-4000000000000000-444-40000000000000000000000000000000000
χ624-44-44-44-4-404-400400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ634-44-44-44-4-404-40040000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ644-4-4444-4-404004-40-4004-4-440000000000000000000000000000000000000000000000
χ654-4-4444-4-404004-40-400-444-40000000000000000000000000000000000000000000000
χ664-4-4444-4-40-400-44040000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ674-4-4444-4-40-400-4404000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ684-4-4-4-444444-4-4-4-444-4400000000000000000000000000000000000000000000000000

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