Finite Group Databasebeta

← Group #306146

Character table — Group #306146

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-11-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-11-11-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11111-1-1-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111111-1-1-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1111-1-1-1-111-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1111111-1-111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1111-1-111-1-1-1-111-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-111-1-111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111-1-1-111-1-111-1-111-1-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-11-1-111-1-1-1-111111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-11-1-1-1111111-1-1-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-111111-1-1-1-111-1-111-11
χ17222222222-2-2222-2-2-2-22222-2-2-2-2000000000000000022220000-20-2000000000000000
χ18222222222-2-2222-2-2-2-22222-2-2-2-20000000000000000-2-2-2-20000202000000000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-22222000000000000000022-2-20000-202000000000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-222220000000000000000-2-222000020-2000000000000000
χ2122222222-222-2-2-222-2-2000000002222-2-2-2-200000000000022-2-2020-200000000000000
χ2222222222-222-2-2-222-2-2000000002222-2-2-2-2000000000000-2-2220-20200000000000000
χ2322222222-222-2-2-222-2-200000000-2-2-2-2222200000000000022-2-20-20200000000000000
χ2422222222-222-2-2-222-2-200000000-2-2-2-22222000000000000-2-222020-200000000000000
χ252222-2-2-2-22002-2-2000022-2-2000022−2−222−2−22222−2−2−2−22-22-2000000000000002−22−20000
χ262222-2-2-2-22002-2-2000022-2-2000022−2−222−2−22222−2−2−2−2-22-2200000000000000−22−220000
χ272222-2-2-2-22002-2-2000022-2-20000−2−222−2−222−2−2−2−222222-22-200000000000000−22−220000
χ282222-2-2-2-22002-2-2000022-2-20000−2−222−2−222−2−2−2−22222-22-22000000000000002−22−20000
χ292222-2-2-2-22002-2-20000-2-222000022−2−222−2−2−2−2−2−222222-2-22000000000000002−2−220000
χ302222-2-2-2-22002-2-20000-2-222000022−2−222−2−2−2−2−2−22222-222-200000000000000−222−20000
χ312222-2-2-2-22002-2-20000-2-2220000−2−222−2−2222222−2−2−2−22-2-2200000000000000−222−20000
χ322222-2-2-2-22002-2-20000-2-2220000−2−222−2−2222222−2−2−2−2-222-2000000000000002−2−220000
χ3322-2-222-2-2222-22-2-2-2-22000000000000000022-2-222-2-200002-22-2000000002-200000000
χ3422-2-222-2-2222-22-2-2-2-22000000000000000022-2-222-2-20000-22-2200000000-2200000000
χ3522-2-222-2-2222-22-2-2-2-220000000000000000-2-222-2-22200002-22-200000000-2200000000
χ3622-2-222-2-2222-22-2-2-2-220000000000000000-2-222-2-2220000-22-22000000002-200000000
χ3722-2-222-2-2-2222-22-2-22-22-22-222-2-2000000000000000000002-2-22000000000000002-200
χ3822-2-222-2-2-2222-22-2-22-22-22-222-2-200000000000000000000-222-200000000000000-2200
χ3922-2-222-2-2-2222-22-2-22-2-22-22-2-222000000000000000000002-2-2200000000000000-2200
χ4022-2-222-2-2-2222-22-2-22-2-22-22-2-22200000000000000000000-222-2000000000000002-200
χ4122-2-222-2-2-2-2-22-2222-222-22-2-2-22200000000000000000000000000002i−2i2i−2i0000000000
χ4222-2-222-2-2-2-2-22-2222-222-22-2-2-2220000000000000000000000000000−2i2i−2i2i0000000000
χ4322-2-222-2-2-2-2-22-2222-22-22-2222-2-200000000000000000000000000002i−2i−2i2i0000000000
χ4422-2-222-2-2-2-2-22-2222-22-22-2222-2-20000000000000000000000000000−2i2i2i−2i0000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-4-400-4440000000000002222−22−22−22−2222220000000000000000000000000000000000
χ474444-4-4-4-4-400-444000000000000−22−2222222222−22−220000000000000000000000000000000000
χ4844-4-444-4-44-4-4-44-4444-400000000000000000000000000000000000000000000000000
χ4944-4-4-4-444400-4-44000000000000000000002222−22−22−22−22222200000000000000000000000000
χ5044-4-4-4-444400-4-4400000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5144-4-4-4-444-40044-400004-4-440000000000000000000000000000000000000000000000
χ5244-4-4-4-444-40044-40000-444-40000000000000000000000000000000000000000000000
χ534-44-44-44-40000000000000022−2222−22000022−2222−222-22-22-22-200000000000000000000000000
χ544-44-44-44-40000000000000022−2222−220000−2222−2222-22-22-22-2200000000000000000000000000
χ554-44-44-44-400000000000000−2222−2222000022−2222−22-22-22-22-2200000000000000000000000000
χ564-44-44-44-400000000000000−2222−22220000−2222−22222-22-22-22-200000000000000000000000000
χ574-44-4-44-4404-40004-400000000000000000022−2222−22−2222−222200000000000000000000000000
χ584-44-4-44-4404-40004-4000000000000000000−2222−222222−2222−2200000000000000000000000000
χ594-44-4-44-440-44000-44000000000000004-4-440000000000000000000000000000000000
χ604-44-4-44-440-44000-4400000000000000-444-40000000000000000000000000000000000
χ614-4-444-4-440000000000000022−22−222222−2222−2200002-2-222-2-2200000000000000000000000000
χ624-4-444-4-440000000000000022−22−2222−2222−22220000-222-2-222-200000000000000000000000000
χ634-4-444-4-4400000000000000−222222−2222−2222−220000-222-2-222-200000000000000000000000000
χ644-4-444-4-4400000000000000−222222−22−2222−222200002-2-222-2-2200000000000000000000000000
χ654-4-44-444-404-4000-4400000000000000000022−22−2222−222222−2200000000000000000000000000
χ664-4-44-444-404-4000-44000000000000000000−222222−2222−22−222200000000000000000000000000
χ674-4-44-444-40-440004-400000000004-4-4400000000000000000000000000000000000000
χ684-4-44-444-40-440004-40000000000-444-400000000000000000000000000000000000000

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