Finite Group Databasebeta

← Group #454713

Character table — Group #454713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111111111112222222244448888888888888888888888888888888888161616161616161616161616
order12222222222222224444444444442244444444444444448888888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111
χ9111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ10111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111
χ11111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ12111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1
χ13111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ14111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ15111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ16111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-20000-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-222220000-2-200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-200002200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22200002200000000000000000000000000000000
χ2122222-2-2-222-2-2-22-2-222-2-2-22-220000000000000000002i2i−2i−2i22-2-2000000000000000000002i−2i00
χ2222222-2-2-222-2-2-22-2-222-2-2-22-220000000000000000002i2i−2i−2i-2-22200000000000000000000−2i2i00
χ2322222-2-2-222-2-2-22-2-222-2-2-22-22000000000000000000−2i−2i2i2i22-2-200000000000000000000−2i2i00
χ2422222-2-2-222-2-2-22-2-222-2-2-22-22000000000000000000−2i−2i2i2i-2-222000000000000000000002i−2i00
χ25222-2-222-22-2-22-2-2-22000000002i2i−2i−2i00002-22i−2i0000000000i2−i2i2−i222−2−222−2−2i2i2−i2−i2000000000000
χ26222-2-222-22-2-22-2-2-22000000002i2i−2i−2i00002-22i−2i0000000000−i2i2−i2i2−2−222−2−222−i2−i2i2i2000000000000
χ27222-2-222-22-2-22-2-2-22000000002i2i−2i−2i0000-22−2i2i0000000000i2−i2i2−i222−2−2−2−222−i2−i2i2i2000000000000
χ28222-2-222-22-2-22-2-2-22000000002i2i−2i−2i0000-22−2i2i0000000000−i2i2−i2i2−2−22222−2−2i2i2−i2−i2000000000000
χ29222-2-222-22-2-22-2-2-2200000000−2i−2i2i2i00002-2−2i2i0000000000i2−i2i2−i2−2−222−2−222i2i2−i2−i2000000000000
χ30222-2-222-22-2-22-2-2-2200000000−2i−2i2i2i00002-2−2i2i0000000000−i2i2−i2i222−2−222−2−2−i2−i2i2i2000000000000
χ31222-2-222-22-2-22-2-2-2200000000−2i−2i2i2i0000-222i−2i0000000000i2−i2i2−i2−2−22222−2−2−i2−i2i2i2000000000000
χ32222-2-222-22-2-22-2-2-2200000000−2i−2i2i2i0000-222i−2i0000000000−i2i2−i2i222−2−2−2−222i2i2−i2−i2000000000000
χ3322-22-22-22-2-22-2-22-222-222-22-2-200000000000022-2-20000000000000000002i−2i2i−2i00002i−2i000000
χ3422-22-22-22-2-22-2-22-222-222-22-2-200000000000022-2-2000000000000000000−2i2i−2i2i0000−2i2i000000
χ3522-22-22-22-2-22-2-22-222-222-22-2-2000000000000-2-2220000000000000000002i−2i2i−2i0000−2i2i000000
χ3622-22-22-22-2-22-2-22-222-222-22-2-2000000000000-2-222000000000000000000−2i2i−2i2i00002i−2i000000
χ372-22-22-2-2-2-2-22222-22-2-22-222-220000000000002-22-2000000000000002-22-20000002-200000000
χ382-22-22-2-2-2-2-22222-22-2-22-222-220000000000002-22-200000000000000-22-22000000-2200000000
χ392-22-22-2-2-2-2-22222-22-2-22-222-22000000000000-22-22000000000000002-22-2000000-2200000000
χ402-22-22-2-2-2-2-22222-22-2-22-222-22000000000000-22-2200000000000000-22-220000002-200000000
χ412-2-2-2-22-2222-2222-2-2-22-2222-2-20000000000000000002i−2i2i−2i00002i−2i2i−2i000000002-20000000000
χ422-2-2-2-22-2222-2222-2-2-22-2222-2-20000000000000000002i−2i2i−2i0000−2i2i−2i2i00000000-220000000000
χ432-2-2-2-22-2222-2222-2-2-22-2222-2-2000000000000000000−2i2i−2i2i00002i−2i2i−2i00000000-220000000000
χ442-2-2-2-22-2222-2222-2-2-22-2222-2-2000000000000000000−2i2i−2i2i0000−2i2i−2i2i000000002-20000000000
χ452-2-2-2-2-22-2222-2-22222-2-222-2-222-22-20000000000002-2000000000000000000000000002-2002-2
χ462-2-2-2-2-22-2222-2-22222-2-222-2-222-22-20000000000002-200000000000000000000000000-2200-22
χ472-2-2-2-2-22-2222-2-22222-2-222-2-22-22-22000000000000-22000000000000000000000000002-200-22
χ482-2-2-2-2-22-2222-2-22222-2-222-2-22-22-22000000000000-2200000000000000000000000000-22002-2
χ492-2-2-2-2-22-2222-2-2222-222-2-222-22-22-2000000002-2-22-222-2-220000000000000000000000000000
χ502-2-2-2-2-22-2222-2-2222-222-2-222-22-22-200000000-222-2-22-222-20000000000000000000000000000
χ512-2-2-2-2-22-2222-2-2222-222-2-222-2-22-22000000002-2-222-2-222-20000000000000000000000000000
χ522-2-2-2-2-22-2222-2-2222-222-2-222-2-22-2200000000-222-22-22-2-220000000000000000000000000000
χ5344444-4-4-444-4-4-44-4-4-4-4444-44-400000000000000000000000000000000000000000000000000
χ54444-4-4-4-444-44-44-44-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ55444-4-4-4-444-44-44-44-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ5644-44-44-44-4-44-4-44-44-44-4-44-44400000000000000000000000000000000000000000000000000
χ5744-44-4-44-4-4-4-44444-44-4-4-4444-400000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-4-4-44444-4-4444-4-4-4400000000000000000000000000000000000000000000000000
χ5944-4-444-4-4-44-4-44-44400000000000000000000000000000000000000000022−22−2222000000000000
χ6044-4-444-4-4-44-4-44-444000000000000000000000000000000000000000000−222222−22000000000000
χ6144-4-44-444-4444-4-4-4-4000000000000004-4000000000000000000000000000000000000000000
χ6244-4-44-444-4444-4-4-4-400000000000000-44000000000000000000000000000000000000000000
χ634-444-444-4-444-44-4-4-40000000000004-400000000000000000000000000000000000000000000
χ644-444-444-4-444-44-4-4-4000000000000-4400000000000000000000000000000000000000000000
χ654-444-4-4-44-44-44-4-4440000000000000000000000000000000000000022−22−22220000000000000000
χ664-444-4-4-44-44-44-4-44400000000000000000000000000000000000000−222222−220000000000000000
χ674-44-44444-4-4-4-4-444-4444-44-4-4-400000000000000000000000000000000000000000000000000
χ684-44-44444-4-4-4-4-444-4-4-4-44-444400000000000000000000000000000000000000000000000000
χ694-44-44-4-4-4-4-44444-4444-44-4-44-400000000000000000000000000000000000000000000000000
χ704-4-4444-4-44-444-4-44-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ714-4-4444-4-44-444-4-44-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ724-4-444-4444-4-4-44-4-44000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ734-4-444-4444-4-4-44-4-4400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ744-4-4-4-44-4444-4444-4-44-44-4-4-44400000000000000000000000000000000000000000000000000

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