Finite Group Databasebeta

← Group #209713

Character table — Group #209713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222444444444444444444444444888888888888888888888888161616161616161616161616
order12222222444444444444444444448888888888888888222244444444444444444444224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111
χ9111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-111
χ11111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1
χ12111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-111-1-1-1-111-1-111
χ13111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111
χ16111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-11111-1-111-1-1
χ17111-1-11-1-111-1-1ii−i−i11-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i1-11-11-1i−i1-1i−i11-1-1i−ii−iii−i−i1-1i−i1-1i−i1-1i−i
χ18111-1-11-1-111-1-1ii−i−i11-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i1-1-111-1i−i-11−ii-1-111i−i−ii−i−iii-11−ii1-1i−i-11−ii
χ19111-1-11-1-111-1-1ii−i−i11-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i-111-1-11−ii1-1i−i-1-111−iii−i−i−iii-11−ii-11−ii1-1i−i
χ20111-1-11-1-111-1-1ii−i−i11-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i-11-11-11−ii-11−ii11-1-1−ii−iiii−i−i1-1i−i-11−ii-11−ii
χ21111-1-11-1-111-1-1ii−i−i11-1-1ii−i−ii−i1-1-1-1-1-11111−i−i−i−iiiii1-11-11-1i−i1-1i−i11-1-1i−ii−iii−i−i-11−ii-11−ii-11−ii
χ22111-1-11-1-111-1-1ii−i−i11-1-1ii−i−ii−i1-1-1-1-1-11111−i−i−i−iiiii1-1-111-1i−i-11−ii-1-111i−i−ii−i−iii1-1i−i-11−ii1-1i−i
χ23111-1-11-1-111-1-1ii−i−i11-1-1ii−i−ii−i1-1-1-1-1-11111−i−i−i−iiiii-111-1-11−ii1-1i−i-1-111−iii−i−i−iii1-1i−i1-1i−i-11−ii
χ24111-1-11-1-111-1-1ii−i−i11-1-1ii−i−ii−i1-1-1-1-1-11111−i−i−i−iiiii-11-11-11−ii-11−ii11-1-1−ii−iiii−i−i-11−ii1-1i−i1-1i−i
χ25111-1-11-1-111-1-1−i−iii11-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii1-11-11-1−ii1-1−ii11-1-1−ii−ii−i−iii1-1−ii1-1−ii1-1−ii
χ26111-1-11-1-111-1-1−i−iii11-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii1-1-111-1−ii-11i−i-1-111−iii−iii−i−i-11i−i1-1−ii-11i−i
χ27111-1-11-1-111-1-1−i−iii11-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii-111-1-11i−i1-1−ii-1-111i−i−iiii−i−i-11i−i-11i−i1-1−ii
χ28111-1-11-1-111-1-1−i−iii11-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii-11-11-11i−i-11i−i11-1-1i−ii−i−i−iii1-1−ii-11i−i-11i−i
χ29111-1-11-1-111-1-1−i−iii11-1-1−i−iii−ii1-1-1-1-1-11111iiii−i−i−i−i1-11-11-1−ii1-1−ii11-1-1−ii−ii−i−iii-11i−i-11i−i-11i−i
χ30111-1-11-1-111-1-1−i−iii11-1-1−i−iii−ii1-1-1-1-1-11111iiii−i−i−i−i1-1-111-1−ii-11i−i-1-111−iii−iii−i−i1-1−ii-11i−i1-1−ii
χ31111-1-11-1-111-1-1−i−iii11-1-1−i−iii−ii1-1-1-1-1-11111iiii−i−i−i−i-111-1-11i−i1-1−ii-1-111i−i−iiii−i−i1-1−ii1-1−ii-11i−i
χ32111-1-11-1-111-1-1−i−iii11-1-1−i−iii−ii1-1-1-1-1-11111iiii−i−i−i−i-11-11-11i−i-11i−i11-1-1i−ii−i−i−iii-11i−i1-1−ii1-1−ii
χ33222222222-22-222222-22-22-22-2-2-2-2-2000000000000000000220000-2-2-2-2000000220000000000000000
χ34222222222-22-222222-22-22-22-2-2-2-2-2000000000000000000-2-200002222000000-2-20000000000000000
χ35222222222-22-2-2-2-2-22-22-2-22-2222-2-2000000000000000000220000-2-222000000-2-20000000000000000
χ36222222222-22-2-2-2-2-22-22-2-22-2222-2-2000000000000000000-2-2000022-2-2000000220000000000000000
χ3722222222-22-222222-22-22-22-22-2-2-2-200000000000000002200-2-2-2-20000000022000000000000000000
χ3822222222-22-222222-22-22-22-22-2-2-2-20000000000000000-2-200222200000000-2-2000000000000000000
χ3922222222-22-22-2-2-2-2-22-222-22-222-2-200000000000000002200-2-22200000000-2-2000000000000000000
χ4022222222-22-22-2-2-2-2-22-222-22-222-2-20000000000000000-2-20022-2-20000000022000000000000000000
χ4122222222-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000002-22-200002-22-2000000000000
χ4222222222-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000-22-220000-22-22000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000002-22-20000-22-22000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000000000000000-22-2200002-22-2000000000000
χ45222-2-22-2-22-2-222i2i−2i−2i2-2-222i−2i−2i2i−2i2i-220000000000000000002-20000-22−2i2i0000002i−2i0000000000000000
χ46222-2-22-2-22-2-222i2i−2i−2i2-2-222i−2i−2i2i−2i2i-22000000000000000000-2200002-22i−2i000000−2i2i0000000000000000
χ47222-2-22-2-22-2-22−2i−2i2i2i2-2-22−2i2i2i−2i2i−2i-220000000000000000002-20000-222i−2i000000−2i2i0000000000000000
χ48222-2-22-2-22-2-22−2i−2i2i2i2-2-22−2i2i2i−2i2i−2i-22000000000000000000-2200002-2−2i2i0000002i−2i0000000000000000
χ49222-2-22-2-2-222-22i2i−2i−2i-222-2−2i2i2i−2i−2i2i-2200000000000000002-200-22−2i2i000000002i−2i000000000000000000
χ50222-2-22-2-2-222-22i2i−2i−2i-222-2−2i2i2i−2i−2i2i-220000000000000000-22002-22i−2i00000000−2i2i000000000000000000
χ51222-2-22-2-2-222-2−2i−2i2i2i-222-22i−2i−2i2i2i−2i-2200000000000000002-200-222i−2i00000000−2i2i000000000000000000
χ52222-2-22-2-2-222-2−2i−2i2i2i-222-22i−2i−2i2i2i−2i-220000000000000000-22002-2−2i2i000000002i−2i000000000000000000
χ53222-2-22-2-2-2-2222i2i−2i−2i-2-222−2i−2i2i2i2i−2i2-200000000000000000000000000002-2-2200002i−2i−2i2i000000000000
χ54222-2-22-2-2-2-2222i2i−2i−2i-2-222−2i−2i2i2i2i−2i2-20000000000000000000000000000-222-20000−2i2i2i−2i000000000000
χ55222-2-22-2-2-2-222−2i−2i2i2i-2-2222i2i−2i−2i−2i2i2-200000000000000000000000000002-2-220000−2i2i2i−2i000000000000
χ56222-2-22-2-2-2-222−2i−2i2i2i-2-2222i2i−2i−2i−2i2i2-20000000000000000000000000000-222-200002i−2i−2i2i000000000000
χ5744-44-4-44-4040-400000-404000000002i22i2−2i2−2i22i22i2−2i2−2i200000000000000000000000000000000000000000000
χ5844-44-4-44-4040-400000-40400000000−2i2−2i22i22i2−2i2−2i22i22i200000000000000000000000000000000000000000000
χ5944-44-4-44-40-4040000040-400000000000000002i22i2−2i2−2i22i22i2−2i2−2i2000000000000000000000000000000000000
χ6044-44-4-44-40-4040000040-40000000000000000−2i2−2i22i22i2−2i2−2i22i22i2000000000000000000000000000000000000
χ6144-4-44-4-44040400000-40-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000000000
χ6244-4-44-4-44040400000-40-400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000000000
χ6344-4-44-4-440-40-40000040400000000000000002222−22−22−22−222222000000000000000000000000000000000000
χ6444-4-44-4-440-40-4000004040000000000000000−22−2222222222−22−22000000000000000000000000000000000000
χ654-444-4-4-4440400000-40-40000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ664-444-4-4-4440400000-40-4000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ674-444-4-4-44-40-4000004040000000000000000022−2222−2222−2222−22000000000000000000000000000000000000
χ684-444-4-4-44-40-40000040400000000000000000−2222−2222−2222−2222000000000000000000000000000000000000
χ694-44-44-44-440-400000-4040000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ704-44-44-44-440-400000-404000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ714-44-44-44-4-4040000040-4000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ724-44-44-44-4-4040000040-400000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ734-4-4444-4-400004i−4i4i−4i0000000000002-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ744-4-4444-4-400004i−4i4i−4i000000000000-222-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ754-4-4444-4-40000−4i4i−4i4i0000000000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ764-4-4444-4-40000−4i4i−4i4i000000000000-222-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ774-4-4-4-444400004-4-440000000000002-2-22-222-22-2-22-222-2000000000000000000000000000000000000
χ784-4-4-4-444400004-4-44000000000000-222-22-2-22-222-22-2-22000000000000000000000000000000000000
χ794-4-4-4-44440000-444-40000000000002-2-22-222-2-222-22-2-22000000000000000000000000000000000000
χ804-4-4-4-44440000-444-4000000000000-222-22-2-222-2-22-222-2000000000000000000000000000000000000

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