Finite Group Databasebeta

← Group #196521

Character table — Group #196521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222222222444444444444444444444444444444444444888888888888888888888888888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i111-1-11-1-1iiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-111-111−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii111-1-11-1-1−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-1-111-111iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-11-1-11-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-11-111-11−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-11-1-11-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-11-111-11ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-1111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11-1-11-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-111-111-1-1-1-111
χ1711111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ1811111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ1911111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ2011111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-1-111-11-1-11-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-11-111-11-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-111-1-1-11-11-111-11-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-1111-11-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-111-1-11
χ2611111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11111-1-1-1-111-1-111-1
χ2711111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1111-111-1-111-1
χ2811111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-11-1-111-1-11
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1i−i−ii−iii−i
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-111−iii−ii−i−ii
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1−iii−ii−i−ii
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1-1-111i−i−ii−iii−i
χ33222222222222222222222222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2-2-22222-2-222000000000000000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-222-2-2-2-2222222-2-2000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-22222000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-2222222222222-2-22222-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ41222-2-22-2-20000000022-2-200002i2i−2i−2i22-2-222-2-2002i2i−2i−2i00002i−2i2i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ42222-2-22-2-20000000022-2-200002i2i−2i−2i22-2-222-2-2002i2i−2i−2i00002i−2i2i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ43222-2-22-2-20000000022-2-200002i2i−2i−2i-2-222-2-222002i2i−2i−2i0000−2i2i−2i2i0000001+i1+i−1−i−1−i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1−i1−i−1+i−1+i0000000000000000
χ44222-2-22-2-20000000022-2-200002i2i−2i−2i-2-222-2-222002i2i−2i−2i0000−2i2i−2i2i000000−1−i−1−i1+i1+i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1+i−1+i1−i1−i0000000000000000
χ45222-2-22-2-20000000022-2-20000−2i−2i2i2i22-2-222-2-200−2i−2i2i2i0000−2i2i−2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ46222-2-22-2-20000000022-2-20000−2i−2i2i2i22-2-222-2-200−2i−2i2i2i0000−2i2i−2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ47222-2-22-2-20000000022-2-20000−2i−2i2i2i-2-222-2-22200−2i−2i2i2i00002i−2i2i−2i0000001−i1−i−1+i−1+i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1+i1+i−1−i−1−i0000000000000000
χ48222-2-22-2-20000000022-2-20000−2i−2i2i2i-2-222-2-22200−2i−2i2i2i00002i−2i2i−2i000000−1+i−1+i1−i1−i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1−i−1−i1+i1+i0000000000000000
χ49222-2-22-2-200000000-2-22200002i2i−2i−2i22-2-2-2-22200−2i−2i2i2i00002i−2i−2i2i0000001−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i0000000000000000
χ50222-2-22-2-200000000-2-22200002i2i−2i−2i22-2-2-2-22200−2i−2i2i2i00002i−2i−2i2i000000−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i0000000000000000
χ51222-2-22-2-200000000-2-22200002i2i−2i−2i-2-22222-2-200−2i−2i2i2i0000−2i2i2i−2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ52222-2-22-2-200000000-2-22200002i2i−2i−2i-2-22222-2-200−2i−2i2i2i0000−2i2i2i−2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ53222-2-22-2-200000000-2-2220000−2i−2i2i2i22-2-2-2-222002i2i−2i−2i0000−2i2i2i−2i0000001+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i0000000000000000
χ54222-2-22-2-200000000-2-2220000−2i−2i2i2i22-2-2-2-222002i2i−2i−2i0000−2i2i2i−2i000000−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i0000000000000000
χ55222-2-22-2-200000000-2-2220000−2i−2i2i2i-2-22222-2-2002i2i−2i−2i00002i−2i−2i2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ56222-2-22-2-200000000-2-2220000−2i−2i2i2i-2-22222-2-2002i2i−2i−2i00002i−2i−2i2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ572-2-2222-2-222-2-222-2-22-22-200002i−2i2i−2i00000000002i−2i2i−2i00000000002i−2i2i−2i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000
χ582-2-2222-2-222-2-222-2-22-22-200002i−2i2i−2i00000000002i−2i2i−2i00000000002i−2i2i−2i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000000000
χ592-2-2222-2-222-2-222-2-22-22-20000−2i2i−2i2i0000000000−2i2i−2i2i0000000000−2i2i−2i2i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ602-2-2222-2-222-2-222-2-22-22-20000−2i2i−2i2i0000000000−2i2i−2i2i0000000000−2i2i−2i2i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
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χ782-2-2-2-2222000000002-2-22-2-2222-2-2200000000-2-22-2-2222-220000-220000-222-200000000-222-2-222-200000000-222-20000000000000000
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χ9144-44-4-44-40000-44-440000000000004i−4i4i−4i0000−4i4i0000−4i4i000000000000000000000000000000000000000000000000000000000000
χ9244-44-4-44-40000-44-44000000000000−4i4i−4i4i00004i−4i00004i−4i000000000000000000000000000000000000000000000000000000000000
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χ9444-4-44-4-444-44-400000000−4i4i−4i4i0000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-44-44-44000000004i−4i4i−4i0000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-44-44-4400000000−4i4i−4i4i00004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-4400004-4-4400004i−4i−4i4i000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-4400004-4-440000−4i4i4i−4i00000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-4-440000-444-400004i−4i−4i4i00000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-4-440000-444-40000−4i4i4i−4i000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ1014-44-44-44-44-4-44000000000000000000004i−4i−4i4i4i−4i0000−4i4i000000000000000000000000000000000000000000000000000000000000
χ1024-44-44-44-44-4-4400000000000000000000−4i4i4i−4i−4i4i00004i−4i000000000000000000000000000000000000000000000000000000000000
χ1034-44-44-44-4-444-4000000000000000000004i−4i−4i4i−4i4i00004i−4i000000000000000000000000000000000000000000000000000000000000
χ1044-44-44-44-4-444-400000000000000000000−4i4i4i−4i4i−4i0000−4i4i000000000000000000000000000000000000000000000000000000000000

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