Finite Group Databasebeta

← Group #72318984

Character table — Group #72318984

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1111111122222222222244444444444488888888888888888888888888161616161616161616161616161616161616161616161616161616161616161616161616161632323232
order12222222444444444444444488888888222244444488888888888888882244444488888888888888161616161616161616161616161616164488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111
χ511111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ711111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ811111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111
χ911111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ1111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1211111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1411111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1511111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1711111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-11-1-1-1-111-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-11i−i
χ1811111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-11-1-1-1-111-1-1iiii−i−i−i−iii−i−i-1-11111-1-1i−iii−i−iii−i−i−i−iii-1-111-1-111−i−iii−i−iii1-1−ii
χ1911111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-11-1-1-1-111-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−ii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-11−ii
χ2011111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-11-1-1-1-111-1-1−i−i−i−iiiii−i−iii-1-11111-1-1−ii−i−iii−i−iiiii−i−i-1-111-1-111ii−i−iii−i−i1-1i−i
χ2111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11111111-1-1iiii−i−i−i−iii−i−i11-1-1-1-111i−i−i−iii−i−iiiii−i−i-1-111-1-111−i−iii−i−iii-11i−i
χ2211111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11111111-1-1iiii−i−i−i−iii−i−i-1-1-1-11111i−i−i−iii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i1-1−ii
χ2311111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11111111-1-1−i−i−i−iiiii−i−iii11-1-1-1-111−iiii−i−iii−i−i−i−iii-1-111-1-111ii−i−iii−i−i-11−ii
χ2411111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11111111-1-1−i−i−i−iiiii−i−iii-1-1-1-11111−iiii−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii1-1i−i
χ2511111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111111-1-1-1-1-1-1-111iiii−i−i−i−i−i−iii11-1-1-1-111−iiii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii1-1−ii
χ2611111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111111-1-1-1-1-1-1-111iiii−i−i−i−i−i−iii-1-1-1-11111−iiii−i−i−i−iii−i−iii-1-11111-1-1−i−iiiii−i−i-11i−i
χ2711111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111111-1-1-1-1-1-1-111−i−i−i−iiiiiii−i−i11-1-1-1-111i−i−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i1-1i−i
χ2811111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111111-1-1-1-1-1-1-111−i−i−i−iiiiiii−i−i-1-1-1-11111i−i−i−iiiii−i−iii−i−i-1-11111-1-1ii−i−i−i−iii-11−ii
χ2911111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11111-1-111iiii−i−i−i−i−i−iii1111-1-1-1-1−ii−i−iiiii−i−iii−i−i-1-11111-1-1−i−iiiii−i−i1-1−ii
χ3011111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11111-1-111iiii−i−i−i−i−i−iii-1-11111-1-1−ii−i−iiiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii-11i−i
χ3111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11111-1-111−i−i−i−iiiiiii−i−i1111-1-1-1-1i−iii−i−i−i−iii−i−iii-1-11111-1-1ii−i−i−i−iii1-1i−i
χ3211111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11111-1-111−i−i−i−iiiiiii−i−i-1-11111-1-1i−iii−i−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i-11−ii
χ33222222222222222222222222-2-2-2-2-2-2-2-20000220000-2-2-2-222-2-222-2-2222200000000-2-200000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-20000220000-2-2-2-2-2-222-2-222-2-2-2-2000000002200000000000000000000000000000000
χ3522222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-20000222222-2-222-2-2-2-2-2-2000000002200000000000000000000000000000000
χ3622222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-200002222-2-222-2-222222200000000-2-200000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-222-2-222-2-2-2-2220000-220000-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000−2i2i00000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-222-2-222-2-2-2-2220000-220000-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000002i−2i00000000000000000000000000000000
χ3922222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22200002-2000022-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000002i−2i00000000000000000000000000000000
χ4022222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22200002-2000022-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000−2i2i00000000000000000000000000000000
χ41222-2-2-2-222i2i−2i−2i22-2-22i2i−2i−2i00002i−2i22-2-22i−2i22-2-2002i2i−2i−2i00000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000002ζ−2ζ2ζ3−2ζ300000000
χ42222-2-2-2-222i2i−2i−2i22-2-22i2i−2i−2i00002i−2i22-2-22i−2i22-2-2002i2i−2i−2i0000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000−2ζ2ζ−2ζ32ζ300000000
χ43222-2-2-2-222i2i−2i−2i22-2-22i2i−2i−2i00002i−2i22-2-22i−2i-2-22200−2i−2i2i2i00000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000−2ζ2ζ−2ζ32ζ300000000
χ44222-2-2-2-222i2i−2i−2i22-2-22i2i−2i−2i00002i−2i22-2-22i−2i-2-22200−2i−2i2i2i0000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000002ζ−2ζ2ζ3−2ζ300000000
χ45222-2-2-2-22−2i−2i2i2i22-2-2−2i−2i2i2i0000−2i2i22-2-2−2i2i22-2-200−2i−2i2i2i00000000000000000000000000000000002ζ3−2ζ32ζ−2ζ000000002ζ3−2ζ32ζ−2ζ00000000
χ46222-2-2-2-22−2i−2i2i2i22-2-2−2i−2i2i2i0000−2i2i22-2-2−2i2i22-2-200−2i−2i2i2i0000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000−2ζ32ζ3−2ζ2ζ00000000
χ47222-2-2-2-22−2i−2i2i2i22-2-2−2i−2i2i2i0000−2i2i22-2-2−2i2i-2-222002i2i−2i−2i00000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000−2ζ32ζ3−2ζ2ζ00000000
χ48222-2-2-2-22−2i−2i2i2i22-2-2−2i−2i2i2i0000−2i2i22-2-2−2i2i-2-222002i2i−2i−2i0000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000002ζ3−2ζ32ζ−2ζ00000000
χ4922-222-2-2-222222-22-2-2-2-2-20000222-22-2-2-22-22-2002-22-200000000000000002-2002-200000000000000002-22-20000000000000000
χ5022-222-2-2-222222-22-2-2-2-2-20000222-22-2-2-22-22-2002-22-20000000000000000-2200-220000000000000000-22-220000000000000000
χ5122-222-2-2-222222-22-2-2-2-2-20000222-22-2-2-2-22-2200-22-2200000000000000002-2002-20000000000000000-22-220000000000000000
χ5222-222-2-2-222222-22-2-2-2-2-20000222-22-2-2-2-22-2200-22-220000000000000000-2200-2200000000000000002-22-20000000000000000
χ5322-222-2-2-2-2-2-2-22-22-222220000-2-22-22-2222-22-200-22-2200000000000000002-200-2200000000000000002-2-220000000000000000
χ5422-222-2-2-2-2-2-2-22-22-222220000-2-22-22-2222-22-200-22-220000000000000000-22002-20000000000000000-222-20000000000000000
χ5522-222-2-2-2-2-2-2-22-22-222220000-2-22-22-222-22-22002-22-200000000000000002-200-220000000000000000-222-20000000000000000
χ5622-222-2-2-2-2-2-2-22-22-222220000-2-22-22-222-22-22002-22-20000000000000000-22002-200000000000000002-2-220000000000000000
χ5722-2-2-222-22i2i−2i−2i2-2-22−2i−2i2i2i00002i−2i2-2-22−2i2i2-2-22002i−2i−2i2i00002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ5822-2-2-222-22i2i−2i−2i2-2-22−2i−2i2i2i00002i−2i2-2-22−2i2i2-2-22002i−2i−2i2i0000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ5922-2-2-222-22i2i−2i−2i2-2-22−2i−2i2i2i00002i−2i2-2-22−2i2i-222-200−2i2i2i−2i00002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ6022-2-2-222-22i2i−2i−2i2-2-22−2i−2i2i2i00002i−2i2-2-22−2i2i-222-200−2i2i2i−2i0000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ6122-2-2-222-22i2i−2i−2i2-2-22−2i−2i2i2i0000−2i2i-222-22i−2i000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000002-2002i−2i0000002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ6222-2-2-222-22i2i−2i−2i2-2-22−2i−2i2i2i0000−2i2i-222-22i−2i000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000-2200−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ6322-2-2-222-22i2i−2i−2i2-2-22−2i−2i2i2i0000−2i2i-222-22i−2i00000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000002-2002i−2i000000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ6422-2-2-222-22i2i−2i−2i2-2-22−2i−2i2i2i0000−2i2i-222-22i−2i00000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000-2200−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ6522-2-2-222-2−2i−2i2i2i2-2-222i2i−2i−2i00002i−2i-222-2−2i2i000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000002-200−2i2i0000002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ6622-2-2-222-2−2i−2i2i2i2-2-222i2i−2i−2i00002i−2i-222-2−2i2i000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000-22002i−2i000000−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ6722-2-2-222-2−2i−2i2i2i2-2-222i2i−2i−2i00002i−2i-222-2−2i2i00000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000002-200−2i2i000000−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ6822-2-2-222-2−2i−2i2i2i2-2-222i2i−2i−2i00002i−2i-222-2−2i2i00000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000-22002i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ6922-2-2-222-2−2i−2i2i2i2-2-222i2i−2i−2i0000−2i2i2-2-222i−2i2-2-2200−2i2i2i−2i00002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ7022-2-2-222-2−2i−2i2i2i2-2-222i2i−2i−2i0000−2i2i2-2-222i−2i2-2-2200−2i2i2i−2i0000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ7122-2-2-222-2−2i−2i2i2i2-2-222i2i−2i−2i0000−2i2i2-2-222i−2i-222-2002i−2i−2i2i00002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ7222-2-2-222-2−2i−2i2i2i2-2-222i2i−2i−2i0000−2i2i2-2-222i−2i-222-2002i−2i−2i2i0000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ73444444444-44-4-4-4-4-44-44-44444000000000000-4-400000000000000000000000000000000000000000000000000000000000000
χ74444444444-44-4-4-4-4-44-44-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000000000000000
χ7544444444-44-44-4-4-4-4-44-4444-4-40000000000004-400000000000000000000000000000000000000000000000000000000000000
χ7644444444-44-44-4-4-4-4-44-44-4-444000000000000-4400000000000000000000000000000000000000000000000000000000000000
χ77444-4-4-4-444i4i−4i−4i44-4-44i4i−4i−4i0000−4i4i-4-444−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ78444-4-4-4-444i−4i−4i4i-4-4444i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000
χ79444-4-4-4-444i−4i−4i4i-4-4444i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000
χ80444-4-4-4-44−4i4i4i−4i-4-444−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000
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χ82444-4-4-4-44−4i−4i4i4i44-4-4−4i−4i4i4i00004i−4i-4-4444i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ8344-444-4-4-444444-44-4-4-4-4-40000-4-4-44-444400000000000000000000000000000000000000000000000000000000000000000000
χ8444-444-4-4-44-44-4-44-44-44-4400000000000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ8544-444-4-4-44-44-4-44-44-44-440000000000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ8644-444-4-4-4-44-44-44-444-44-400000000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ8744-444-4-4-4-44-44-44-444-44-40000000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ8844-444-4-4-4-4-4-4-44-44-44444000044-44-44-4-400000000000000000000000000000000000000000000000000000000000000000000
χ8944-4-4-444-44i−4i−4i4i-444-4−4i4i4i−4i00000000000000000000000000000000004ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000
χ9044-4-4-444-44i−4i−4i4i-444-4−4i4i4i−4i0000000000000000000000000000000000−4ζ34ζ3−4ζ4ζ000000000000000000000000000000000000000000
χ9144-4-4-444-4−4i4i4i−4i-444-44i−4i−4i4i00000000000000000000000000000000004ζ−4ζ4ζ3−4ζ3000000000000000000000000000000000000000000
χ9244-4-4-444-4−4i4i4i−4i-444-44i−4i−4i4i0000000000000000000000000000000000−4ζ4ζ−4ζ34ζ3000000000000000000000000000000000000000000
χ938-888-88-8-80000000000008i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ948-888-88-8-8000000000000−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ958-88-88-88-80000000000000000000000000000000000004i2−4i2000000000000000000000000000000000000000000000000000000
χ968-88-88-88-8000000000000000000000000000000000000−4i24i2000000000000000000000000000000000000000000000000000000
χ978-8-88-8-888000000000000000000000000000000000042−4200000000000000000000000000000000000000000000000000000000
χ988-8-88-8-8880000000000000000000000000000000000−424200000000000000000000000000000000000000000000000000000000
χ998-8-8-888-88000000000000008-80000000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-8-888-8800000000000000-880000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.