Finite Group Databasebeta

← Group #72340535

Character table — Group #72340535

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size1124448888888816161616161616161632323232323232323232326464646464646464646464128128128128128128128128128128128128128128128128128128128128128128
order1222222222224422244444422224448888244444444884444444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-111-1-1111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-111-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ7111111111111111111111111-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ9111111111111111-1-111-1-1-1-1-11-1-1-11-11111-1-111-11-1-1-1111-111-1-1ii−i−ii−ii−iii−i−ii−ii−i
χ10111111111111111-1-111-1-1-1-1-11-1-1-11-11111-1-111-11-1-1-1111-111-1-1−i−iii−ii−ii−i−iii−ii−ii
χ11111111111111111-1-111-1-1-1-1-11-1-1-11-1-1-1-1-11111-11-111-1-11-1-1-111ii−i−i−ii−iiii−i−i−ii−ii
χ12111111111111111-1-111-1-1-1-1-11-1-1-11-1-1-1-1-11111-11-111-1-11-1-1-111−i−iiii−ii−i−i−iiii−ii−i
χ13111111111111111-1-111-1-1-1-1-1-11-1-1-111111-1-111-1-11-1-111-11-1-111ii−i−ii−i−ii−i−iiii−i−ii
χ14111111111111111-1-111-1-1-1-1-1-11-1-1-111111-1-111-1-11-1-111-11-1-111−i−iii−iii−iii−i−i−iii−i
χ15111111111111111-1-111-1-1-1-1-1-11-1-1-11-1-1-1-11111-1-1111-1-1-1111-1-1ii−i−i−iii−i−i−iii−iii−i
χ16111111111111111-1-111-1-1-1-1-1-11-1-1-11-1-1-1-11111-1-1111-1-1-1111-1-1−i−iiii−i−iiii−i−ii−i−ii
χ17222222222222222222222-2-222-2-222-2000000-2-2-22-20000-2200000000000000000000
χ18222222222222222222222-2-22-22-22-22000000-2-2-2-2200002-200000000000000000000
χ19222222222222222-2-222-2-222-2222-222000000-2-22220000-2-200000000000000000000
χ20222222222222222-2-222-2-222-2-2-22-2-2-2000000-2-22-2-200002200000000000000000000
χ2122222222-2-2-2-222222-2-2-2-222-20022000000002-2-2000000000000000022000000-2-200
χ2222222222-2-2-2-222222-2-2-2-222-20022000000002-2-20000000000000000-2-20000002200
χ2322222222-2-2-2-222222-2-2-2-2-2-2-200-2200000000-2220000000000000000002i−2i000000−2i2i
χ2422222222-2-2-2-222222-2-2-2-2-2-2-200-2200000000-222000000000000000000−2i2i0000002i−2i
χ2522222222-2-2-2-2222-2-2-2-222222002-200000000-22-200000000000000000022000000-2-2
χ2622222222-2-2-2-2222-2-2-2-222222002-200000000-22-2000000000000000000-2-200000022
χ2722222222-2-2-2-2222-2-2-2-222-2-2200-2-2000000002-2200000000000000002i−2i000000−2i2i00
χ2822222222-2-2-2-2222-2-2-2-222-2-2200-2-2000000002-220000000000000000−2i2i0000002i−2i00
χ294444444444-4-4-4-4-4004-4000000400040000000000-400000000000000000000000000
χ304444444444-4-4-4-4-4004-4000000-4000-40000000000400000000000000000000000000
χ3144444444-4-444-4-4-400-4400000400040000000000-4000000000000000000000000000
χ3244444444-4-444-4-4-400-4400000-4000-400000000004000000000000000000000000000
χ33444444-4-4000044-400000044000-40002222-2-20000022-2-20000000000000000000000
χ34444444-4-4000044-400000044000-4000-2-2-2-22200000-2-2220000000000000000000000
χ35444444-4-4000044-4000000-4-4000400022222200000-2-2-2-20000000000000000000000
χ36444444-4-4000044-4000000-4-40004000-2-2-2-2-2-20000022220000000000000000000000
χ37444-4-444-40044000000-4000004000-4022-2-20000000002-2002-2000000000000000000
χ38444-4-444-40044000000-4000004000-40-2-222000000000-2200-22000000000000000000
χ39444-4-444-40044000000-400000-40004022-2-20000000002-200-22000000000000000000
χ40444-4-444-40044000000-400000-400040-2-222000000000-22002-2000000000000000000
χ41444-4-44-44440000000-400000004000-422-2-2000000000-2200002-20000000000000000
χ42444-4-44-44440000000-400000004000-4-2-2220000000002-20000-220000000000000000
χ43444-4-44-44440000000-40000000-4000422-2-2000000000-220000-220000000000000000
χ44444-4-44-44440000000-40000000-40004-2-2220000000002-200002-20000000000000000
χ45888888-8-80000-8-880000000000000000000000000000000000000000000000000000
χ468888-8-800000000000004400-4000000000000000000000000000000000002-22-20000
χ478888-8-800000000000004400-400000000000000000000000000000000000-22-220000
χ488888-8-80000000000000-4-4004000000000000000000000000000000000002i−2i−2i2i0000
χ498888-8-80000000000000-4-400400000000000000000000000000000000000−2i2i2i−2i0000
χ50888-88-8000000000440000000000-4000000000000000000000002-22-2000000000000
χ51888-88-8000000000440000000000-400000000000000000000000-22-22000000000000
χ52888-88-8000000000-4-400000000004000000000000000000000002i−2i−2i2i000000000000
χ53888-88-8000000000-4-40000000000400000000000000000000000−2i2i2i−2i000000000000
χ54888-8-888-800-8-80000008000000000000000000000000000000000000000000000000
χ55888-8-88-88-8-8000000080000000000000000000000000000000000000000000000000
χ5688-8000004-44-4-4404-4004-4000000000004-42-2000002-2000000000000000000000000
χ5788-8000004-44-4-4404-4004-400000000000-44-2200000-22000000000000000000000000
χ5888-8000004-44-4-440-4400-44000000000004-4-2200000-22000000000000000000000000
χ5988-8000004-44-4-440-4400-4400000000000-442-2000002-2000000000000000000000000
χ6088-800000-44-44-4404-400-440000000004-4002-200000-22000000000000000000000000
χ6188-800000-44-44-4404-400-44000000000-4400-22000002-2000000000000000000000000
χ6288-800000-44-44-440-44004-40000000004-400-22000002-2000000000000000000000000
χ6388-800000-44-44-440-44004-4000000000-44002-200000-22000000000000000000000000
χ641616-16000008-8-888-800000000000000000000000000000000000000000000000000000
χ651616-1600000-888-88-800000000000000000000000000000000000000000000000000000
χ6632-3200000000000000000008-800000000000000000000000000000000000000000000
χ6732-320000000000000000000-8800000000000000000000000000000000000000000000

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