Finite Group Databasebeta

← Group #72337643

Character table — Group #72337643

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size112444888888888816161616161616161616161632323232323232323232326464646464646464646464646464646464646464646464646464128128128128128128128128256256256
order1222222222224444222222244444222444444444444444444444444444444888844444488488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1
χ31111111111111111111111111111111111-1-1111-111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-111
χ51111111111111-1-11111-1-111111-11-1-1111-111-1-1-11111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1
χ61111111111111-1-11111-1-111111-11-1-1111-111-1-1-111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-111
χ71111111111111-1-11111-1-111111-11-1-1111-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111
χ81111111111111-1-11111-1-111111-11-1-1111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111111-1-1
χ911111111-1-1-1-11111111-1-1-1-1-1-11111111-1-1111-1-111-111iiii−i−i−i−iiiii−i−i−i−i-111-1-1-1-1ii−i−i11-1i−i
χ1011111111-1-1-1-11111111-1-1-1-1-1-11111111-1-1111-1-111-111−i−i−i−iiiii−i−i−i−iiiii-111-1-1-1-1−i−iii11-1−ii
χ1111111111-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-11-1-1-11-1-1-1iiii−i−i−i−iiiii−i−i−i−i-111-1-111−i−iii-1-11−ii
χ1211111111-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-11-1-1-11-1-1-1−i−i−i−iiiii−i−i−i−iiiii-111-1-111ii−i−i-1-11i−i
χ1311111111-1-1-1-11-1-1111111-1-1-1-11-11-1-111-1111-11111-111iiii−i−i−i−i−i−i−i−iiiii-1-1-111-1-1ii−i−i-1-11−ii
χ1411111111-1-1-1-11-1-1111111-1-1-1-11-11-1-111-1111-11111-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-111-1-1−i−iii-1-11i−i
χ1511111111-1-1-1-11-1-1111111-1-1-1-11-11-1-111-11-1-1-111-11-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-11111−i−iii11-1i−i
χ1611111111-1-1-1-11-1-1111111-1-1-1-11-11-1-111-11-1-1-111-11-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-11111ii−i−i11-1−ii
χ172222222222222002222002222-20-200-2220000000-2-20022-2-222-2-200000000-2000000000000000
χ182222222222222002222002222-20-200-2220000000-2-200-2-222-2-22200000000-2000000000000000
χ1922222222222220022-2-200-2-222-20-200-2-2-200000002-2000000000022-2-222-2-22000000000000000
χ2022222222222220022-2-200-2-222-20-200-2-2-200000002-20000000000-2-222-2-2222000000000000000
χ2122222222222222222-2-222-2-222222222-2-22002220-22000000000000000000-2-2-2-2-200000000000
χ222222222222222-2-222-2-2-2-2-2-2222-22-2-22-2-2-200-2-2-20-22000000000000000000-2222200000000000
χ2322222222-2-2-2-2200222200-2-2-2-2-20-200-22-20000000-22002i2i−2i−2i−2i−2i2i2i000000002000000000000000
χ2422222222-2-2-2-2200222200-2-2-2-2-20-200-22-20000000-2200−2i−2i2i2i2i2i−2i−2i000000002000000000000000
χ2522222222-2-2-2-220022-2-20022-2-2-20-200-2-2200000002200000000002i2i−2i−2i−2i−2i2i2i-2000000000000000
χ2622222222-2-2-2-220022-2-20022-2-2-20-200-2-220000000220000000000−2i−2i2i2i2i2i−2i−2i-2000000000000000
χ2722222222-2-2-2-222222-2-2-2-222-2-2222222-22-2002-2-20-2-20000000000000000002-2-22200000000000
χ2822222222-2-2-2-22-2-222-2-22222-2-22-22-2-22-22200-2220-2-2000000000000000000222-2-200000000000
χ294444444444-4-4-400-4-40000004-400000000022000200-2-20000000000000000000002-2000000000
χ304444444444-4-4-400-4-40000004-4000000000-2-2000-20022000000000000000000000-22000000000
χ3144444444-4-444-400-4-4000000-4400000000022000200-2-2000000000000000000000-22000000000
χ3244444444-4-444-400-4-4000000-44000000000-2-2000-200220000000000000000000002-2000000000
χ33444444-4-400004004-400440000-40-4004004000-4-40000000000000000000000000000000000000
χ34444444-4-400004004-400-4-40000-40-400400-4000440000000000000000000000000000000000000
χ35444444-4-400004444-400000000444-4-4-4000004000000000000000000000000000000000000000
χ36444444-4-400004-4-44-4000000004-4444-400000-4000000000000000000000000000000000000000
χ37444-44-44-40044022000022000-40202-2000-200-22-200000002-2002-22-2002-2000000000000000000
χ38444-44-44-40044022000022000-40202-2000-200-22-20000000-2200-22-2200-22000000000000000000
χ39444-44-44-400440-2-20000-2-2000-40-20-220002002-2200000002-2002-2-2200-22000000000000000000
χ40444-44-44-400440-2-20000-2-2000-40-20-220002002-220000000-2200-222-2002-2000000000000000000
χ41444-44-44-400-4-40220000-2-200040202-2000200-2-2200000002i−2i00−2i2i2i−2i00−2i2i000000000000000000
χ42444-44-44-400-4-40220000-2-200040202-2000200-2-220000000−2i2i002i−2i−2i2i002i−2i000000000000000000
χ43444-44-44-400-4-40-2-200002200040-20-22000-20022-200000002i−2i00−2i2i−2i2i002i−2i000000000000000000
χ44444-44-44-400-4-40-2-200002200040-20-22000-20022-20000000−2i2i002i−2i2i−2i00−2i2i000000000000000000
χ45444-44-4-44440002200002200-40020-22000-200-2-22000002-2002-200002-2002-20000000000000000
χ46444-44-4-44440002200002200-40020-22000-200-2-2200000-2200-220000-2200-220000000000000000
χ47444-44-4-4444000-2-20000-2-200-400-202-200020022-2000002-2002-20000-2200-220000000000000000
χ48444-44-4-4444000-2-20000-2-200-400-202-200020022-200000-2200-2200002-2002-20000000000000000
χ49444-44-4-44-4-4000220000-2-20040020-22000200-22-2000002i−2i00−2i2i00002i−2i00−2i2i0000000000000000
χ50444-44-4-44-4-4000220000-2-20040020-22000200-22-200000−2i2i002i−2i0000−2i2i002i−2i0000000000000000
χ51444-44-4-44-4-4000-2-200002200400-202-2000-2002-22000002i−2i00−2i2i0000−2i2i002i−2i0000000000000000
χ52444-44-4-44-4-4000-2-200002200400-202-2000-2002-2200000−2i2i002i−2i00002i−2i00−2i2i0000000000000000
χ53888888-8-80000-800-8800000000000000000000000000000000000000000000000000000000000
χ548888-8-800000000000000044000000000-400000000000000000000000000000000002-22-200000
χ558888-8-800000000000000044000000000-40000000000000000000000000000000000-22-2200000
χ568888-8-8000000000000000-4-4000000000400000000000000000000000000000000002i−2i−2i2i00000
χ578888-8-8000000000000000-4-400000000040000000000000000000000000000000000−2i2i2i−2i00000
χ58888-8-880000000000044000000000000-40044000-4000000000000000000000000000000000000
χ59888-8-880000000000044000000000000-400-4-40004000000000000000000000000000000000000
χ60888-8-8800000000000-4-4000000000000400000000004-400000000000000000000000000000000
χ61888-8-8800000000000-4-400000000000040000000000-4400000000000000000000000000000000
χ6288-8000004-44-4-444404-44-44-4000-400000000000000000000000000000000002-22-200000000000
χ6388-8000004-44-4-44440-444-4-44000-40000000000000000000000000000000000-22-2200000000000
χ6488-8000004-44-4-4-4-4404-4-444-400040000000000000000000000000000000000-22-2200000000000
χ6588-8000004-44-4-4-4-440-44-44-44000400000000000000000000000000000000002-22-200000000000
χ6688-800000-44-44-444404-4-44-44000-400000000000000000000000000000000002-2-2200000000000
χ6788-800000-44-44-44440-44-444-4000-40000000000000000000000000000000000-222-200000000000
χ6888-800000-44-44-4-4-4404-44-4-4400040000000000000000000000000000000000-222-200000000000
χ6988-800000-44-44-4-4-440-444-44-4000400000000000000000000000000000000002-2-2200000000000
χ701616-16000008-8-88800-8000000000000000000000000000000000000000000000000000000000000
χ711616-1600000-888-8800-8000000000000000000000000000000000000000000000000000000000000
χ7216-16000000000008-8000000000040-40000004i−4i000000000000000000000000000000000002i−2i000
χ7316-16000000000008-8000000000040-4000000−4i4i00000000000000000000000000000000000−2i2i000
χ7416-1600000000000-88000000000040-40000004i−4i00000000000000000000000000000000000−2i2i000
χ7516-1600000000000-88000000000040-4000000−4i4i000000000000000000000000000000000002i−2i000
χ7632-3200000000000000000000000-808000000000000000000000000000000000000000000000000

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