Finite Group Databasebeta

← Group #72317162

Character table — Group #72317162

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1122244448888888881616161616161616323232323232323232646464646464646464646464646464646464646464646464
order12222222222222222222222444444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-11-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ611111111111111111111-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ711111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ811111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ911111111111111-1-1-1-1-1-11-1-11-1-111-11-11111-1-11-111-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ1011111111111111-1-1-1-1-1-11-1-11-1-111-11-11111-1-11-111-1-1−i−iii−i−iii−ii−ii−ii−ii
χ1111111111111111-1-1-1-1-1-11-1-11-1-111-11-1-1-1-1-1111-1-1-111ii−i−iii−i−i−ii−ii−ii−ii
χ1211111111111111-1-1-1-1-1-11-1-11-1-111-11-1-1-1-1-1111-1-1-111−i−iii−i−iiii−ii−ii−ii−i
χ1311111111111111-1-1-1-1-1-1-11-1-11-111-1-111111-1-1-11-1-111ii−i−i−i−iiii−i−iii−i−ii
χ1411111111111111-1-1-1-1-1-1-11-1-11-111-1-111111-1-1-11-1-111−i−iiiii−i−i−iii−i−iii−i
χ1511111111111111-1-1-1-1-1-1-11-1-11-111-1-11-1-1-1-111-1111-1-1ii−i−i−i−iii−iii−i−iii−i
χ1611111111111111-1-1-1-1-1-1-11-1-11-111-1-11-1-1-1-111-1111-1-1−i−iiiii−i−ii−i−iii−i−ii
χ17222222222222222222222-2-22-2-2-2-2-22-2000000-2200000000000000000000
χ1822222222222222222222-22-2-22-2-2-2-2-220000002-200000000000000000000
χ1922222222222222-2-2-2-2-2-2222222-2-2222000000-2-200000000000000000000
χ2022222222222222-2-2-2-2-2-2-2-22-2-22-2-22-2-20000002200000000000000000000
χ212222222222-2-2-2-222-2-22-20020022-2-200000000000000000000002200-2-200
χ222222222222-2-2-2-222-2-22-20020022-2-20000000000000000000000-2-2002200
χ232222222222-2-2-2-222-2-22-200-200-2-2220000000000000000000000002i−2i00−2i2i
χ242222222222-2-2-2-222-2-22-200-200-2-222000000000000000000000000−2i2i002i−2i
χ252222222222-2-2-2-2-2-222-22002002-22-20000000000000000000000002200-2-2
χ262222222222-2-2-2-2-2-222-22002002-22-2000000000000000000000000-2-20022
χ272222222222-2-2-2-2-2-222-2200-200-22-2200000000000000000000002i−2i00−2i2i00
χ282222222222-2-2-2-2-2-222-2200-200-22-220000000000000000000000−2i2i002i−2i00
χ294444444-4-4-4000000000000400-40000022-2-22-20000000000000000000000
χ304444444-4-4-4000000000000400-400000-2-222-220000000000000000000000
χ314444444-4-4-4000000000000-40040000022-2-2-220000000000000000000000
χ324444444-4-4-4000000000000-400400000-2-2222-20000000000000000000000
χ3344444-4-444-44-44-40000000400400000-40000000000000000000000000000
χ3444444-4-444-44-44-40000000-400-40000040000000000000000000000000000
χ3544444-4-444-4-44-44000000400400000-400000000000000000000000000000
χ3644444-4-444-4-44-44000000-400-400000400000000000000000000000000000
χ37444-4-4004-40040-4000000400-400000002i−2i2i−2i00002i−2i000000000000000000
χ38444-4-4004-40040-4000000400-40000000−2i2i−2i2i0000−2i2i000000000000000000
χ39444-4-4004-40040-4000000-400400000002i−2i2i−2i0000−2i2i000000000000000000
χ40444-4-4004-40040-4000000-40040000000−2i2i−2i2i00002i−2i000000000000000000
χ41444-4-400-44040-400000000400-40000002i−2i−2i2i0000002i−2i0000000000000000
χ42444-4-400-44040-400000000400-4000000−2i2i2i−2i000000−2i2i0000000000000000
χ43444-4-400-44040-400000000-40040000002i−2i−2i2i000000−2i2i0000000000000000
χ44444-4-400-44040-400000000-4004000000−2i2i2i−2i0000002i−2i0000000000000000
χ4588888-8-8-8-880000000000000000000000000000000000000000000000000
χ46888-8-8008-800-808000000000000000000000000000000000000000000000
χ47888-8-800-880-8080000000000000000000000000000000000000000000000
χ4888-88-800000000000440-40000000000000000000000000002-22-200000000
χ4988-88-800000000000440-4000000000000000000000000000-22-2200000000
χ5088-88-800000000000-4-4040000000000000000000000000002i−2i−2i2i00000000
χ5188-88-800000000000-4-404000000000000000000000000000−2i2i2i−2i00000000
χ5288-8-880000000004400-40000000000000000000000002-22-2000000000000
χ5388-8-880000000004400-4000000000000000000000000-22-22000000000000
χ5488-8-88000000000-4-40040000000000000000000000002i−2i−2i2i000000000000
χ5588-8-88000000000-4-4004000000000000000000000000−2i2i2i−2i000000000000
χ5616-160008-80000000008-800000000000000000000000000000000000000000
χ5716-160008-8000000000-8800000000000000000000000000000000000000000
χ5816-16000-8800000008-80000000000000000000000000000000000000000000
χ5916-16000-880000000-880000000000000000000000000000000000000000000

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