Finite Group Databasebeta

← Group #72310528

Character table — Group #72310528

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122244444488888816161616161616161616161616323232323232323232323232326464646464646464646464646464646464128128
order12222222222224444222222224444444444444444444444444444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11-111111111-1-1-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-11-11-1-111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-11-11-1-11-1-1-1-111111111-1-1
χ911111111111-1-111-1-11-1-111-1-1-1-111-1-1111111111111-1-1-1-1-1-1ii−i−iii−i−iii−i−ii−i
χ1011111111111-1-111-1-11-1-111-1-1-1-111-1-1111111111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−ii
χ1111111111111-1-111-1-11-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-111-111ii−i−i−i−iiiii−i−i−ii
χ1211111111111-1-111-1-11-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-111-111−i−iiiii−i−i−i−iiii−i
χ1311111111111-1-111-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-11ii−i−iii−i−i−i−iii−ii
χ1411111111111-1-111-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-11−i−iii−i−iiiii−i−ii−i
χ1511111111111-1-111-1-11-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-11-111-1ii−i−i−i−iii−i−iiii−i
χ1611111111111-1-111-1-11-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-11-111-1−i−iiiii−i−iii−i−i−ii
χ172222222222222222222-22222-222222-2-200000000-2-2-200-20000000000000000
χ182222222222222222222-2-2-2-2-2-22-2-2-2-2-2-20000000022-20020000000000000000
χ192222222222222-2-2-2-2-2-2200002200002-222-2-2000000-2200-2000000000000000
χ202222222222222-2-2-2-2-2-2200002200002-2-2-222000000-2-2002000000000000000
χ212222222222222-2-2-2-2-2-2-20000-220000-22000022-2-20020200-200000000000000
χ222222222222222-2-2-2-2-2-2-20000-220000-220000-2-2220020-200200000000000000
χ2322222222222-2-222-2-22-2222-2-22-222-2-2-2-200000000-2-220020000000000000000
χ2422222222222-2-222-2-22-22-2-2222-2-2-222-2-20000000022200-20000000000000000
χ2522222222222-2-2-2-222-22200002-20000-22000022-2-200-20-200200000000000000
χ2622222222222-2-2-2-222-22200002-20000-220000-2-22200-20200-200000000000000
χ2722222222222-2-2-2-222-22-20000-2-200002-222-2-20000002-2002000000000000000
χ2822222222222-2-2-2-222-22-20000-2-200002-2-2-2220000002200-2000000000000000
χ294444444-4-4-4-40000440-400000000000000000000000000000000000002-22-200
χ304444444-4-4-4-40000440-40000000000000000000000000000000000000-22-2200
χ314444444-4-4-4-40000-4-40400000000000000000000000000000000000002i−2i−2i2i00
χ324444444-4-4-4-40000-4-4040000000000000000000000000000000000000−2i2i2i−2i00
χ3344444-4-444-4-444000000000000-400000000000000000000002-22-20000000000
χ3444444-4-444-4-444000000000000-40000000000000000000000-22-220000000000
χ3544444-4-444-4-4-4-4000000000000400000000000000000000002i−2i−2i2i0000000000
χ3644444-4-444-4-4-4-400000000000040000000000000000000000−2i2i2i−2i0000000000
χ3744444-4-4-4-444004400-4004-400004-40000000000000000000000000000000000
χ3844444-4-4-4-444004400-400-440000-440000000000000000000000000000000000
χ3944444-4-4-4-44400-4-400400000000000000000000004-400000000000000000000
χ4044444-4-4-4-44400-4-40040000000000000000000000-4400000000000000000000
χ41444-4-400004-4004-4000000400000-400002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ42444-4-400004-4004-4000000400000-40000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ43444-4-400004-4004-4000000-400000400002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ44444-4-400004-4004-4000000-40000040000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ45444-4-400004-400-4400000400000-4000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ46444-4-400004-400-4400000400000-400000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ47444-4-400004-400-4400000-4000004000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ48444-4-400004-400-4400000-400000400000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ49888-8-80000-8800000000000440000-4-400000000000000000000000000000000
χ50888-8-80000-8800000000000-4-400004400000000000000000000000000000000
χ5188-88-8008-800000000000004-400004-400000000000000000000000000000000
χ5288-88-8008-80000000000000-440000-4400000000000000000000000000000000
χ5388-88-800-88008-80000000000000000000000000000000000000000000000000
χ5488-88-800-8800-880000000000000000000000000000000000000000000000000
χ5588-8-888-80000000000000004-40000-4400000000000000000000000000000000
χ5688-8-888-8000000000000000-4400004-400000000000000000000000000000000
χ5788-8-88-88000000008-8000000000000000000000000000000000000000000000
χ5888-8-88-8800000000-88000000000000000000000000000000000000000000000
χ5916-160000000000000000040000-40000000000000000000000000002i−2i2i−2i000000
χ6016-160000000000000000040000-4000000000000000000000000000−2i2i−2i2i000000
χ6116-1600000000000000000-4000040000000000000000000000000002-2-22000000
χ6216-1600000000000000000-400004000000000000000000000000000-222-2000000

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