Finite Group Databasebeta

← Group #72237605

Character table — Group #72237605

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222444488888888816161616161632323232323232323232323232326464646464646464646464646464128128128128
order12222222222222222222244422444444444444444444444444444888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111-11-11111-1-1111111-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-11-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ5111111111111111111111111-11-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111-11-1111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ922222222222222222222-2-2-2-20000-2-20000000000000022-2-200000000
χ1022222222222222222222-2-2-2-20000-2-200000000000000-2-22200000000
χ1122222222222-2-2222-2-2-2-222-2-220202-2220000000000-2-2000000000000
χ1222222222222-2-2222-2-2-2-222-2-2-20-202-2-2-2000000000022000000000000
χ1322222222222-2-2222-2-2-2-2-2-2220000-2200002222-2-20000000000000000
χ1422222222222-2-2222-2-2-2-2-2-2220000-220000-2-2-2-2220000000000000000
χ15222222222-2-2222-2-2-2-22-222220202-2-20022000000-2-200000000000000
χ16222222222-2-2222-2-2-2-22-222220-20-2-2-200-2-20000002200000000000000
χ17222222222-2-2222-2-2-2-22-2-2-2-2-20000220000000000000000002i2i−2i−2i0000
χ18222222222-2-2222-2-2-2-22-2-2-2-2-2000022000000000000000000−2i−2i2i2i0000
χ19222222222-2-2-2-22-2-222-2222-2-20000-2200000000000000000000002-200
χ20222222222-2-2-2-22-2-222-2222-2-20000-220000000000000000000000-2200
χ21222222222-2-2-2-22-2-222-22-2-22200002-20000000000000000000000002-2
χ22222222222-2-2-2-22-2-222-22-2-22200002-2000000000000000000000000-22
χ234444444-4-40000-40000004-400000000000022-2-22-20000000000000000
χ244444444-4-40000-40000004-4000000000000-2-222-220000000000000000
χ254444444-4-40000-4000000-4400000000000022-2-2-220000000000000000
χ264444444-4-40000-4000000-44000000000000-2-2222-20000000000000000
χ2744444-4-4444-400-44-40000000002020000-2-20000002-200000000000000
χ2844444-4-4444-400-44-4000000000-20-2000022000000-2200000000000000
χ2944444-4-444-4400-4-440000000002020000-2-2000000-2200000000000000
χ3044444-4-444-4400-4-44000000000-20-20000220000002-200000000000000
χ3144444-4-4-4-400004000000004-4202000-2-200000000002-2000000000000
χ3244444-4-4-4-400004000000004-4-20-2000220000000000-22000000000000
χ3344444-4-4-4-40000400000000-44202000-2-20000000000-22000000000000
χ3444444-4-4-4-40000400000000-44-20-20002200000000002-2000000000000
χ35444-4-4004-4040000-40000000020-20002-2002i−2i2i−2i000000002i−2i00000000
χ36444-4-4004-4040000-40000000020-20002-200−2i2i−2i2i00000000−2i2i00000000
χ37444-4-4004-4040000-400000000-202000-22002i−2i2i−2i00000000−2i2i00000000
χ38444-4-4004-4040000-400000000-202000-2200−2i2i−2i2i000000002i−2i00000000
χ39444-4-400-4440000-400000000020-2000-22002i−2i−2i2i0000002i−2i0000000000
χ40444-4-400-4440000-400000000020-2000-2200−2i2i2i−2i000000−2i2i0000000000
χ41444-4-400-4440000-4000000000-2020002-2002i−2i−2i2i000000−2i2i0000000000
χ42444-4-400-4440000-4000000000-2020002-200−2i2i2i−2i0000002i−2i0000000000
χ43888-8-8008-80-8000080000000000000000000000000000000000000000
χ44888-8-800-88-80000800000000000000000000000000000000000000000
χ4588-88-800000000000440-400000000000000000000000000002-22-20000
χ4688-88-800000000000440-40000000000000000000000000000-22-220000
χ4788-88-800000000000-4-40400000000000000000000000000002i−2i−2i2i0000
χ4888-88-800000000000-4-4040000000000000000000000000000−2i2i2i−2i0000
χ4988-8-880000004400000-400000040-40000000000000000000000000000
χ5088-8-880000004400000-4000000-4040000000000000000000000000000
χ5188-8-88000000-4-400000400000000000004-40000000000000000000000
χ5288-8-88000000-4-40000040000000000000-440000000000000000000000
χ5316-160008-80000000008-800000000000000000000000000000000000000
χ5416-160008-8000000000-8800000000000000000000000000000000000000
χ5516-16000-8800008-80000000000000000000000000000000000000000000
χ5616-16000-880000-880000000000000000000000000000000000000000000

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