Finite Group Databasebeta

← Group #72337727

Character table — Group #72337727

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1122244444488161616161616161616161632323232323232323232323232323264646464646464646464646464128128128128
order12222222222222222222244444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-111-1-1-1-1111-11-1-11111-1-1-1-111-1-1
χ41111111111111111111111111-1-1-1-1-1-111-1-1-1-1111-11-1-1-1-1-1-11111-1-111
χ51111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-11-11-11111-1-1-1-1-1-111
χ61111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1111111-1-1
χ71111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1111111111-1-1-1-1
χ81111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-11-1-1-1-1-1-1-1-11111
χ911111111111-1-11111111-11-1-111111-1-1-1-111-1-1-1-11-1-1-11ii−i−iii−i−ii−ii−i
χ1011111111111-1-11111111-11-1-111111-1-1-1-111-1-1-1-11-1-1-11−i−iii−i−iii−ii−ii
χ1111111111111-1-11111111-11-1-11-1-1-1-111-1-1-1-111-1-111-11-1ii−i−i−i−iiii−i−ii
χ1211111111111-1-11111111-11-1-11-1-1-1-111-1-1-1-111-1-111-11-1−i−iiiii−i−i−iii−i
χ1311111111111-1-1111-1-1-1-1-11-1-1111111111-1-111-1-1-1-11-1-1ii−i−i−i−iii−iii−i
χ1411111111111-1-1111-1-1-1-1-11-1-1111111111-1-111-1-1-1-11-1-1−i−iiiii−i−ii−i−ii
χ1511111111111-1-1111-1-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-1-11111ii−i−iii−i−i−ii−ii
χ1611111111111-1-1111-1-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-1-11111−i−iii−i−iiii−ii−i
χ17222222222222222-22222-2-22-2-2000000-2-200002-2-20200000000000000
χ18222222222222222-2-2-2-2-2-2-22-2-20000002200002-220-200000000000000
χ192222222222222-2-2200002222-200002200-2-2-2-2-2-200002000000000000
χ202222222222222-2-2200002222-20000-2-2002222-2-20000-2000000000000
χ212222222222222-2-2-20000-2-22-2222-2-200000000-22020-20000000000000
χ222222222222222-2-2-20000-2-22-22-2-22200000000-220-2020000000000000
χ2322222222222-2-222-222222-2-22-2000000220000-22-20-200000000000000
χ2422222222222-2-222-2-2-2-2-22-2-22-2000000-2-20000-2220200000000000000
χ2522222222222-2-2-2-220000-22-2-2-20000220022-2-2220000-2000000000000
χ2622222222222-2-2-2-220000-22-2-2-20000-2-200-2-2222200002000000000000
χ2722222222222-2-2-2-2-200002-2-22222-2-2000000002-20-2020000000000000
χ2822222222222-2-2-2-2-200002-2-222-2-222000000002-2020-20000000000000
χ294444444-4-4-4-40000400000-400000004i−4i0000000000000000000000000
χ304444444-4-4-4-40000400000-40000000−4i4i0000000000000000000000000
χ314444444-4-4-4-40000-400000400000000000004i−4i0000000000000000000
χ324444444-4-4-4-40000-40000040000000000000−4i4i0000000000000000000
χ3344444-4-44-44-4000000000400-40000000000000000000000002-22-20000
χ3444444-4-44-44-4000000000400-4000000000000000000000000-22-220000
χ3544444-4-44-44-4000000000-40040000000000000000000000002i−2i−2i2i0000
χ3644444-4-44-44-4000000000-4004000000000000000000000000−2i2i2i−2i0000
χ3744444-4-4-44-4444000000000-40000000000000000000002-22-200000000
χ3844444-4-4-44-4444000000000-4000000000000000000000-22-2200000000
χ3944444-4-4-44-44-4-400000000040000000000000000000002i−2i−2i2i00000000
χ4044444-4-4-44-44-4-40000000004000000000000000000000−2i2i2i−2i00000000
χ41888-8-800080-800000000000000000000004i−4i000000000000000000000
χ42888-8-800080-80000000000000000000000−4i4i000000000000000000000
χ43888-8-8000-8088-80000000000000000000000000000000000000000000
χ44888-8-8000-808-880000000000000000000000000000000000000000000
χ4588-88-80080-8000000000000000004i−4i000000000000000000000000000
χ4688-88-80080-800000000000000000−4i4i000000000000000000000000000
χ4788-88-800-8080000000000000000000004-400000000000000000000000
χ4888-88-800-808000000000000000000000-4400000000000000000000000
χ4988-8-888-80000000000000000004-400000000000000000000000000000
χ5088-8-888-8000000000000000000-4400000000000000000000000000000
χ5188-8-88-8800000000044-4-4000000000000000000000000000000000000
χ5288-8-88-88000000000-4-444000000000000000000000000000000000000
χ5316-16000000000004-404-44-4000000000000000000000000000000000000
χ5416-16000000000004-40-44-44000000000000000000000000000000000000
χ5516-1600000000000-4404-4-44000000000000000000000000000000000000
χ5616-1600000000000-440-444-4000000000000000000000000000000000000

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