Finite Group Databasebeta

← Group #72338971

Character table — Group #72338971

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222444444161616161616161616161616161616163232323232323232323232323232326464646464646464128128128128128128
order12222224444222222224444444424444448888888844448888448888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−ii−iii−i−i
χ61111111111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−ii−i−iii
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−ii−i−i−iii
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iii−iiii−i−i
χ9111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1111111-1-11-11-1
χ10111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-11-11
χ11111111111111111-1-1-1-111-1-1-1-1111-1-1-1-111-1-1-1-1111111-1-11111-1-1-11-11
χ12111111111111111-1-1-1-111-1-1-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111-11-1
χ13111111111111111-1-1-1-111-1-1-1-1-1-1-11111-1-111111111-1-1-1-1ii−i−i−iii−i−ii
χ14111111111111111-1-1-1-111-1-1-1-1-1-1-11111-1-111111111-1-1-1-1−i−iiii−i−iii−i
χ15111111111111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111ii−i−i−ii−iii−i
χ16111111111111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−iiii−ii−i−ii
χ172222222222222-2-222-2-2-2-222-2-222222-2-2-2-20000000000000000000000
χ182222222222222-2-222-2-2-2-222-2-2-2-2-2-2-222220000000000000000000000
χ192222222222222-2-2-2-222-2-2-2-222222-2-222-2-20000000000000000000000
χ202222222222222-2-2-2-222-2-2-2-222-2-2-222-2-2220000000000000000000000
χ2122222222222-2-22-200002-2000022-200002-2000022-2-22-2000000000000
χ2222222222222-2-22-200002-2000022-200002-20000-2-222-22000000000000
χ2322222222222-2-22-200002-20000-2-220000-22000022-2-2-22000000000000
χ2422222222222-2-22-200002-20000-2-220000-220000-2-2222-2000000000000
χ2522222222222-2-2-220000-22000022-20000-2222-2-20000002-20000000000
χ2622222222222-2-2-220000-22000022-20000-22-2-222000000-220000000000
χ2722222222222-2-2-220000-220000-2-2200002-222-2-2000000-220000000000
χ2822222222222-2-2-220000-220000-2-2200002-2-2-2220000002-20000000000
χ294444444-4-4-4-44-4000000000000000004-4000000000000000000000000
χ304444444-4-4-4-44-400000000000000000-44000000000000000000000000
χ314444444-4-4-4-4-440000000000000004-400000000000000000000000000
χ324444444-4-4-4-4-44000000000000000-4400000000000000000000000000
χ3344444-4-444-4-4000400000-40000000000000004i−4i000000000000000000
χ3444444-4-444-4-4000400000-4000000000000000−4i4i000000000000000000
χ3544444-4-444-4-4000-400000400000000000004i−4i00000000000000000000
χ3644444-4-444-4-4000-40000040000000000000−4i4i00000000000000000000
χ3744444-4-4-4-44400400000-4000000000000000000004i−4i00000000000000
χ3844444-4-4-4-44400400000-400000000000000000000−4i4i00000000000000
χ3944444-4-4-4-44400-40000040000000000000000004i−4i0000000000000000
χ4044444-4-4-4-44400-4000004000000000000000000−4i4i0000000000000000
χ41888-8-800008-80000004-400004-40000000000000000000000000000000
χ42888-8-800008-8000000-440000-440000000000000000000000000000000
χ43888-8-80000-8800004-400004-4000000000000000000000000000000000
χ44888-8-80000-880000-440000-44000000000000000000000000000000000
χ4588-88-8008-8000000004-40000-440000000000000000000000000000000
χ4688-88-8008-800000000-4400004-40000000000000000000000000000000
χ4788-88-800-880000004-40000-44000000000000000000000000000000000
χ4888-88-800-88000000-4400004-4000000000000000000000000000000000
χ4988-8-888-80000000000440000-4-40000000000000000000000000000000
χ5088-8-888-80000000000-4-40000440000000000000000000000000000000
χ5188-8-88-8800000000440000-4-4000000000000000000000000000000000
χ5288-8-88-8800000000-4-4000044000000000000000000000000000000000
χ5316-16000000000000000000000004-400000000000000000002i−2i2i−2i000000
χ5416-16000000000000000000000004-40000000000000000000−2i2i−2i2i000000
χ5516-1600000000000000000000000-4400000000000000000002-2-22000000
χ5616-1600000000000000000000000-440000000000000000000-222-2000000

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