Finite Group Databasebeta

← Group #72339102

Character table — Group #72339102

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size112224444448888161616161616323232323232323232323232323232646464646464646464646464646464646464128128
order12222224444444422224422244444488888844444448888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-11-111111111-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-11-111-1-11-1-1-1-1-1-1-11-111111-11-1-1-1-11111-1-1
χ61111111111111111111111-11-111-1-11-1-1-1-1-1-1-11-1-1-1-1-11-111111-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-11-1-1-1-1111-111111-11-1-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-11-1-1-1-1111-11-1-1-1-1-11-111111111-1-1
χ91111111111111-1-11-1-1-1-1-1111111-1-1-111-1-1-1-1-1-11ii−i−i-111ii−i−iii−i−ii−i
χ101111111111111-1-11-1-1-1-1-1111111-1-1-111-1-1-1-1-1-11−i−iii-111−i−iii−i−iii−ii
χ111111111111111-1-11-1-1-1-1-111-11-11-1-1-111-1-11111-1ii−i−i1-1-1ii−i−i−i−iii−ii
χ121111111111111-1-11-1-1-1-1-111-11-11-1-1-111-1-11111-1−i−iii1-1-1−i−iiiii−i−ii−i
χ131111111111111-1-11-1-1-1-1-11-11-11111-1-1-111111-1-1ii−i−i-1-11−i−iiiii−i−i−ii
χ141111111111111-1-11-1-1-1-1-11-11-11111-1-1-111111-1-1−i−iii-1-11ii−i−i−i−iiii−i
χ151111111111111-1-11-1-1-1-1-11-1-1-1-1111-1-1-111-1-1-111ii−i−i11-1−i−iii−i−iiii−i
χ161111111111111-1-11-1-1-1-1-11-1-1-1-1111-1-1-111-1-1-111−i−iii11-1ii−i−iii−i−i−ii
χ172222222222222222222-2-2-22020-222-2-2-2-2-20000000000000000000000
χ182222222222222222222-2-2-2-20-20-2-2-2-222220000000000000000000000
χ192222222222222-2-22-2-2-222-22020-2-2-22-2-2220000000000000000000000
χ202222222222222-2-22-2-2-222-2-20-20-222222-2-20000000000000000000000
χ2122222222222-2-222-22-2-222-20000200-2000022-20200000-200000000000
χ2222222222222-2-222-22-2-222-20000200-20000-2-220-200000200000000000
χ2322222222222-2-222-22-2-2-2-220202-20020000000-20000020-20000000000
χ2422222222222-2-222-22-2-2-2-220-20-2-20020000000200000-2020000000000
χ2522222222222-2-2-2-2-2-2222220202-200-20000000200000-20-20000000000
χ2622222222222-2-2-2-2-2-2222220-20-2-200-20000000-2000002020000000000
χ2722222222222-2-2-2-2-2-222-2-2-200002002000022-20-200000200000000000
χ2822222222222-2-2-2-2-2-222-2-2-2000020020000-2-220200000-200000000000
χ294444444-4-4-4-40000004-4000000000000000000002i−2i2i−2i0000000000000
χ304444444-4-4-4-40000004-400000000000000000000−2i2i−2i2i0000000000000
χ314444444-4-4-4-4000000-44000000000000000000002-2-220000000000000
χ324444444-4-4-4-4000000-4400000000000000000000-222-20000000000000
χ3344444-4-444-4-400440-4000000000000000000000000000002-22-2000000
χ3444444-4-444-4-400440-400000000000000000000000000000-22-22000000
χ3544444-4-444-4-400-4-404000000000000000000000000000002i−2i−2i2i000000
χ3644444-4-444-4-400-4-40400000000000000000000000000000−2i2i2i−2i000000
χ3744444-4-4-4-4444400-400000000000000004-40000000000000000000000
χ3844444-4-4-4-4444400-40000000000000000-440000000000000000000000
χ3944444-4-4-4-444-4-4004000000000004-4000000000000000000000000000
χ4044444-4-4-4-444-4-400400000000000-44000000000000000000000000000
χ41888-8-88-80000000000000000000000000004i−4i00000000000000000000
χ42888-8-88-8000000000000000000000000000−4i4i00000000000000000000
χ43888-8-8-88000000000000000040-4000000000000000000000000000000
χ44888-8-8-880000000000000000-404000000000000000000000000000000
χ4588-88-800008-800000000000000000004-4000000000000000000000000
χ4688-88-800008-80000000000000000000-44000000000000000000000000
χ4788-88-80000-888-80000000000000000000000000000000000000000000
χ4888-88-80000-88-880000000000000000000000000000000000000000000
χ4988-8-88008-8000000000000040-40000000000000000000000000000000
χ5088-8-88008-80000000000000-4040000000000000000000000000000000
χ5188-8-8800-8800008-800000000000000000000000000000000000000000
χ5288-8-8800-880000-8800000000000000000000000000000000000000000
χ5316-16000000000000000004-4000000000000000000000000000002i−2i2i−2i00
χ5416-16000000000000000004-400000000000000000000000000000−2i2i−2i2i00
χ5516-1600000000000000000-44000000000000000000000000000002-2-2200
χ5616-1600000000000000000-4400000000000000000000000000000-222-200

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