Finite Group Databasebeta

← Group #72339067

Character table — Group #72339067

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1122244444416161616161616163232323232323232323232323232323232323264646464646464646464646464646464128128
order12222224444222244442224444448888888888444444444448888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1
χ3111111111111111111111-11-11-1-1111-1-111-1-1-1-11-1-11111-1-1-1-1-11111-1-1
χ4111111111111111111111-11-11-1-1111-1-111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-111
χ511111111111111111111-11-111-1-11-1-111-1-111-1-1-11-11111-1-1-1-1-1-1-1-1-111
χ611111111111111111111-11-111-1-11-1-111-1-111-1-1-11-1-1-1-1-11111-11111-1-1
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-11111111
χ9111111111111-1-1-11-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-11ii−i−iii−i−i1ii−i−ii−i
χ10111111111111-1-1-11-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-11−i−iii−i−iii1−i−iii−ii
χ11111111111111-1-1-11-1-1-111-11-1111-111-1-1-1-11111-11-1ii−i−i−i−iii-1ii−i−i−ii
χ12111111111111-1-1-11-1-1-111-11-1111-111-1-1-1-11111-11-1−i−iiiii−i−i-1−i−iiii−i
χ13111111111111-1-1-11-1-1-11-11-11111-1-1-11111-1-1111-1-1ii−i−i−i−iii-1−i−iiii−i
χ14111111111111-1-1-11-1-1-11-11-11111-1-1-11111-1-1111-1-1−i−iiiii−i−i-1ii−i−i−ii
χ15111111111111-1-1-11-1-1-11-1-1-1-11-1-1-1-1-1-1-11111-1-1111ii−i−iii−i−i1−i−iii−ii
χ16111111111111-1-1-11-1-1-11-1-1-1-11-1-1-1-1-1-1-11111-1-1111−i−iii−i−iii1ii−i−ii−i
χ1722222222222222222-2-2-20000-222-200000000-2-200200000000-2000000
χ1822222222222222222-2-2-20000-2-2-2-2000000002200-2000000002000000
χ19222222222222-2-2-22-222-20000-222200000000-2-200-2000000002000000
χ20222222222222-2-2-22-222-20000-2-2-22000000002200200000000-2000000
χ2122222222222-222-2-2-22220202-200-200-2-200-2-200020000000000000000
χ2222222222222-222-2-2-22220-20-2-200-200220022000-20000000000000000
χ2322222222222-222-2-2-2-2-2-220202002-2-200-2-20000200000000000000000
χ2422222222222-222-2-2-2-2-2-2-20-2020022200220000-200000000000000000
χ2522222222222-2-2-22-2222-22020200-2-2-200220000-200000000000000000
χ2622222222222-2-2-22-2222-2-20-20200-22200-2-20000200000000000000000
χ2722222222222-2-2-22-22-2-220202-200200-2-20022000-20000000000000000
χ2822222222222-2-2-22-22-2-220-20-2-2002002200-2-200020000000000000000
χ294444444-4-4-4-404-400000000000000000000000000000002i−2i2i−2i0000000
χ304444444-4-4-4-404-40000000000000000000000000000000−2i2i−2i2i0000000
χ314444444-4-4-4-40-4400000000000000000000000000000002-2-220000000
χ324444444-4-4-4-40-440000000000000000000000000000000-222-20000000
χ3344444-4-444-4-44000-40000000004i−4i00000000000000000000000000000
χ3444444-4-444-4-44000-4000000000−4i4i00000000000000000000000000000
χ3544444-4-444-4-4-40004000000000000000000004i−4i000000000000000000
χ3644444-4-444-4-4-4000400000000000000000000−4i4i000000000000000000
χ3744444-4-4-4-44400040-40000000000000000000000002-22-200000000000
χ3844444-4-4-4-44400040-4000000000000000000000000-22-2200000000000
χ3944444-4-4-4-444000-4040000000000000000000000002i−2i−2i2i00000000000
χ4044444-4-4-4-444000-404000000000000000000000000−2i2i2i−2i00000000000
χ41888-8-800008-8000000000000000000000004-400000000000000000000
χ42888-8-800008-800000000000000000000000-4400000000000000000000
χ43888-8-80000-88000000000000000004-400000000000000000000000000
χ44888-8-80000-8800000000000000000-4400000000000000000000000000
χ4588-88-8008-80000000000000000000004-4000000000000000000000000
χ4688-88-8008-8000000000000000000000-44000000000000000000000000
χ4788-88-800-880000000000040-4000000000000000000000000000000000
χ4888-88-800-8800000000000-404000000000000000000000000000000000
χ4988-8-888-800000000000000000000000004-40000000000000000000000
χ5088-8-888-80000000000000000000000000-440000000000000000000000
χ5188-8-88-880000000000000040-400000000000000000000000000000000
χ5288-8-88-8800000000000000-40400000000000000000000000000000000
χ5316-160000000000000004-400000000000000000000000000000002i−2i2i−2i00
χ5416-160000000000000004-40000000000000000000000000000000−2i2i−2i2i00
χ5516-16000000000000000-4400000000000000000000000000000002-2-2200
χ5616-16000000000000000-440000000000000000000000000000000-222-200

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