Finite Group Databasebeta

← Group #72339069

Character table — Group #72339069

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1122244444488888888161616161616161616161616161616161616161632323232323232323232323232323264646464646464646464128128128128
order12222224444222244442222444444448888888824444444488888824444444484488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ311111111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1-111
χ411111111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-11-1-1-1-11111-111-1-1
χ5111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-111-111111111-1-1-1-1-1
χ6111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111-1-1-1-11-1-1111-1-111-1-11111-1-1-1-111-1-111111-1-1-1-1-1-1-11111-1-1-1-1111-1-1
χ8111111111111111-1-1-1-11-1-1111-1-111-1-11111-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-111111-1-111
χ91111111111111-1-11111-111-11-111111111111111-11-1-1-1-111-1-1-111-1-1-1ii−i−iii−i−i-1i−ii−i
χ101111111111111-1-11111-111-11-111111111111111-11-1-1-1-111-1-1-111-1-1-1−i−iii−i−iii-1−ii−ii
χ111111111111111-1-11111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1ii−i−i−i−iii1−iii−i
χ121111111111111-1-11111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1−i−iiiii−i−i1i−i−ii
χ131111111111111-1-1-1-1-1-1-111-11-11111-1-1-1-1-1-11111-11-1-111-1-1-111-1-1-1-11ii−i−iii−i−i1−ii−ii
χ141111111111111-1-1-1-1-1-1-111-11-11111-1-1-1-1-1-11111-11-1-111-1-1-111-1-1-1-11−i−iii−i−iii1i−ii−i
χ151111111111111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-1-1-1-1111-1-111-111-1-1111ii−i−i−i−iii-1i−i−ii
χ161111111111111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-1-1-1-1111-1-111-111-1-1111−i−iiiii−i−i-1−iii−i
χ17222222222222222000022222222-2-2000000-2-2-2-2-2-2220000-20000-2-200000000000000
χ1822222222222222200002-2-2222-2-2-2-20000002222-2-2-2-20000-200002200000000000000
χ192222222222222-2-20000-222-22-222-2-2000000-2-2-2-22-2-2-20000200002200000000000000
χ202222222222222-2-20000-2-2-2-22-2-2-2-2-200000022222-222000020000-2-200000000000000
χ2122222222222-2-2220000-200-2-2200-2-20022220000220022-2-2-2000000000000000-20000
χ2222222222222-2-2220000-200-2-2200-2-200-2-2-2-200002200-2-222-200000000000000020000
χ2322222222222-2-2222222-200-2-2200222200000000-2-2000000222-2-200-20000000000000
χ2422222222222-2-222-2-2-2-2-200-2-220022-2-200000000-2-20000002-2-2220020000000000000
χ2522222222222-2-2-2-200002002-2-200-2-20022220000-2200-2-2-2-2200000000000000020000
χ2622222222222-2-2-2-200002002-2-200-2-200-2-2-2-20000-220022222000000000000000-20000
χ2722222222222-2-2-2-222222002-2-2002222000000002-2000000-2-2-2-2-20020000000000000
χ2822222222222-2-2-2-2-2-2-2-22002-2-20022-2-2000000002-2000000-2222200-20000000000000
χ294444444-4-4-4-400000000400-40000000000000000000000000000000000002i−2i2i−2i00000
χ304444444-4-4-4-400000000400-4000000000000000000000000000000000000−2i2i−2i2i00000
χ314444444-4-4-4-400000000-40040000000000000000000000000000000000002-2-2200000
χ324444444-4-4-4-400000000-4004000000000000000000000000000000000000-222-200000
χ3344444-4-44-44-40044000000000-40000000000000000000000000000002-22-2000000000
χ3444444-4-44-44-40044000000000-4000000000000000000000000000000-22-22000000000
χ3544444-4-44-44-400-4-400000000040000000000000000000000000000002i−2i−2i2i000000000
χ3644444-4-44-44-400-4-40000000004000000000000000000000000000000−2i2i2i−2i000000000
χ3744444-4-4-44-44440000000000-40000000000044-4-400000000000000000000000000000
χ3844444-4-4-44-44440000000000-400000000000-4-44400000000000000000000000000000
χ3944444-4-4-44-44-4-400000004-40404-400000000000000000000000000000000000000000
χ4044444-4-4-44-44-4-40000000-44040-4400000000000000000000000000000000000000000
χ41444-4-400040-44-40022-2-200000000002-22i2i−2i−2i004i−4i0000002i−2i0002-20000000000000000
χ42444-4-400040-44-40022-2-200000000002-2−2i−2i2i2i00−4i4i000000−2i2i0002-20000000000000000
χ43444-4-400040-44-400-2-2220000000000-222i2i−2i−2i00−4i4i0000002i−2i000-220000000000000000
χ44444-4-400040-44-400-2-2220000000000-22−2i−2i2i2i004i−4i000000−2i2i000-220000000000000000
χ45444-4-400040-4-440022-2-200000000002-22i2i−2i−2i4i−4i00000000−2i2i000-220000000000000000
χ46444-4-400040-4-440022-2-200000000002-2−2i−2i2i2i−4i4i000000002i−2i000-220000000000000000
χ47444-4-400040-4-4400-2-2220000000000-222i2i−2i−2i−4i4i00000000−2i2i0002-20000000000000000
χ48444-4-400040-4-4400-2-2220000000000-22−2i−2i2i2i4i−4i000000002i−2i0002-20000000000000000
χ4944-4-4400-4040004-4222202-2000-2200-2-22-22-20000002-22-20002-2000000000000000000
χ5044-4-4400-4040004-422220-220002-200-2-2-22-22000000-22-220002-2000000000000000000
χ5144-4-4400-4040004-4-2-2-2-202-2000-220022-22-220000002-2-22000-22000000000000000000
χ5244-4-4400-4040004-4-2-2-2-20-220002-200222-22-2000000-222-2000-22000000000000000000
χ5344-4-4400-404000-44222202-2000-2200-2-22-22-2000000-22-22000-22000000000000000000
χ5444-4-4400-404000-4422220-220002-200-2-2-22-220000002-22-2000-22000000000000000000
χ5544-4-4400-404000-44-2-2-2-202-2000-220022-22-22000000-222-20002-2000000000000000000
χ5644-4-4400-404000-44-2-2-2-20-220002-200222-22-20000002-2-220002-2000000000000000000
χ57888-8-8000-808000000000000000000000000000000000000000004-400000000000000
χ58888-8-8000-80800000000000000000000000000000000000000000-4400000000000000
χ5988-88-88-80000000000000000000000004i−4i−4i4i000000000000000000000000000000000
χ6088-88-88-8000000000000000000000000−4i4i4i−4i000000000000000000000000000000000
χ6188-88-8-880000000044-4-40000000000-440000000000000000000000000000000000000
χ6288-88-8-8800000000-4-44400000000004-40000000000000000000000000000000000000
χ6388-8-880080-8000000000044000-4-400000000000000000000000000000000000000000
χ6488-8-880080-80000000000-4-40004400000000000000000000000000000000000000000
χ6516-160000000000000008-8000000004-4000000000000000000000000000000000000000
χ6616-16000000000000000-88000000004-4000000000000000000000000000000000000000
χ6716-1600000000000008-80000000000-44000000000000000000000000000000000000000
χ6816-160000000000000-880000000000-44000000000000000000000000000000000000000

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