Finite Group Databasebeta

← Group #72339099

Character table — Group #72339099

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1122244444488888888161616161616161616161616161616161616161632323232323232323232323232323264646464646464646464128128128128
order12222224444444444442222224444448888888824444444488888824444888884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-111111-1-1-1-1-111-1-1
χ41111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-11-1-1-1-1-11111-1-111
χ511111111111111111-1-11-1-111-111111111111111-11-1-1-1-111-1-1-111-1-1-1ii−i−i-1ii−i−ii−ii−i
χ611111111111111111-1-11-1-111-111111111111111-11-1-1-1-111-1-1-111-1-1-1−i−iii-1−i−iii−ii−ii
χ711111111111111111-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1ii−i−i1−i−iiii−i−ii
χ811111111111111111-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1−i−iii1ii−i−i−iii−i
χ91111111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-111-11111-11111-1-1-1-1
χ101111111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ111111111111111-1-1-1-111111-1-11-1-111-1-11111-1-1-1-111-1-111111-1-1-1-1-1-1-111111-1-1-1-1-1-111
χ121111111111111-1-1-1-111111-1-11-1-111-1-11111-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1
χ131111111111111-1-1-1-1-1-11-1-111-11111-1-1-1-1-1-11111-11-1-111-1-1-111-1-1-1-11ii−i−i1ii−i−i−ii−ii
χ141111111111111-1-1-1-1-1-11-1-111-11111-1-1-1-1-1-11111-11-1-111-1-1-111-1-1-1-11−i−iii1−i−iiii−ii−i
χ151111111111111-1-1-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111-1-111-111-1-1111ii−i−i-1−i−iii−iii−i
χ161111111111111-1-1-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111-1-111-111-1-1111−i−iii-1ii−i−ii−i−ii
χ17222222222222200002222222222-2-2000000-2-2-2-2-2-2220000-20000-2-200000000000000
χ182222222222222000022222-2-22-2-2-2-20000002222-2-2-2-20000-200002200000000000000
χ1922222222222220000-2-22-2-222-222-2-2000000-2-2-2-22-2-2-20000200002200000000000000
χ2022222222222220000-2-22-2-2-2-2-2-2-2-2-200000022222-222000020000-2-200000000000000
χ2122222222222-2-2000022-22-200-200-2-20022220000220022-2-2-200000000000-200000000
χ2222222222222-2-2000022-22-200-200-2-200-2-2-2-200002200-2-222-200000000000200000000
χ2322222222222-2-20000-2-2-2-2200200-2-20022220000-2200-2-2-2-2200000000000200000000
χ2422222222222-2-20000-2-2-2-2200200-2-200-2-2-2-20000-22002222200000000000-200000000
χ2522222222222-2-2222222-22-200-200222200000000-2-2000000222-2-200-20000000000000
χ2622222222222-2-22222-2-2-2-22002002222000000002-2000000-2-2-2-2-20020000000000000
χ2722222222222-2-2-2-2-2-222-22-200-20022-2-200000000-2-20000002-2-2220020000000000000
χ2822222222222-2-2-2-2-2-2-2-2-2-220020022-2-2000000002-2000000-2222200-20000000000000
χ294444444-4-4-4-40000000000400-40000000000000000000000000000002i−2i2i−2i000000000
χ304444444-4-4-4-40000000000400-4000000000000000000000000000000−2i2i−2i2i000000000
χ314444444-4-4-4-40000000000-40040000000000000000000000000000002-2-22000000000
χ324444444-4-4-4-40000000000-4004000000000000000000000000000000-222-2000000000
χ3344444-4-44-44-4000000440-40000000000000000000000000000000000000002-22-20000
χ3444444-4-44-44-4000000440-4000000000000000000000000000000000000000-22-220000
χ3544444-4-44-44-4000000-4-4040000000000000000000000000000000000000002i−2i−2i2i0000
χ3644444-4-44-44-4000000-4-404000000000000000000000000000000000000000−2i2i2i−2i0000
χ3744444-4-4-44-4444000000-400000000000000044-4-400000000000000000000000000000
χ3844444-4-4-44-4444000000-4000000000000000-4-44400000000000000000000000000000
χ3944444-4-4-44-44-4-40000004004-404-400000000000000000000000000000000000000000
χ4044444-4-4-44-44-4-4000000400-440-4400000000000000000000000000000000000000000
χ41444-4-400040-44-422-2-20000000000002-22i2i−2i−2i004i−4i0000002i−2i0002-20000000000000000
χ42444-4-400040-44-422-2-20000000000002-2−2i−2i2i2i00−4i4i000000−2i2i0002-20000000000000000
χ43444-4-400040-44-4-2-222000000000000-222i2i−2i−2i00−4i4i0000002i−2i000-220000000000000000
χ44444-4-400040-44-4-2-222000000000000-22−2i−2i2i2i004i−4i000000−2i2i000-220000000000000000
χ45444-4-400040-4-4422-2-20000000000002-22i2i−2i−2i4i−4i00000000−2i2i000-220000000000000000
χ46444-4-400040-4-4422-2-20000000000002-2−2i−2i2i2i−4i4i000000002i−2i000-220000000000000000
χ47444-4-400040-4-44-2-222000000000000-222i2i−2i−2i−4i4i00000000−2i2i0002-20000000000000000
χ48444-4-400040-4-44-2-222000000000000-22−2i−2i2i2i4i−4i000000002i−2i0002-20000000000000000
χ4944-4-4400-40400022224-40002-20-2200-2-22-22-20000002-22-20002-2000000000000000000
χ5044-4-4400-40400022224-4000-2202-200-2-2-22-22000000-22-220002-2000000000000000000
χ5144-4-4400-4040002222-440002-20-2200-2-22-22-2000000-22-22000-22000000000000000000
χ5244-4-4400-4040002222-44000-2202-200-2-2-22-220000002-22-2000-22000000000000000000
χ5344-4-4400-404000-2-2-2-24-40002-20-220022-22-220000002-2-22000-22000000000000000000
χ5444-4-4400-404000-2-2-2-24-4000-2202-200222-22-2000000-222-2000-22000000000000000000
χ5544-4-4400-404000-2-2-2-2-440002-20-220022-22-22000000-222-20002-2000000000000000000
χ5644-4-4400-404000-2-2-2-2-44000-2202-200222-22-20000002-2-220002-2000000000000000000
χ57888-8-8000-808000000000000000000000000000000000000000004-400000000000000
χ58888-8-8000-80800000000000000000000000000000000000000000-4400000000000000
χ5988-88-88-80000000000000000000000004i−4i−4i4i000000000000000000000000000000000
χ6088-88-88-8000000000000000000000000−4i4i4i−4i000000000000000000000000000000000
χ6188-88-8-8800000044-4-4000000000000-440000000000000000000000000000000000000
χ6288-88-8-88000000-4-4440000000000004-40000000000000000000000000000000000000
χ6388-8-880080-8000000000000440-4-400000000000000000000000000000000000000000
χ6488-8-880080-8000000000000-4-404400000000000000000000000000000000000000000
χ6516-1600000000000008-800000000004-4000000000000000000000000000000000000000
χ6616-160000000000000-8800000000004-4000000000000000000000000000000000000000
χ6716-16000000000008-8000000000000-44000000000000000000000000000000000000000
χ6816-1600000000000-88000000000000-44000000000000000000000000000000000000000

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