Finite Group Databasebeta

← Group #72241411

Character table — Group #72241411

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size112224444448888888888888888881616161616161616161616161616163232323232323232323232323232323232646464646464646464128128128128
order12222224444222222444444444444222224444448888222244444888888884444888884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-1-1-1111111111-1-1-1-1
χ411111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ5111111111111111-1-11111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-1ii−i−i-1ii−i−ii−ii−i
χ6111111111111111-1-11111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-1−i−iii-1−i−iii−ii−ii
χ7111111111111111-1-1111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1111-111-1-1-111-1-11111ii−i−i-1ii−i−i−ii−ii
χ8111111111111111-1-1111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1111-111-1-1-111-1-11111−i−iii-1−i−iiii−ii−i
χ911111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-11-11-1-11-1-11111-1-11111-1-1-1-1-111-1-1
χ1011111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-11-11-1-11-1-11111-1-1-1-1-1-1-11111-1-111
χ1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111-1-11111-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111
χ1211111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111-1-11111-1-11111111-1-1-1-1-1-111-1-1-1-1-1111111-1-1
χ1311111111111-1-1-1-1-1-111-1-1-1-11111-1-11-1-111111111-1-1-1-1-1-11-111-1-1-1-1-111-1-111ii−i−i1−i−iiii−i−ii
χ1411111111111-1-1-1-1-1-111-1-1-1-11111-1-11-1-111111111-1-1-1-1-1-11-111-1-1-1-1-111-1-111−i−iii1ii−i−i−iii−i
χ1511111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1111111-1-1-1111-1-1-1-1-111-1-1ii−i−i1−i−iii−iii−i
χ1611111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1111111-1-1-1111-1-1-1-1-111-1-1−i−iii1ii−i−ii−i−ii
χ1722222222222000022-2-200000000-2-2-22-20000-2-200222200-2-2-22-2-22000000220000000000000
χ1822222222222000022-2-200000000-2-2-22-20000-2-200-2-2-2-2002-222222000000-2-20000000000000
χ1922222222222000022-2-200002222-2-2-22-200002222000022020-200-200-2-2-2-2000000000000000
χ2022222222222000022-2-20000-2-2-2-2-2-2-22-2000022-2-20000-2-2020-200-2002222000000000000000
χ21222222222220000-2-2-2-20000000022-2-220000-2-2002222002222-2-2-2000000-2-20000000000000
χ22222222222220000-2-2-2-20000000022-2-220000-2-200-2-2-2-200-22-2222-2000000220000000000000
χ23222222222220000-2-2-2-20000222222-2-22000022220000-2-20-20-200200-2-222000000000000000
χ24222222222220000-2-2-2-20000-2-2-2-222-2-22000022-2-20000220-20-20020022-2-2000000000000000
χ25222222222222222222222220000222222222-2-2000000000-20-200-2-2-20000000000-200000000
χ26222222222222222-2-22222220000-2-22-2-2-2-2-2-2-2-200000000020-2002-2-20000000000200000000
χ2722222222222-2-2-2-22222-2-2-2-2000022222-2-2-2-2-2-2000000000-20-200-2220000000000200000000
χ2822222222222-2-2-2-2-2-222-2-2-2-20000-2-22-2-22222-2-200000000020-2002220000000000-200000000
χ294444444-4-4-4-40000440000000000000-40000000000000000000000000000002-22-2000000000
χ304444444-4-4-4-40000440000000000000-4000000000000000000000000000000-22-22000000000
χ314444444-4-4-4-40000-4-4000000000000040000000000000000000000000000002i−2i−2i2i000000000
χ324444444-4-4-4-40000-4-400000000000004000000000000000000000000000000−2i2i2i−2i000000000
χ3344444-4-44-44-400000000000000004400-400000000000000000000000000000000002-22-20000
χ3444444-4-44-44-400000000000000004400-40000000000000000000000000000000000-22-220000
χ3544444-4-44-44-40000000000000000-4-400400000000000000000000000000000000002i−2i−2i2i0000
χ3644444-4-44-44-40000000000000000-4-40040000000000000000000000000000000000−2i2i2i−2i0000
χ3744444-4-4-44-44000000-4-400000000004000000000000000000000004-40000000000000000000
χ3844444-4-4-44-44000000-4-40000000000400000000000000000000000-440000000000000000000
χ3944444-4-4-44-4444-4-4004444-4-4000000-400000000000000000000000000000000000000000000
χ4044444-4-4-44-44-4-4440044-4-444000000-400000000000000000000000000000000000000000000
χ41444-4-4000-404004-4004-4004-422-2-2000000000002-222-2-20000002-20002-200000000000000000
χ42444-4-4000-404004-4004-4004-4-2-22200000000000-22-2-222000000-22000-2200000000000000000
χ43444-4-4000-40400-44004-400-4422-2-2000000000002-2-2-222000000-220002-200000000000000000
χ44444-4-4000-40400-44004-400-44-2-22200000000000-2222-2-20000002-2000-2200000000000000000
χ45444-4-4000-4044-40000-444-40022-2-2000000000002-222-2-2000000-22000-2200000000000000000
χ46444-4-4000-4044-40000-444-400-2-22200000000000-22-2-2220000002-20002-200000000000000000
χ47444-4-4000-404-440000-44-440022-2-2000000000002-2-2-2220000002-2000-2200000000000000000
χ48444-4-4000-404-440000-44-4400-2-22200000000000-2222-2-2000000-220002-200000000000000000
χ4944-44-400-404022-2-20000-2-22222224-400022-2-200-2-22-22-20020-2000000002-2000000000000000
χ5044-44-400-404022-2-20000-2-2222222-44000-2-22200-2-22-22-200-20200000000-22000000000000000
χ5144-44-400-404022-2-20000-2-222-2-2-2-24-400022-2-20022-22-2200-20200000000-22000000000000000
χ5244-44-400-404022-2-20000-2-222-2-2-2-2-44000-2-2220022-22-220020-2000000002-2000000000000000
χ5344-44-400-4040-2-222000022-2-222224-4000-2-22200-2-2-22-2200-202000000002-2000000000000000
χ5444-44-400-4040-2-222000022-2-22222-4400022-2-200-2-2-22-220020-200000000-22000000000000000
χ5544-44-400-4040-2-222000022-2-2-2-2-2-24-4000-2-22200222-22-20020-200000000-22000000000000000
χ5644-44-400-4040-2-222000022-2-2-2-2-2-2-4400022-2-200222-22-200-202000000002-2000000000000000
χ5744-4-44-4400002-2-224-400-222-222-2-2000002-22-200-222-2-222-200000000000002-20000000000000
χ5844-4-44-4400002-2-224-400-222-2-2-222000002-22-2002-2-222-2-220000000000000-220000000000000
χ5944-4-44-4400002-2-22-4400-222-222-2-200000-22-2200-222-2-22-220000000000000-220000000000000
χ6044-4-44-4400002-2-22-4400-222-2-2-22200000-22-22002-2-222-22-200000000000002-20000000000000
χ6144-4-44-440000-222-24-4002-2-2222-2-200000-22-2200-22-222-22-20000000000000-220000000000000
χ6244-4-44-440000-222-24-4002-2-22-2-22200000-22-22002-22-2-22-2200000000000002-20000000000000
χ6344-4-44-440000-222-2-44002-2-2222-2-2000002-22-200-22-222-2-2200000000000002-20000000000000
χ6444-4-44-440000-222-2-44002-2-22-2-222000002-22-2002-22-2-222-20000000000000-220000000000000
χ65888-8-800080-80000000000000000000004-4-4400000000000000000000000000000000000000
χ66888-8-800080-8000000000000000000000-444-400000000000000000000000000000000000000
χ6788-88-80080-8044440000-4-4-4-4000000000000000000000000000000000000000000000000000
χ6888-88-80080-80-4-4-4-400004444000000000000000000000000000000000000000000000000000
χ6988-8-888-800004-44-40000-44-44000000000000000000000000000000000000000000000000000
χ7088-8-888-80000-44-4400004-44-4000000000000000000000000000000000000000000000000000
χ7116-16000000000000000000000008-80000000004-4000000000000000000000000000000000000
χ7216-1600000000000000000000000-880000000004-4000000000000000000000000000000000000
χ7316-160000000000000000000008-800000000000-44000000000000000000000000000000000000
χ7416-16000000000000000000000-8800000000000-44000000000000000000000000000000000000

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