Finite Group Databasebeta

← Group #72219505

Character table — Group #72219505

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112224444448888888816161616161616161616161616161616161616163232323232323232323232323232323232323264646464128128128128128128
order12222224444222244442222224444448888888822244444444444488888888448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-11111-1-1-1-11-1-11-111-1-1-1-1-1-1-1-111-1-1ii−i−ii−iii−i−i
χ611111111111111111111111111111-1-11111-1-1-1-11-1-11-111-1-1-1-1-1-1-1-111-1-1−i−iii−ii−i−iii
χ711111111111111111111111111111-1-1-1-1-1-11111-11-1-11-1-111-1-1-1-1-1-1-1-111ii−i−ii−i−i−iii
χ811111111111111111111111111111-1-1-1-1-1-11111-11-1-11-1-111-1-1-1-1-1-1-1-111−i−iii−iiii−i−i
χ9111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-11-1-111-1-1-1-11111-1-11111-1-11-11-1
χ10111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-11-1-111-1-1-1-11111-1-1-1-1-1-111-11-11
χ11111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-111-111-1-1-1-1-1-111-1-1111111-1-1-11-11
χ12111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-111-111-1-1-1-1-1-111-1-111-1-1-1-1111-11-1
χ13111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-11111ii−i−i−iii−i−ii
χ14111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-11111−i−iiii−i−iii−i
χ15111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1-1-1-1-1ii−i−i−ii−iii−i
χ16111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1-1-1-1-1−i−iiii−ii−i−ii
χ172222222222222-2-222-2-2-2-2000000002200002222-20-2-20220000002-200-2-20000000000
χ182222222222222-2-222-2-2-2-200000000220000-2-2-2-220-220-2-20000002-200220000000000
χ192222222222222-2-222-2-2-2-200000000-2-20000222220220-2-2000000-2200-2-20000000000
χ202222222222222-2-222-2-2-2-200000000-2-20000-2-2-2-2-202-2022000000-2200220000000000
χ2122222222222-2-222-2-222-2-20000000022222200000-2-20-200220000-22-2-2000000000000
χ2222222222222-2-222-2-222-2-20000000022-2-2-2-2000002-20200-2-20000-2222000000000000
χ2322222222222-2-222-2-222-2-200000000-2-2222200000220200-2-200002-2-2-2000000000000
χ2422222222222-2-222-2-222-2-200000000-2-2-2-2-2-200000-220-2002200002-222000000000000
χ2522222222222-2-2-2-2-2-2-2-22222-2-222-2-2220000000000200000022-2-2-2-200000000000000
χ2622222222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-20000000000-2000000-2-2222200000000000000
χ2722222222222-2-2-2-2-2-2-2-222-2-222-2-2222200000000002000000-2-222-2-200000000000000
χ2822222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-20000000000-200000022-2-22200000000000000
χ294444444-4-4-4-4000000004-4000000000000000000000000000004-40000000000000000
χ304444444-4-4-4-4000000004-400000000000000000000000000000-440000000000000000
χ314444444-4-4-4-400000000-440000000000000000000000000004-4000000000000000000
χ324444444-4-4-4-400000000-44000000000000000000000000000-44000000000000000000
χ3344444-4-44-44-4004400-4-400000000000044-4-4000000000000000000000000000000000
χ3444444-4-44-44-4004400-4-4000000000000-4-444000000000000000000000000000000000
χ3544444-4-44-44-400-4-40044000000000000000000000000000000000004-4000000000000
χ3644444-4-44-44-400-4-4004400000000000000000000000000000000000-44000000000000
χ3744444-4-4-44-444400-4-400000000000000000044-4-400000000000000000000000000000
χ3844444-4-4-44-444400-4-4000000000000000000-4-44400000000000000000000000000000
χ3944444-4-4-44-44-4-400440000000000000000000000000000000000000004-40000000000
χ4044444-4-4-44-44-4-40044000000000000000000000000000000000000000-440000000000
χ4144-44-4000-4044-4000000002-22-22-22-2000000004-40200-2002-200000000000000000000
χ4244-44-4000-4044-4000000002-22-22-22-200000000-440-200200-2200000000000000000000
χ4344-44-4000-4044-400000000-22-22-22-22000000004-40-200200-2200000000000000000000
χ4444-44-4000-4044-400000000-22-22-22-2200000000-440200-2002-200000000000000000000
χ4544-44-4000-404-44000000002-2-222-2-220000004-4000200-200-2200000000000000000000
χ4644-44-4000-404-44000000002-2-222-2-22000000-44000-2002002-200000000000000000000
χ4744-44-4000-404-4400000000-222-2-222-20000004-4000-2002002-200000000000000000000
χ4844-44-4000-404-4400000000-222-2-222-2000000-44000200-200-2200000000000000000000
χ4944-4-4400-4040004-40000002-22-2-22-2200004-40000200-202-20000000000000000000000
χ5044-4-4400-4040004-40000002-22-2-22-220000-440000-20020-220000000000000000000000
χ5144-4-4400-4040004-4000000-22-222-22-200004-40000-20020-220000000000000000000000
χ5244-4-4400-4040004-4000000-22-222-22-20000-440000200-202-20000000000000000000000
χ5344-4-4400-404000-440000002-2-22-222-2004-4000000200-20-220000000000000000000000
χ5444-4-4400-404000-440000002-2-22-222-200-44000000-200202-20000000000000000000000
χ5544-4-4400-404000-44000000-222-22-2-22004-4000000-200202-20000000000000000000000
χ5644-4-4400-404000-44000000-222-22-2-2200-44000000200-20-220000000000000000000000
χ57888-8-88-800000000000000004400-4-4000000000000000000000000000000000000000
χ58888-8-88-80000000000000000-4-40044000000000000000000000000000000000000000
χ59888-8-8-88000000000000004400-4-400000000000000000000000000000000000000000
χ60888-8-8-8800000000000000-4-4004400000000000000000000000000000000000000000
χ6188-88-800080-800008-8000000000000000000000000000000000000000000000000000
χ6288-88-800080-80000-88000000000000000000000000000000000000000000000000000
χ6388-8-880080-800000008-80000000000000000000000000000000000000000000000000
χ6488-8-880080-80000000-880000000000000000000000000000000000000000000000000
χ6516-160000000000000000000000000004-40000000000000000000000000002i−2i2i−2i000000
χ6616-160000000000000000000000000004-4000000000000000000000000000−2i2i−2i2i000000
χ6716-16000000000000000000000000000-440000000000000000000000000002-2-22000000
χ6816-16000000000000000000000000000-44000000000000000000000000000-222-2000000

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