Finite Group Databasebeta

← Group #72251765

Character table — Group #72251765

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1122244444444888161616161616161616161616161616163232323232323232323232323232323232323232323232323232646464646464128128128128
order12222222244442222222224444444444224444444444444488888888884444484888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-11111111-1-111-1-11111-1-1-1-1-1-1-11111-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-111-1
χ41111111111111111111111111-1-1-1-11111-1-1111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11
χ5111111111111111111-1-1111-1-11111111-1111-1-1-11-1-111111111111111111-1-1-1-11-1-1-1-1
χ6111111111111111111-1-1111-1-11111111-1-1-11-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1111-1-1-1-1-1-1111-1111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-11-1-11
χ8111111111111111111-1-1111-1-1-1-1-1-1111-1-1-11-1-1-11-1-111-1-111-1-1-1-1-1-1-1-111-111111-111-1
χ911111-1-1111111-1-1-11-11111-1-1-11111111-111-111-1-11-1-1-1-1-11111-1-111-1-1-1-1-111-1-11-11-11
χ1011111-1-1111111-1-1-11-11111-1-1-11111111-1-1-1-111-1-11-111-1-1-1-111-1-1-1-11111111-1-1-11-11-1
χ1111111-1-1111111-1-1-11-11111-1-1-1-1-1-1-1111-111-111-1-11-11111-1-1-1-11111-1-111-1-1-111-111-1-1
χ1211111-1-1111111-1-1-11-11111-1-1-1-1-1-1-1111-1-1-1-111-1-11-1-1-11111-1-111-1-111-1-11-1-1111-1-111
χ1311111-1-1111111-1-1-11-1-1-111-1111111111111-1-1-11-1-11-1-1-1-11111-1-111-1-1-1-1-1-1-11111-11-1
χ1411111-1-1111111-1-1-11-1-1-111-11111111111-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-111111-1-111-1-11-11
χ1511111-1-1111111-1-1-11-1-1-111-111-1-1-1-1111111-1-1-11-1-111111-1-1-1-11111-1-111-111-1-1-1-1-111
χ1611111-1-1111111-1-1-11-1-1-111-111-1-1-1-11111-1-1-1-1-11-1-11-1-11111-1-111-1-111-1-1111-1-1111-1-1
χ172222200-2-222-2-20002000-2-20222i2i−2i−2i22-2-200000-20020000002i−2i000000000002i−2i00000
χ182222200-2-222-2-20002000-2-2022−2i−2i2i2i22-2-200000-2002000000−2i2i00000000000−2i2i00000
χ192222200-2-222-2-20002000-2-20-2-22i2i−2i−2i22-2200000200-20000002i−2i00000000000−2i2i00000
χ202222200-2-222-2-20002000-2-20-2-2−2i−2i2i2i22-2200000200-2000000−2i2i000000000002i−2i00000
χ212222200-2-222-2-200020222-20002i2i−2i−2i-2-2200002-200-20000000−2i2i0000000002i−2i0000000
χ222222200-2-222-2-200020222-2000−2i−2i2i2i-2-2200002-200-200000002i−2i000000000−2i2i0000000
χ232222200-2-222-2-200020-2-22-20002i2i−2i−2i-2-220000-220020000000−2i2i000000000−2i2i0000000
χ242222200-2-222-2-200020-2-22-2000−2i−2i2i2i-2-220000-2200200000002i−2i0000000002i−2i0000000
χ2522222222222222222200-222002222-2-2-2000-2000-200002200-2-2-2-20000000000000000
χ2622222222222222222200-22200-2-2-2-2-2-2-2000-2000-20000-2-20022220000000000000000
χ2722222222222222-2-2-2-2002-220000002-2-20002000-20022002200000000-2-200000-20000
χ2822222222222222-2-2-2-2002-220000002-2-20002000-200-2-200-2-200000000220000020000
χ2922222222222222-2-2-2-200-2-22000000-222022-20002000000000000-2-2-2-2002000000000
χ3022222222222222-2-2-2-200-2-22000000-2220-2-2-20002000000000000222200-2000000000
χ3122222-2-2222222-222-22002-2-20000002-2-2000-20002002200-2-200000000-2-20000020000
χ3222222-2-2222222-222-22002-2-20000002-2-2000-2000200-2-20022000000002200000-20000
χ3322222-2-2222222-222-2200-2-2-2000000-2220222000-2000000000000-2-22200-2000000000
χ3422222-2-2222222-222-2200-2-2-2000000-2220-2-22000-200000000000022-2-2002000000000
χ3522222-2-2222222-2-2-22-200-22-2002222-2-2-2000200020000-2-200-2-2220000000000000000
χ3622222-2-2222222-2-2-22-200-22-200-2-2-2-2-2-2-2000200020000220022-2-20000000000000000
χ374444400-4-444-4-4000-4000440000000-44-4000000000000000000000000000000000000
χ384444400-4-444-4-4000-4000-4400000004-44000000000000000000000000000000000000
χ394444400-4-4-4-4440440-422000-2-200000002000-2-2-202200000000000000000000000000
χ404444400-4-4-4-4440440-4-2-2000220000000-20002220-2-200000000000000000000000000
χ414444400-4-4-4-4440-4-40422000220000000-2000-2-2202-200000000000000000000000000
χ424444400-4-4-4-4440-4-404-2-2000-2-20000000200022-20-2200000000000000000000000000
χ43444444444-4-4-4-4400002200-42200000002000-22-20-2-200000000000000000000000000
χ44444444444-4-4-4-440000-2-200-4-2-20000000-20002-2202200000000000000000000000000
χ4544444-4-444-4-4-4-4-4000022004-2-20000000-2000-2220-2200000000000000000000000000
χ4644444-4-444-4-4-4-4-40000-2-200422000000020002-2-202-200000000000000000000000000
χ47444-4-4444-40000-4000000000002i−2i2i−2i00000000000002i−2i2i−2i2i−2i00002-22-2000000000000
χ48444-4-4444-40000-4000000000002i−2i2i−2i0000000000000−2i2i2i−2i−2i2i0000-22-22000000000000
χ49444-4-4444-40000-400000000000−2i2i−2i2i00000000000002i−2i−2i2i2i−2i0000-22-22000000000000
χ50444-4-4444-40000-400000000000−2i2i−2i2i0000000000000−2i2i−2i2i−2i2i00002-22-2000000000000
χ51444-4-4-4-44-400004000000000002i−2i2i−2i00000000000002i−2i−2i2i−2i2i0000-222-2000000000000
χ52444-4-4-4-44-400004000000000002i−2i2i−2i0000000000000−2i2i−2i2i2i−2i00002-2-22000000000000
χ53444-4-4-4-44-40000400000000000−2i2i−2i2i00000000000002i−2i2i−2i−2i2i00002-2-22000000000000
χ54444-4-4-4-44-40000400000000000−2i2i−2i2i0000000000000−2i2i2i−2i2i−2i0000-222-2000000000000
χ55888-8-800-8800000000000000004-4-44000000000000000000000000000000000000000
χ56888-8-800-880000000000000000-444-4000000000000000000000000000000000000000
χ5788-88-800008-80000000000000000000000000000000000000000000004i−4i0000000000
χ5888-88-800008-8000000000000000000000000000000000000000000000−4i4i0000000000
χ5988-88-80000-8800000000000000000000004-4000000000000000000000000000000000
χ6088-88-80000-880000000000000000000000-44000000000000000000000000000000000
χ6188-8-880000008-800000000000000000000000000000000000004-40000000000000000
χ6288-8-880000008-80000000000000000000000000000000000000-440000000000000000
χ6388-8-88000000-8808-80000000000000000000000000000000000000000000000000000
χ6488-8-88000000-880-880000000000000000000000000000000000000000000000000000
χ6516-160008-8000000000004-40004-40000000000000000000000000000000000000000000
χ6616-160008-800000000000-44000-440000000000000000000000000000000000000000000
χ6716-16000-88000000000004-4000-440000000000000000000000000000000000000000000
χ6816-16000-8800000000000-440004-40000000000000000000000000000000000000000000

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