Finite Group Databasebeta

← Group #72251764

Character table — Group #72251764

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122244444444888161616161616161616161616161616161616161616161616161616163232323232323232323232323232323232323232646464646464128128128128
order12222222244442222222222244444444444488888888244444444444448888884444484888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1
χ311111111111111111111-1-111111-1-1111111111111111-111-1-1-1-1-11111111111111-1-1-1-11-1-1-1-1
χ411111111111111111111-1-111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-111-1-1-1-1-111111-1-111
χ5111111111111111111-1-111111-1-1111111111-1-1-1-1111111111111-1-111-1-1-1-111-1-1-11111-1-1-1-1-1
χ6111111111111111111-1-111111-1-111-1-1-1-11111111-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-111
χ7111111111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-11111-111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-1
χ911111-1-1111111-1-1-11-1111111-111-1-11111111-1-1-1-11111-1-1-111-11-1-1-1-1-111-1-1-1-111-111-1-111-11-1
χ1011111-1-1111111-1-1-11-1111111-111-1-1-1-1-1-11111111-1-1-1-1-1-1-111-11-1-1-111-1-1-1-111-1-11-1-11111-1-11
χ1111111-1-1111111-1-1-11-111-1-111-111111111111-1-1-1-111111-1-1-1-11-11-1-1-1-111-1-1-1-111-1-1-1111-11-11
χ1211111-1-1111111-1-1-11-111-1-111-11111-1-1-1-11111111-1-1-1-11-1-1-1-11-11-1-111-1-1-1-111-1-1111-1-11-111-1
χ1311111-1-1111111-1-1-11-1-1-11111-1-1-1-1-1111111111111111-1-1-111-11-111-1-1-1-111-1-1-1-1111-1-1-1-11-11
χ1411111-1-1111111-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-111-11-1111111111111-1-1-111-1-111-1
χ1511111-1-1111111-1-1-11-1-1-1-1-111-1-1-1111111111111111111-1-1-1-11-1111-1-1-1-111-1-1-1-11-1-111-11-11-1
χ1611111-1-1111111-1-1-11-1-1-1-1-111-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-11-11111111111111-111-1-1-11-1-11
χ172222200-2-222-2-2000200000-2-2000222i2i−2i−2i22-200002i2i−2i−2i-2000020-20000000000000002i−2i00000
χ182222200-2-222-2-2000200000-2-200022−2i−2i2i2i22-20000−2i−2i2i2i-2000020-2000000000000000−2i2i00000
χ192222200-2-222-2-2000200000-2-2000-2-22i2i−2i−2i22-200002i2i−2i−2i20000-202000000000000000−2i2i00000
χ202222200-2-222-2-2000200000-2-2000-2-2−2i−2i2i2i22-20000−2i−2i2i2i20000-2020000000000000002i−2i00000
χ212222200-2-222-2-20002000222-2000002i2i−2i−2i-2-220000−2i−2i2i2i000-2-202000000000000002i−2i0000000
χ222222200-2-222-2-20002000222-200000−2i−2i2i2i-2-2200002i2i−2i−2i000-2-20200000000000000−2i2i0000000
χ232222200-2-222-2-20002000-2-22-2000002i2i−2i−2i-2-220000−2i−2i2i2i000220-200000000000000−2i2i0000000
χ242222200-2-222-2-20002000-2-22-200000−2i−2i2i2i-2-2200002i2i−2i−2i000220-2000000000000002i−2i0000000
χ252222222222222222220000-22200002222-2-2-20000-2-2-2-20-2-20000000220000-2-2000000000000
χ262222222222222222220000-2220000-2-2-2-2-2-2-2000022220-2-20000000-2-2000022000000000000
χ2722222222222222-2-2-2-20000-2-2200000000-2222222000002-2000000000-2-2000022-2000000000
χ2822222222222222-2-2-2-20000-2-2200000000-222-2-2-2-2000002-2000000000220000-2-22000000000
χ2922222222222222-2-2-2-222002-22220000002-2-2000000000-2200000220000-2-2000000000-20000
χ3022222222222222-2-2-2-2-2-2002-22-2-20000002-2-2000000000-2200000-2-200002200000000020000
χ3122222-2-2222222-222-220000-2-2-200000000-222222200000-22000000000220000-2-2-2000000000
χ3222222-2-2222222-222-220000-2-2-200000000-222-2-2-2-200000-22000000000-2-20000222000000000
χ3322222-2-2222222-222-2222002-2-2220000002-2-20000000002-200000-2-2000022000000000-20000
χ3422222-2-2222222-222-22-2-2002-2-2-2-20000002-2-20000000002-200000220000-2-200000000020000
χ3522222-2-2222222-2-2-22-20000-22-200002222-2-2-20000-2-2-2-20220000000-2-2000022000000000000
χ3622222-2-2222222-2-2-22-20000-22-20000-2-2-2-2-2-2-2000022220220000000220000-2-2000000000000
χ374444400-4-444-4-4000-40000044000000000-44-400000000000000000000000000000000000000
χ384444400-4-444-4-4000-400000-440000000004-4400000000000000000000000000000000000000
χ394444400-4-4-4-4440440-4002200000-2-20000000000000002002-22-2-20000000000000000000000
χ404444400-4-4-4-4440440-400-2-20000022000000000000000-200-22-2220000000000000000000000
χ414444400-4-4-4-4440-4-40400220000022000000000000000-2002-2-2-220000000000000000000000
χ424444400-4-4-4-4440-4-40400-2-200000-2-2000000000000000200-2222-20000000000000000000000
χ43444444444-4-4-4-440000002200-40022000000000000000200-22-2-2-20000000000000000000000
χ44444444444-4-4-4-44000000-2-200-400-2-2000000000000000-2002-22220000000000000000000000
χ4544444-4-444-4-4-4-4-40000002200400-2-2000000000000000-200-222-220000000000000000000000
χ4644444-4-444-4-4-4-4-4000000-2-200400220000000000000002002-2-22-20000000000000000000000
χ47444-4-40000004-404-4002200000-2-20000000002i2i−2i−2i2i−2i2i−2i0000000000002i−2i2-22i−2i000000000000
χ48444-4-40000004-404-4002200000-2-2000000000−2i−2i2i2i−2i2i−2i2i000000000000−2i2i2-2−2i2i000000000000
χ49444-4-40000004-404-400-2-200000220000000002i2i−2i−2i−2i2i−2i2i0000000000002i−2i-22−2i2i000000000000
χ50444-4-40000004-404-400-2-20000022000000000−2i−2i2i2i2i−2i2i−2i000000000000−2i2i-222i−2i000000000000
χ51444-4-40000004-40-44002200000-2-20000000002i2i−2i−2i−2i2i−2i2i000000000000−2i2i-222i−2i000000000000
χ52444-4-40000004-40-44002200000-2-2000000000−2i−2i2i2i2i−2i2i−2i0000000000002i−2i-22−2i2i000000000000
χ53444-4-40000004-40-4400-2-200000220000000002i2i−2i−2i2i−2i2i−2i000000000000−2i2i2-2−2i2i000000000000
χ54444-4-40000004-40-4400-2-20000022000000000−2i−2i2i2i−2i2i−2i2i0000000000002i−2i2-22i−2i000000000000
χ5544-44-4444-40000-400002-2000002-2002i−2i2i−2i0002i−2i2i−2i0000000000002-22i−2i0000002i−2i0000000000
χ5644-44-4444-40000-400002-2000002-200−2i2i−2i2i000−2i2i−2i2i0000000000002-2−2i2i000000−2i2i0000000000
χ5744-44-4444-40000-40000-2200000-22002i−2i2i−2i000−2i2i−2i2i000000000000-222i−2i000000−2i2i0000000000
χ5844-44-4444-40000-40000-2200000-2200−2i2i−2i2i0002i−2i2i−2i000000000000-22−2i2i0000002i−2i0000000000
χ5944-44-4-4-44-40000400002-2000002-2002i−2i2i−2i000−2i2i−2i2i000000000000-22−2i2i0000002i−2i0000000000
χ6044-44-4-4-44-40000400002-2000002-200−2i2i−2i2i0002i−2i2i−2i000000000000-222i−2i000000−2i2i0000000000
χ6144-44-4-4-44-4000040000-2200000-22002i−2i2i−2i0002i−2i2i−2i0000000000002-2−2i2i000000−2i2i0000000000
χ6244-44-4-4-44-4000040000-2200000-2200−2i2i−2i2i000−2i2i−2i2i0000000000002-22i−2i0000002i−2i0000000000
χ63888-8-8000000-880000000000000000000000000004-4-44000000000000000000000000000000
χ64888-8-8000000-88000000000000000000000000000-444-4000000000000000000000000000000
χ6588-88-800-88000000000000000000004-4-4400000000000000000000000000000000000000000
χ6688-88-800-8800000000000000000000-444-400000000000000000000000000000000000000000
χ6788-8-8800008-800000000000000000000000004-4-440000000000000000000000000000000000
χ6888-8-8800008-80000000000000000000000000-444-40000000000000000000000000000000000
χ6988-8-880000-8800000004-400000-4400000000000000000000000000000000000000000000000
χ7088-8-880000-880000000-44000004-400000000000000000000000000000000000000000000000
χ7116-160008-800000000000004-4000004-4000000000000000000000000000000000000000000000
χ7216-160008-80000000000000-4400000-44000000000000000000000000000000000000000000000
χ7316-16000-8800000000000004-400000-44000000000000000000000000000000000000000000000
χ7416-16000-880000000000000-44000004-4000000000000000000000000000000000000000000000

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