Finite Group Databasebeta

← Group #72320178

Character table — Group #72320178

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size112224444448888881616161616161616161616161616163232323232323232323232323232323232323232646464646464646464128128128128
order12222224444222222222444444444444224444444444448888884444448884488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-11-111111111-1-111-1-1-1-1-1-11111-11-1-1-1-1-1
χ311111111111111111111111111111111-11-111-1-1-1-11-1-11111111111-1-1-1-1111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111-11-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-11-111-1-1-1-11-1-111-1-1-1-1-1-1-1-111111-11-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-11-1-1-1-1-1-11111111111-1-1-111-1-1
χ911111111111-1-1-1-111-1111-11111-1-1-1-11111-11-11-11-1-11-1-1-111-1-1111-111-1-1-1-111-11-1
χ1011111111111-1-1-1-111-1111-11111-1-1-1-1111-1-1-1-11-11-1-11-1111111-1-1-1111-1-11-1-1-11-11
χ1111111111111-1-1-1-111-1111-11111-1-1-1-111-1111-1-11-11-1-11-1-111-1-1111-1-1-111-1-11-11-11
χ1211111111111-1-1-1-111-1111-11111-1-1-1-111-1-11-1-1-11-11-1-11111111-1-1-11-1-1111-1-11-11-1
χ1311111111111-1-1-1-111-1111-1-1-1-1-111111111-11-11-11-1-11-1-1-1-1-111-1-1-11-1-111-1111-1-11
χ1411111111111-1-1-1-111-1111-1-1-1-1-11111111-1-1-1-11-11-1-11-111-1-1-1-1111-1-1-11111-1-111-1
χ1511111111111-1-1-1-111-1111-1-1-1-1-1111111-1111-1-11-11-1-11-1-1-1-111-1-1-1111-1-1-111-111-1
χ1611111111111-1-1-1-111-1111-1-1-1-1-1111111-1-11-1-1-11-11-1-1111-1-1-1-1111-111-1-111-11-1-11
χ17222222222222222222-2-22222222222-2-20000-20000-20000-2-200000000000-200000
χ18222222222222222222-2-222-2-2-2-2-2-2-2-2-2-20000-20000-200002200000000000200000
χ192222222222222-2-2-2-2222-2-200000000-2-2020220000-20022000000000000-20-20000
χ202222222222222-2-2-2-2222-2-200000000-2-20-20-220000-200-2-20000000000002020000
χ212222222222222-2-2-2-22-2-2-2-200000000220000-2000020000002222-2-200000000000
χ222222222222222-2-2-2-22-2-2-2-200000000220000-200002000000-2-2-2-22200000000000
χ2322222222222-2-222-2-2-222-2200000000-2-20202-20000200-2-200000000000020-20000
χ2422222222222-2-222-2-2-222-2200000000-2-20-20-2-2000020022000000000000-2020000
χ2522222222222-2-222-2-2-2-2-2-220000000022000020000-200000022-2-22-200000000000
χ2622222222222-2-222-2-2-2-2-2-220000000022000020000-2000000-2-222-2200000000000
χ2722222222222-2-2-2-222-2-2-22-22222-2-2-2-2-2-200002000020000-2-200000000000200000
χ2822222222222-2-2-2-222-2-2-22-2-2-2-2-22222-2-2000020000200002200000000000-200000
χ2922222-2-22-2-2200002202-2-2022-2-200002-2002000-20200-2002-2000000002-20000000
χ3022222-2-22-2-2200002202-2-2022-2-200002-200-200020-2002002-200000000-220000000
χ3122222-2-22-2-2200002202-2-20-2-22200002-2002000-20200-200-2200000000-220000000
χ3222222-2-22-2-2200002202-2-20-2-22200002-200-200020-200200-22000000002-20000000
χ3322222-2-22-2-220000220-22-2022-2-20000-2220000-20200-2000-220000002-2000000000
χ3422222-2-22-2-220000220-22-2022-2-20000-22-2000020-2002000-22000000-22000000000
χ3522222-2-22-2-220000220-22-20-2-2220000-2220000-20200-20002-2000000-22000000000
χ3622222-2-22-2-220000220-22-20-2-2220000-22-2000020-20020002-20000002-2000000000
χ374444444-4-4-4-4440000-4000000000000002020022-2-20-2-2000000000000000000000
χ384444444-4-4-4-4440000-400000000000000-20-200-2-222022000000000000000000000
χ394444444-4-4-4-4-4-4000040000000000000020-2002-2-220-22000000000000000000000
χ404444444-4-4-4-4-4-40000400000000000000-20200-222-202-2000000000000000000000
χ4144444-4-44-4-440000-4-404-44000000000-44000000000000000000000000000000000
χ4244444-4-44-4-440000-4-40-4440000000004-4000000000000000000000000000000000
χ4344444-4-4-444-40044000000-4000000000020200-2-2-2-2022000000000000000000000
χ4444444-4-4-444-40044000000-40000000000-20-20022220-2-2000000000000000000000
χ4544444-4-4-444-400-4-40000004000000000020-200-22-2202-2000000000000000000000
χ4644444-4-4-444-400-4-400000040000000000-202002-22-20-22000000000000000000000
χ47444-4-44-400004-40000000002i−2i2i−2i2i2i−2i−2i00020-2000000002-2002i−2i2i−2i0000000000000
χ48444-4-44-400004-40000000002i−2i2i−2i2i2i−2i−2i000-20200000000-2200−2i2i−2i2i0000000000000
χ49444-4-44-400004-4000000000−2i2i−2i2i−2i−2i2i2i00020-2000000002-200−2i2i−2i2i0000000000000
χ50444-4-44-400004-4000000000−2i2i−2i2i−2i−2i2i2i000-20200000000-22002i−2i2i−2i0000000000000
χ51444-4-44-40000-440000000002i−2i2i−2i−2i−2i2i2i00020-200000000-2200−2i2i2i−2i0000000000000
χ52444-4-44-40000-440000000002i−2i2i−2i−2i−2i2i2i000-202000000002-2002i−2i−2i2i0000000000000
χ53444-4-44-40000-44000000000−2i2i−2i2i2i2i−2i−2i00020-200000000-22002i−2i−2i2i0000000000000
χ54444-4-44-40000-44000000000−2i2i−2i2i2i2i−2i−2i000-202000000002-200−2i2i2i−2i0000000000000
χ55888-8-8-880000000000000004i−4i−4i4i000000000000000000000000000000000000000
χ56888-8-8-88000000000000000−4i4i4i−4i000000000000000000000000000000000000000
χ5788-88-800800-80000000000000004i−4i4i−4i00000000000000000000000000000000000
χ5888-88-800800-8000000000000000−4i4i−4i4i00000000000000000000000000000000000
χ5988-88-800-800800008-8000000000000000000000000000000000000000000000000
χ6088-88-800-80080000-88000000000000000000000000000000000000000000000000
χ6188-8-880008-800000000000000004-4-4400000000000000000000000000000000000
χ6288-8-880008-80000000000000000-444-400000000000000000000000000000000000
χ6388-8-88000-880008-800000000000000000000000000000000000000000000000000
χ6488-8-88000-88000-8800000000000000000000000000000000000000000000000000
χ6532-32000000000000000000000000000000000000000000000000000000000000000

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