Finite Group Databasebeta

← Group #72251758

Character table — Group #72251758

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112224444444481616161616161616161616161616161616161616163232323232323232323232323232323232323232323264646464646464128128128128
order12222222244442222222244444444448888244444444444448888888844444484888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-111111-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1
χ4111111111111111111111111-1-1-1-1111-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-1-1-1-11-1-11
χ511111111111111111-1-1111-1-111111111111-11-11-1-1-1-11111111111111111-1-1-1-11-1-1-1-1
χ611111111111111111-1-1111-1-11111111-1-1-1-1-11-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111
χ711111111111111111-1-1111-1-1-1-1-1-11111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-11-1-11
χ811111111111111111-1-1111-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-1-111-1-111-1-111-1-111-1-11111-1-111-1
χ911111-1-1111111-11-1-11111-1-1-111111111111-1-11-111-1-1-1-1-1-11111-1-1-1-1111-111-1-1-1-11-11
χ1011111-1-1111111-11-1-11111-1-1-11111111-1-1-1-1-1-11-111-1-111-1-1-1-1111111-1-1-1111-1-1-11-11-1
χ1111111-1-1111111-11-1-11111-1-1-1-1-1-1-11111111-1-11-111-1-11111-1-1-1-111-1-1-1-11-1-1-111111-1-1
χ1211111-1-1111111-11-1-11111-1-1-1-1-1-1-1111-1-1-1-1-1-11-111-1-1-1-11111-1-1-1-11111-11-1-1111-1-111
χ1311111-1-1111111-11-1-1-1-111-111111111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-111-11-11-1
χ1411111-1-1111111-11-1-1-1-111-1111111111-1-1-1-11-1-1-1-1-11111-1-1-1-1111111-1-1-11-1-111-1-11-11
χ1511111-1-1111111-11-1-1-1-111-111-1-1-1-111111111-1-1-1-1-1111111-1-1-1-111-1-1-1-11-111-1-11-1-111
χ1611111-1-1111111-11-1-1-1-111-111-1-1-1-1111-1-1-1-11-1-1-1-1-111-1-11111-1-1-1-11111-1111-1-1111-1-1
χ172222200-2-22-22-2020000-2-20222i2i−2i−2i22-20000-2000002-20000002i−2i00000000002i−2i00000
χ182222200-2-22-22-2020000-2-2022−2i−2i2i2i22-20000-2000002-2000000−2i2i0000000000−2i2i00000
χ192222200-2-22-22-2020000-2-20-2-22i2i−2i−2i22-20000200000-220000002i−2i0000000000−2i2i00000
χ202222200-2-22-22-2020000-2-20-2-2−2i−2i2i2i22-20000200000-22000000−2i2i00000000002i−2i00000
χ212222200-2-22-22-20200222-20002i2i−2i−2i-2-22000000-202-200000000−2i2i000000002i−2i0000000
χ222222200-2-22-22-20200222-2000−2i−2i2i2i-2-22000000-202-2000000002i−2i00000000−2i2i0000000
χ232222200-2-22-22-20200-2-22-20002i2i−2i−2i-2-2200000020-2200000000−2i2i00000000−2i2i0000000
χ242222200-2-22-22-20200-2-22-2000−2i−2i2i2i-2-2200000020-22000000002i−2i000000002i−2i0000000
χ252222222222222222200-222002222-2-2-200000-20-20000002200-2-2000000000000-20000
χ262222222222222222200-22200-2-2-2-2-2-2-200000-20-2000000-2-2002200000000000020000
χ2722222222222222-2-2-2002-220000002-2-20000020-2000022002200-2-200-2-200000000000
χ2822222222222222-2-2-2002-220000002-2-20000020-20000-2-200-2-20022002200000000000
χ2922222222222222-2-2-200-2-22000000-22222220-202000000000000002200-2-2000000000
χ3022222222222222-2-2-200-2-22000000-222-2-2-2-20-20200000000000000-2-20022000000000
χ3122222-2-2222222-22-2-200-22-2002222-2-2-200000202000000-2-200-2-200000000000020000
χ3222222-2-2222222-22-2-200-22-200-2-2-2-2-2-2-200000202000000220022000000000000-20000
χ3322222-2-2222222-2-222002-2-20000002-2-200000-20200002200-2-200-2-2002200000000000
χ3422222-2-2222222-2-222002-2-20000002-2-200000-2020000-2-20022002200-2-200000000000
χ3522222-2-2222222-2-22200-2-2-2000000-2222222020-200000000000000-2-200-22000000000
χ3622222-2-2222222-2-22200-2-2-2000000-222-2-2-2-2020-20000000000000022002-2000000000
χ374444400-4-44-44-40-40000440000000-44-40000000000000000000000000000000000000
χ384444400-4-44-44-40-40000-4400000004-440000000000000000000000000000000000000
χ394444400-4-4-44-44004-4220002200000000000-20-20-22-220000000000000000000000000
χ404444400-4-4-44-44004-4-2-2000-2-20000000000020202-22-20000000000000000000000000
χ414444400-4-4-44-4400-4422000-2-20000000000020-20-222-20000000000000000000000000
χ424444400-4-4-44-4400-44-2-20002200000000000-20202-2-220000000000000000000000000
χ43444444444-4-4-4-440002200-422000000000002020-2-2-2-20000000000000000000000000
χ44444444444-4-4-4-44000-2-200-4-2-200000000000-20-2022220000000000000000000000000
χ4544444-4-444-4-4-4-4-400022004-2-200000000000-2020-2-2220000000000000000000000000
χ4644444-4-444-4-4-4-4-4000-2-2004220000000000020-2022-2-20000000000000000000000000
χ47444-4-4444-40000-400000000002-22-20002i2i−2i−2i000000002i−2i2-22i−2i00002i−2i0000000000000
χ48444-4-4444-40000-400000000002-22-2000−2i−2i2i2i00000000−2i2i2-2−2i2i0000−2i2i0000000000000
χ49444-4-4444-40000-40000000000-22-220002i2i−2i−2i00000000−2i2i-22−2i2i00002i−2i0000000000000
χ50444-4-4444-40000-40000000000-22-22000−2i−2i2i2i000000002i−2i-222i−2i0000−2i2i0000000000000
χ51444-4-4-4-44-40000400000000002-22-20002i2i−2i−2i00000000−2i2i-222i−2i0000−2i2i0000000000000
χ52444-4-4-4-44-40000400000000002-22-2000−2i−2i2i2i000000002i−2i-22−2i2i00002i−2i0000000000000
χ53444-4-4-4-44-4000040000000000-22-220002i2i−2i−2i000000002i−2i2-2−2i2i0000−2i2i0000000000000
χ54444-4-4-4-44-4000040000000000-22-22000−2i−2i2i2i00000000−2i2i2-22i−2i00002i−2i0000000000000
χ55888-8-800-880000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ56888-8-800-88000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ5788-88-80000080-80000000000000000004i−4i4i−4i000000000000000000000000000000000
χ5888-88-80000080-8000000000000000000−4i4i−4i4i000000000000000000000000000000000
χ5988-88-800000-8080000000000000000000000000000000000000000004-400000000000
χ6088-88-800000-808000000000000000000000000000000000000000000-4400000000000
χ6188-8-88000080-80000000000000000000000000000000000000004i−4i000000000000000
χ6288-8-88000080-8000000000000000000000000000000000000000−4i4i000000000000000
χ6388-8-880000-80800000000000000000004-4-44000000000000000000000000000000000
χ6488-8-880000-8080000000000000000000-444-4000000000000000000000000000000000
χ6516-160008-800000000004-40004-400000000000000000000000000000000000000000000
χ6616-160008-80000000000-44000-4400000000000000000000000000000000000000000000
χ6716-16000-8800000000004-4000-4400000000000000000000000000000000000000000000
χ6816-16000-880000000000-440004-400000000000000000000000000000000000000000000

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