Finite Group Databasebeta

← Group #72258719

Character table — Group #72258719

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122233446666666661212121212121216161616242424243232484848484848484848484848646464646464646464646464646464969696969696969696969696
order12244222424444444424444442224444436222444448888666666666121212121212248888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11-1111-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-111-11-1-1-111111
χ51111111-1-1111111111-1-11111111-1-1-1-1-1-11111-1-1111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111-1-1111111111-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-1-1-1-1-1111111-1-111
χ71111111-1-1111111111-1-111111-1-111-1-1-1-111-1-111111111111-1-1-1-1-1-11111-1-111-1-1-11-1-1-11-1-111
χ81111111-1-1111111111-1-111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-111111-1111-111-1-1
χ9222222222222222222222222222222222-1-1222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ102222222222222222222222222-2-2-2-22222-1-1-2-2-2-200000000-1-1-1111111-1-1-1-111000000000000
χ112222222-2-2222222222-2-22222222-2-2-2-2-2-2-1-122-2-200000000-111-1-1-1-111-1-11111000000000000
χ122222222-2-2222222222-2-222222-2-222-2-2-2-2-1-1-2-22200000000-1111111-1-1-1-111-1-1000000000000
χ13222-2-222002222-2-2-2-2200-2-22-222-2000000222-2000000000020022-2-200-2-20000000000000000
χ14222-2-222002222-2-2-2-2200-2-22-222-2000000-1-12-20000000000-1−i3i3-1-111−i3i311−i3i3−i3i3000000000000
χ15222-2-222002222-2-2-2-2200-2-22-222-2000000-1-12-20000000000-1i3−i3-1-111i3−i311i3−i3i3−i3000000000000
χ16222-2-222002222-2-2-2-2200-2-22-22-2200000022-220000000000200-2-22200-2-20000000000000000
χ17222-2-222002222-2-2-2-2200-2-22-22-22000000-1-1-220000000000-1−i3i311-1-1i3−i311−i3i3i3−i3000000000000
χ18222-2-222002222-2-2-2-2200-2-22-22-22000000-1-1-220000000000-1i3−i311-1-1−i3i311i3−i3−i3i3000000000000
χ1922-22-22200-22222-2222002-2-2-2-2002-2000022002-200000000-2000000222-200-2-2000000000000
χ2022-22-22200-22222-2222002-2-2-2-2002-20000-1-1002-2000000001−i3i3−i3i3−i3i3-1-1-11i3−i311000000000000
χ2122-22-22200-22222-2222002-2-2-2-2002-20000-1-1002-2000000001i3−i3i3−i3i3−i3-1-1-11−i3i311000000000000
χ2222-22-22200-22222-2222002-2-2-2-200-2200002200-2200000000-2000000-2-22-20022000000000000
χ2322-22-22200-22222-2222002-2-2-2-200-220000-1-100-22000000001−i3i3i3−i3i3−i311-11i3−i3-1-1000000000000
χ2422-22-22200-22222-2222002-2-2-2-200-220000-1-100-22000000001i3−i3−i3i3−i3i311-11−i3i3-1-1000000000000
χ2522-2-22222-2-2222-22-2-222-2-22-22-20000-2-22222000000000000-222000000-22-2-200000000000000
χ2622-2-22222-2-2222-22-2-222-2-22-22-20000-2-222-1-10000000000001-1-1−i3i3i3−i3−i3i31-111i3−i3000000000000
χ2722-2-22222-2-2222-22-2-222-2-22-22-20000-2-222-1-10000000000001-1-1i3−i3−i3i3i3−i31-111−i3i3000000000000
χ2822-2-2222-22-2222-22-2-22-22-22-22-2000022-2-222000000000000-2-2-2000000-222200000000000000
χ2922-2-2222-22-2222-22-2-22-22-22-22-2000022-2-2-1-1000000000000111−i3i3i3−i3i3−i31-1-1-1−i3i3000000000000
χ3022-2-2222-22-2222-22-2-22-22-22-22-2000022-2-2-1-1000000000000111i3−i3−i3i3−i3i31-1-1-1i3−i3000000000000
χ313333333333-1-1-133-1-1-133-1-1-1-1-13333-1-1-1-100-1-1-1-11111-1-1-1-100000000000000011111-1-11-1-1-1-1
χ323333333333-1-1-133-1-1-133-1-1-1-1-13333-1-1-1-100-1-1-1-1-1-1-1-11111000000000000000-1-1-1-1-111-11111
χ333333333333-1-1-133-1-1-133-1-1-1-1-1-3-3-3-3-1-1-1-10011111111-1-1-1-1000000000000000-1-11-11-1-1-11111
χ343333333333-1-1-133-1-1-133-1-1-1-1-1-3-3-3-3-1-1-1-1001111-1-1-1-1111100000000000000011-11-1111-1-1-1-1
χ353333333-3-33-1-1-133-1-1-1-3-3-1-1-1-1-133-3-3111100-1-1111111-1-1-1-100000000000000011-1-1-111-1-1-111
χ363333333-3-33-1-1-133-1-1-1-3-3-1-1-1-1-133-3-3111100-1-111-1-1-1-11111000000000000000-1-1111-1-1111-1-1
χ373333333-3-33-1-1-133-1-1-1-3-3-1-1-1-1-1-3-33311110011-1-11111-1-1-1-1000000000000000-1-1-11-111111-1-1
χ383333333-3-33-1-1-133-1-1-1-3-3-1-1-1-1-1-3-33311110011-1-1-1-1-1-11111000000000000000111-11-1-1-1-1-111
χ394-4000-440004-4-4000040000000000000004-400002-22-222-2-2000000000000000000000000000
χ404-4000-440004-4-4000040000000000000004-40000-22-22-2-222000000000000000000000000000
χ4166666-2-266-222-2-2-222-2-2-2-22-2-2200002-22-2000000000000000000000000000002-202000-20000
χ4266666-2-266-222-2-2-222-2-2-2-22-2-2200002-22-200000000000000000000000000000-220-200020000
χ4366666-2-266-2-2-22-2-2-2-22-2-22-222-20000-22-2200000022-2-200000000000000000000020-20000000
χ4466666-2-266-2-2-22-2-2-2-22-2-22-222-20000-22-22000000-2-222000000000000000000000-2020000000
χ4566666-2-2-6-6-222-2-2-222-222-22-2-220000-22-22000000000000000000000000000002-20-200020000
χ4666666-2-2-6-6-222-2-2-222-222-22-2-220000-22-2200000000000000000000000000000-2202000-20000
χ4766666-2-2-6-6-2-2-22-2-2-2-22222-222-200002-22-200000022-2-2000000000000000000000-2020000000
χ4866666-2-2-6-6-2-2-22-2-2-2-22222-222-200002-22-2000000-2-22200000000000000000000020-20000000
χ49666-6-666006-2-2-2-6-622-20022-22-26-600000000-220000000000000000000000000000000000000
χ50666-6-666006-2-2-2-6-622-20022-22-2-66000000002-20000000000000000000000000000000000000
χ5166-66-66600-6-2-2-26-6-2-2-200-22222006-600000000-2200000000000000000000000000000000000
χ5266-66-66600-6-2-2-26-6-2-2-200-2222200-66000000002-200000000000000000000000000000000000
χ5366-6-66666-6-6-2-2-2-6622-26-62-22-22000022-2-200000000000000000000000000000000000000000
χ5466-6-6666-66-6-2-2-2-6622-2-662-22-220000-2-22200000000000000000000000000000000000000000
χ5566-6-66-2-26-6222-22-2-2-2-2-22222-2-20000-222-200000000000000000000000000000000000002i−2i2i−2i
χ5666-6-66-2-26-6222-22-2-2-2-2-22222-2-20000-222-20000000000000000000000000000000000000−2i2i−2i2i
χ5766-6-66-2-26-62-2-222-2222-22-2-2-22200002-2-2200000000002-22-2000000000000000000002-200000
χ5866-6-66-2-26-62-2-222-2222-22-2-2-22200002-2-220000000000-22-2200000000000000000000-2200000
χ5966-6-66-2-2-66222-22-2-2-2-22-2222-2-200002-2-2200000000000000000000000000000000000002i−2i−2i2i
χ6066-6-66-2-2-66222-22-2-2-2-22-2222-2-200002-2-220000000000000000000000000000000000000−2i2i2i−2i
χ6166-6-66-2-2-662-2-222-22222-2-2-2-2220000-222-200000000002-22-200000000000000000000-2200000
χ6266-6-66-2-2-662-2-222-22222-2-2-2-2220000-222-20000000000-22-22000000000000000000002-200000
χ638-8000-880008-8-800008000000000000000-44000000000000000000000000000000000000000
χ64121212-12-12-4-400-444-444-4-4-4004-4-4440000000000000000000000000000000000000000000000000
χ65121212-12-12-4-400-4-4-444444400-444-4-40000000000000000000000000000000000000000000000000
χ661212-1212-12-4-400444-4-4444-400-4-444-40000000000000000000000000000000000000000000000000
χ671212-1212-12-4-4004-4-44-44-4-440044-4-440000000000000000000000000000000000000000000000000
χ6812-120004-4000-44-4008-840000000000000000000002-2-222-2-22000000000000000000000000000
χ6912-120004-4000-44-4008-84000000000000000000000-222-2-222-2000000000000000000000000000
χ7012-120004-4000-44-400-8840000000000000000000002-2-22-222-2000000000000000000000000000
χ7112-120004-4000-44-400-884000000000000000000000-222-22-2-22000000000000000000000000000
χ7212-12000-1212000-4440000-40000000000000000000002-22-2-2-222000000000000000000000000000
χ7312-12000-1212000-4440000-4000000000000000000000-22-2222-2-2000000000000000000000000000
χ7424-240008-80008-880000-800000000000000000000000000000000000000000000000000000000

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