Finite Group Databasebeta

← Group #72267533

Character table — Group #72267533

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112266668888121212121212121224242424484848484848484848484848484848486464646464646464128128128128128128128128128128128128
order122222222222444444444422444444444488888888336666666666666612121212
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ41111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1
χ51111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32
χ61111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32
χ72-2-222-222-2-22-22-22222-2-2-2-22-22-20000000000000000-1-11111-1-11-11-11-11-11-11-1
χ82-2-222-222-2-22-22-22222-2-2-2-22-22-200000000000000001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1+i321−i32
χ92-2-222-222-2-22-22-22222-2-2-2-22-22-200000000000000001−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1−i321+i32
χ102-2-222-222-2-2-22-222222-2-2-2-2-22-220000000000000000-1-11111-1-11-1-111-1-11-11-11
χ112-2-222-222-2-2-22-222222-2-2-2-2-22-2200000000000000001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ122-2-222-222-2-2-22-222222-2-2-2-2-22-2200000000000000001−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ1333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ143333333333-3-3-3-333333333-3-3-3-3-1-1-1-1-1-1-1-11111111100000000000000000000
χ15333333-1-1-1-133333-1-1-1-1-1-13-1-1-1-13-1-1-13-1-1-133-1-1-1-1-1-100000000000000000000
χ16333333-1-1-1-133333-1-1-1-1-1-13-1-1-1-1-13-1-1-13-1-1-1-133-1-1-1-100000000000000000000
χ17333333-1-1-1-133333-1-1-1-1-1-13-1-1-1-1-1-13-1-1-13-1-1-1-1-133-1-100000000000000000000
χ18333333-1-1-1-133333-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1-13-1-1-1-1-1-13300000000000000000000
χ19333333-1-1-1-1-3-3-3-33-1-1-1-1-1-1311113-1-1-13-1-1-1-3-311111100000000000000000000
χ20333333-1-1-1-1-3-3-3-33-1-1-1-1-1-131111-13-1-1-13-1-111-3-3111100000000000000000000
χ21333333-1-1-1-1-3-3-3-33-1-1-1-1-1-131111-1-13-1-1-13-11111-3-31100000000000000000000
χ22333333-1-1-1-1-3-3-3-33-1-1-1-1-1-131111-1-1-13-1-1-13111111-3-300000000000000000000
χ234444-4-44-44-422-2-20000000022-2-2000000000000000011111111-1-1-1-1-1-1-1-11111
χ244444-4-44-44-422-2-20000000022-2-20000000000000000−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ254444-4-44-44-422-2-20000000022-2-20000000000000000−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ264444-4-44-44-4-2-22200000000-2-222000000000000000011111111-1-111-1-111-1-1-1-1
χ274444-4-44-44-4-2-22200000000-2-2220000000000000000−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i32
χ284444-4-44-44-4-2-22200000000-2-2220000000000000000−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i32
χ294-4-44-444-4-442-2-22000000002-2-22000000000000000011-1-1-1-1111-11-11-11-1-11-11
χ304-4-44-444-4-442-2-22000000002-2-220000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i32−1−i321−i32−1+i32
χ314-4-44-444-4-442-2-22000000002-2-220000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i32−1+i321+i32−1−i32
χ324-4-44-444-4-44-222-200000000-222-2000000000000000011-1-1-1-1111-1-111-1-111-11-1
χ334-4-44-444-4-44-222-200000000-222-20000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ344-4-44-444-4-44-222-200000000-222-20000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ3566666666660000-2-2-2-2-2-2-2-200002222-2-2-2-20000000000000000000000000000
χ3666666666660000-2-2-2-2-2-2-2-20000-2-2-2-222220000000000000000000000000000
χ37666666-2-2-2-20000-26-2-26-2-2-2000022-2-2-2-2220000000000000000000000000000
χ38666666-2-2-2-20000-26-2-26-2-2-20000-2-22222-2-20000000000000000000000000000
χ39666666-2-2-2-20000-2-26-2-26-2-200002-22-2-22-220000000000000000000000000000
χ40666666-2-2-2-20000-2-26-2-26-2-20000-22-222-22-20000000000000000000000000000
χ41666666-2-2-2-20000-2-2-26-2-26-200002-2-22-222-20000000000000000000000000000
χ42666666-2-2-2-20000-2-2-26-2-26-20000-222-22-2-220000000000000000000000000000
χ436-6-666-666-6-60000-2-2-2-222220000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ446-6-666-666-6-60000-2-2-2-22222000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ456-6-666-6-2-2220000-26-2-2-62220000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ466-6-666-6-2-2220000-26-2-2-6222000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ476-6-666-6-2-2220000-2-26-22-6220000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ486-6-666-6-2-2220000-2-26-22-622000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ496-6-666-6-2-2220000-2-2-2622-620000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ506-6-666-6-2-2220000-2-2-2622-62000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ516-6-666-6-2-2226-66-66-2-2-2222-6-22-22000000000000000000000000000000000000
χ526-6-666-6-2-222-66-666-2-2-2222-62-22-2000000000000000000000000000000000000
χ5312121212-12-12-44-4466-6-600000000-2-222000000000000000000000000000000000000
χ5412121212-12-12-44-44-6-6660000000022-2-2000000000000000000000000000000000000
χ5512-12-1212-1212-444-46-6-6600000000-222-2000000000000000000000000000000000000
χ5612-12-1212-1212-444-4-666-6000000002-2-22000000000000000000000000000000000000
χ571616-16-1600000000000000000000000000000000000000-2-22-22-222000000000000
χ581616-16-16000000000000000000000000000000000000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i3000000000000
χ591616-16-16000000000000000000000000000000000000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i3000000000000
χ6016-1616-1600000000000000000000000000000000000000-2-2-22-2222000000000000
χ6116-1616-16000000000000000000000000000000000000001+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i3000000000000
χ6216-1616-16000000000000000000000000000000000000001−i31+i31−i3−1+i31+i3−1−i3−1+i3−1−i3000000000000

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