Finite Group Databasebeta

← Group #72266616

Character table — Group #72266616

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111333344441212121212121212484848484848484896969696969696969696969696969696256256256256256256256256256256256256256256256256
order122222222222222222224444444444444444444444443366666666666666
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111−1−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
χ311111111111111111111111111111111111111111111−1+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
χ422222222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000-1-11111-1-1-11111-1-1-1
χ522222222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000001+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32
χ622222222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000001−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32
χ722-2-222-2-222-2-222-2-222-2-20000000000000000000022-2-2-1-111-1-111-111-1-111-1
χ822-2-222-2-222-2-222-2-222-2-20000000000000000000022-2-21+i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32
χ922-2-222-2-222-2-222-2-222-2-20000000000000000000022-2-21−i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32
χ102-22-22-22-22-22-22-22-22-22-2000000000000000022-2-20000-1-11-11-11-111-11-11-11
χ112-22-22-22-22-22-22-22-22-22-2000000000000000022-2-200001+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32
χ122-22-22-22-22-22-22-22-22-22-2000000000000000022-2-200001−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32
χ133333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1433333333333333333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1533333333333333333333-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-10000000000000000
χ1633333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-10000000000000000
χ1733333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133330000000000000000
χ1844-4-444-4-4-4-44444-4-4-4-4440000000000000000000000001111-1-1-1-1111-1-1-1-11
χ1944-4-444-4-4-4-44444-4-4-4-444000000000000000000000000−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32
χ2044-4-444-4-4-4-44444-4-4-4-444000000000000000000000000−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32
χ214-44-44-44-4-44-444-44-4-44-44000000000000000000000000111-11-1-11-11-11-1-11-1
χ224-44-44-44-4-44-444-44-4-44-44000000000000000000000000−1−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32
χ234-44-44-44-4-44-444-44-4-44-44000000000000000000000000−1+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32
χ244-4-444-4-444-4-444-4-444-4-44000000000000000000000000111-1-111-1-11-1-111-1-1
χ254-4-444-4-444-4-444-4-444-4-44000000000000000000000000−1−i32−1+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ264-4-444-4-444-4-444-4-444-4-44000000000000000000000000−1+i32−1−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ274-4-444-4-44-444-44-4-44-444-400000000000000000000000011-111-11-1-1-111-11-1-1
χ284-4-444-4-44-444-44-4-44-444-4000000000000000000000000−1−i32−1+i321+i32−1−i32−1−i321+i32−1−i321+i321+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32
χ294-4-444-4-44-444-44-4-44-444-4000000000000000000000000−1+i32−1−i321−i32−1+i32−1+i321−i32−1+i321−i321−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32
χ3066666666-6-6-6-66666-6-6-6-6-2-2-2-2222200000000000000000000000000000000
χ3166-6-666-6-666-6-666-6-666-6-600000000000000000000-2-2220000000000000000
χ3266-6-666-6-6-6-666-2-22222-2-20000000022-2-22i2i−2i−2i2i−2i2i−2i00000000000000000000
χ3366-6-666-6-6-6-666-2-22222-2-20000000022-2-2−2i−2i2i2i−2i2i−2i2i00000000000000000000
χ3466-6-666-6-6-6-666-2-22222-2-200000000-2-2222i2i−2i−2i−2i2i−2i2i00000000000000000000
χ3566-6-666-6-6-6-666-2-22222-2-200000000-2-222−2i−2i2i2i2i−2i2i−2i00000000000000000000
χ366-66-66-66-66-66-66-66-66-66-60000000000000000-2-22200000000000000000000
χ376-66-66-66-6-66-66-22-222-22-2000000002-22-22i−2i2i−2i00002i−2i2i−2i0000000000000000
χ386-66-66-66-6-66-66-22-222-22-2000000002-22-2−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ396-66-66-66-6-66-66-22-222-22-200000000-22-222i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ406-66-66-66-6-66-66-22-222-22-200000000-22-22−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ416-6-666-6-666-6-66-222-2-222-222-2-222-2-22-2-222-2-22000000000000000000000000
χ426-6-666-6-666-6-66-222-2-222-222-2-222-2-2-222-2-222-2000000000000000000000000
χ436-6-666-6-666-6-66-222-2-222-2-2-222-2-2222-2-22-222-2000000000000000000000000
χ446-6-666-6-666-6-66-222-2-222-2-2-222-2-222-222-22-2-22000000000000000000000000
χ456-6-666-6-66-666-6-222-22-2-2222-2-2-2-222000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ466-6-666-6-66-666-6-222-22-2-2222-2-2-2-22200000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ476-6-666-6-66-666-6-222-22-2-22-2-22222-2-2000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ486-6-666-6-66-666-6-222-22-2-22-2-22222-2-200000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ49121212121212121212121212-4-4-4-4-4-4-4-40000000000000000000000000000000000000000
χ501212121212121212-12-12-12-12-4-4-4-444440000000000000000000000000000000000000000
χ511212-12-121212-12-121212-12-12-4-444-4-4440000000000000000000000000000000000000000
χ5212-1212-1212-1212-1212-1212-12-44-44-44-440000000000000000000000000000000000000000
χ5324242424-8-8-8-80000000000004-44-4000000000000000000000000000000000000
χ5424242424-8-8-8-8000000000000-44-44000000000000000000000000000000000000
χ552424-24-24-8-88800000000000000004i−4i4i−4i00000000000000000000000000000000
χ562424-24-24-8-8880000000000000000−4i4i−4i4i00000000000000000000000000000000
χ5724-2424-24-88-8800000000000000004i−4i−4i4i00000000000000000000000000000000
χ5824-2424-24-88-880000000000000000−4i4i4i−4i00000000000000000000000000000000
χ5924-24-2424-888-80000000000004-4-44000000000000000000000000000000000000
χ6024-24-2424-888-8000000000000-444-4000000000000000000000000000000000000

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