Finite Group Databasebeta

← Group #72340971

Character table — Group #72340971

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size13444444424244864646464646464646464646464646464969696961344444442424486464646464646464646464646464646496969696
order1222222224423366666666666666444422222222244266666666666666664444
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111−1+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−i321111111111111111−1+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−i321111
χ3111111111111−1−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+i321111111111111111−1−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+i321111
χ422222-2-2-2-222-2-1-11111-1-1-11111-1-1-1000022222-2-2-2-222-2-1-11111-1-1-11111-1-1-10000
χ522222-2-2-2-222-21−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32000022222-2-2-2-222-21−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i320000
χ622222-2-2-2-222-21+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32000022222-2-2-2-222-21+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i320000
χ73333333333330000000000000000-1-1-1-13333333333330000000000000000-1-1-1-1
χ8333333333-1-1-100000000000000003-1-1-1333333333-1-1-100000000000000003-1-1-1
χ9333333333-1-1-10000000000000000-13-1-1333333333-1-1-10000000000000000-13-1-1
χ10333333333-1-1-10000000000000000-1-13-1333333333-1-1-10000000000000000-1-13-1
χ11333333333-1-1-10000000000000000-1-1-13333333333-1-1-10000000000000000-1-1-13
χ12444-4-444-4-40001111-1-11-1-111-1-11-1-10000444-4-444-4-40001111-1-11-1-111-1-11-1-10000
χ13444-4-444-4-4000−1+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i321+i321+i320000444-4-444-4-4000−1+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i321+i321+i320000
χ14444-4-444-4-4000−1−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i321−i321−i320000444-4-444-4-4000−1−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i321−i321−i320000
χ15444-4-4-4-44400011-1-1111-1-1-1-1111-1-10000444-4-4-4-44400011-1-1111-1-1-1-1111-1-10000
χ16444-4-4-4-444000−1+i32−1−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i32−1−i321+i321+i320000444-4-4-4-444000−1+i32−1−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i32−1−i321+i321+i320000
χ17444-4-4-4-444000−1−i32−1+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i32−1+i321−i321−i320000444-4-4-4-444000−1−i32−1+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i32−1+i321−i321−i320000
χ1844-44-44-44-4000111-11-1-11-11-11-1-11-1000044-44-44-44-4000111-11-1-11-11-11-1-11-10000
χ1944-44-44-44-4000−1+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32000044-44-44-44-4000−1+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1−i321+i32−1−i321+i321+i32−1−i321+i320000
χ2044-44-44-44-4000−1−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32000044-44-44-44-4000−1−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1+i321−i32−1+i321−i321−i32−1+i321−i320000
χ2144-44-4-44-4400011-11-11-11-1-11-11-11-1000044-44-4-44-4400011-11-11-11-1-11-11-11-10000
χ2244-44-4-44-44000−1+i32−1−i321−i32−1+i321−i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32000044-44-4-44-44000−1+i32−1−i321−i32−1+i321−i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i321+i32−1−i321+i320000
χ2344-44-4-44-44000−1−i32−1+i321+i32−1−i321+i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32000044-44-4-44-44000−1−i32−1+i321+i32−1−i321+i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i321−i32−1+i321−i320000
χ2444-4-444-4-44000111-1-11-1-111-1-11-1-11000044-4-444-4-44000111-1-11-1-111-1-11-1-110000
χ2544-4-444-4-44000−1+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32000044-4-444-4-44000−1+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i320000
χ2644-4-444-4-44000−1−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32000044-4-444-4-44000−1−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i320000
χ2744-4-44-444-400011-111-1-1-11-111-1-1-11000044-4-44-444-400011-111-1-1-11-111-1-1-110000
χ2844-4-44-444-4000−1+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32000044-4-44-444-4000−1+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i320000
χ2944-4-44-444-4000−1−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32000044-4-44-444-4000−1−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i320000
χ3066666-6-6-6-6-2-220000000000000000000066666-6-6-6-6-2-2200000000000000000000
χ3124-800000004-400000000000000000000024-800000004-4000000000000000000000
χ3224-80000000-4400000000000000000000024-80000000-44000000000000000000000
χ3311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ34111111111111−1+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−i321111-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i32-1-1-1-1
χ35111111111111−1−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+i321111-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i32-1-1-1-1
χ3622222-2-2-2-222-2-1-11111-1-1-11111-1-1-10000-2-2-2-2-22222-2-2211-1-1-1-1111-1-1-1-11110000
χ3722222-2-2-2-222-21−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i320000-2-2-2-2-22222-2-22−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i320000
χ3822222-2-2-2-222-21+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i320000-2-2-2-2-22222-2-22−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i320000
χ393333333333330000000000000000-1-1-1-1-3-3-3-3-3-3-3-3-3-3-3-300000000000000001111
χ40333333333-1-1-100000000000000003-1-1-1-3-3-3-3-3-3-3-3-31110000000000000000-3111
χ41333333333-1-1-10000000000000000-13-1-1-3-3-3-3-3-3-3-3-311100000000000000001-311
χ42333333333-1-1-10000000000000000-1-13-1-3-3-3-3-3-3-3-3-3111000000000000000011-31
χ43333333333-1-1-10000000000000000-1-1-13-3-3-3-3-3-3-3-3-31110000000000000000111-3
χ44444-4-444-4-40001111-1-11-1-111-1-11-1-10000-4-4-444-4-444000-1-1-1-111-111-1-111-1110000
χ45444-4-444-4-4000−1+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i321+i321+i320000-4-4-444-4-4440001−i321+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i320000
χ46444-4-444-4-4000−1−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i321−i321−i320000-4-4-444-4-4440001+i321−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i320000
χ47444-4-4-4-44400011-1-1111-1-1-1-1111-1-10000-4-4-44444-4-4000-1-111-1-1-11111-1-1-1110000
χ48444-4-4-4-444000−1+i32−1−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i32−1−i321+i321+i320000-4-4-44444-4-40001−i321+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i320000
χ49444-4-4-4-444000−1−i32−1+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i32−1+i321−i321−i320000-4-4-44444-4-40001+i321−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i320000
χ5044-44-44-44-4000111-11-1-11-11-11-1-11-10000-4-44-44-44-44000-1-1-11-111-11-11-111-110000
χ5144-44-44-44-4000−1+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1−i321+i32−1−i321+i321+i32−1−i321+i320000-4-44-44-44-440001−i321+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i320000
χ5244-44-44-44-4000−1−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1+i321−i32−1+i321−i321−i32−1+i321−i320000-4-44-44-44-440001+i321−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i320000
χ5344-44-4-44-4400011-11-11-11-1-11-11-11-10000-4-44-444-44-4000-1-11-11-11-111-11-11-110000
χ5444-44-4-44-44000−1+i32−1−i321−i32−1+i321−i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i321+i32−1−i321+i320000-4-44-444-44-40001−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i320000
χ5544-44-4-44-44000−1−i32−1+i321+i32−1−i321+i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i321−i32−1+i321−i320000-4-44-444-44-40001+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i320000
χ5644-4-444-4-44000111-1-11-1-111-1-11-1-110000-4-444-4-444-4000-1-1-111-111-1-111-111-10000
χ5744-4-444-4-44000−1+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i320000-4-444-4-444-40001−i321+i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i320000
χ5844-4-444-4-44000−1−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i320000-4-444-4-444-40001+i321−i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i320000
χ5944-4-44-444-400011-111-1-1-11-111-1-1-110000-4-444-44-4-44000-1-11-1-1111-11-1-1111-10000
χ6044-4-44-444-4000−1+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i320000-4-444-44-4-440001−i321+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i320000
χ6144-4-44-444-4000−1−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i320000-4-444-44-4-440001+i321−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i320000
χ6266666-6-6-6-6-2-2200000000000000000000-6-6-6-6-6666622-200000000000000000000
χ6324-800000004-4000000000000000000000-2480000000-44000000000000000000000
χ6424-80000000-44000000000000000000000-24800000004-4000000000000000000000

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