Finite Group Databasebeta

← Group #72241390

Character table — Group #72241390

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size11114888888121216161624242424242424242424242448484848484864646464646464649696969696969696969696969696128128128128128128128128128128128128256256256256256256256256
order1222222222222444222222444444222444336666664444444444444466666666666666121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111111111−1+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
χ31111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111111111−1−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
χ41111111-1-1-1-1111-1-111-1-1-1-11111111111-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-11-1-1
χ51111111-1-1-1-1111-1-111-1-1-1-11111111111-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111-1-1-1-1-1-1-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ61111111-1-1-1-1111-1-111-1-1-1-11111111111-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111-1-1-1-1-1-1-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ711111-1-111-1-111-11-1-1-111-1-1111111111-11-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-11-1-11-1
χ811111-1-111-1-111-11-1-1-111-1-1111111111-11-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-11111-1-1-1-11−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ911111-1-111-1-111-11-1-1-111-1-1111111111-11-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-11111-1-1-1-11+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ1011111-1-1-1-11111-1-11-1-1-1-111111111111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11-1-11
χ1111111-1-1-1-11111-1-11-1-1-1-111111111111-1-11−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-1-1-1-1-111111−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ1211111-1-1-1-11111-1-11-1-1-1-111111111111-1-11−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-1-1-1-1-111111+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ13333333333333333333-1-1-1-133-1-1-1-13-1-13-1-100000000-1-1-1-1-1-13-1-1-13-1-1-100000000000000000000
χ143333333333333333-1-133-1-1-1-133-1-1-13-1-13-100000000-1-13-1-1-1-1-1-1-1-13-1-100000000000000000000
χ153333333333333333-1-1-1-133-1-1-1-133-1-13-1-1300000000-1-1-13-1-1-13-1-1-1-1-1-100000000000000000000
χ163333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000003-1-1-13-1-1-13-1-1-13-100000000000000000000
χ173333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-13-1-1-13-1-1-13-1-1-1300000000000000000000
χ183333333-3-3-3-3333-3-333111133-1-1-1-13-1-131100000000-1-1-1-1-1-1-3111-311100000000000000000000
χ193333333-3-3-3-3333-3-3-1-11111-1-1-1-1-1-1-1-1-1-111000000003-1-1-13-111-3111-3100000000000000000000
χ203333333-3-3-3-3333-3-3-1-11111-1-1-1-1-1-1-1-1-1-11100000000-13-1-1-13111-3111-300000000000000000000
χ213333333-3-3-3-3333-3-3-1-111-3-3-1-1-1-133-1-13-11-300000000-1-1-13-1-11-311111100000000000000000000
χ223333333-3-3-3-3333-3-3-1-1-3-311-1-133-1-1-13-1-1-3100000000-1-13-1-1-111111-31100000000000000000000
χ2333333-3-333-3-333-33-3113311-1-133-1-1-13-113100000000-1-1-3111-1-1-1-11-31100000000000000000000
χ2433333-3-333-3-333-33-311-1-111-1-1-1-1-1-1-1-1-11-11000000003-111-31-1-13-111-3100000000000000000000
χ2533333-3-333-3-333-33-311-1-111-1-1-1-1-1-1-1-1-11-1100000000-13111-3-1-1-13111-300000000000000000000
χ2633333-3-333-3-333-33-311-1-1-3-3-1-1-1-133-1-131-1-300000000-1-11-311-13-1-1111100000000000000000000
χ2733333-3-333-3-333-33-3-3-3-1-11133-1-1-1-13-1-1-3-1100000000-1-111113-1-1-1-311100000000000000000000
χ2833333-3-3-3-33333-3-33111133-1-1-1-133-1-1311300000000-1-11-3111-311-1-1-1-100000000000000000000
χ2933333-3-3-3-33333-3-331111-1-1-1-1-1-1-1-1-1-1-111-1000000003-111-3111-31-1-13-100000000000000000000
χ3033333-3-3-3-33333-3-331111-1-1-1-1-1-1-1-1-1-1-111-100000000-13111-3111-3-1-1-1300000000000000000000
χ3133333-3-3-3-33333-3-3311-3-3-1-1-1-133-1-1-13-11-3-100000000-1-1-31111111-13-1-100000000000000000000
χ3233333-3-3-3-33333-3-33-3-311-1-133-1-1-1-13-1-1-31-100000000-1-11111-31113-1-1-100000000000000000000
χ334444-44444444-4-4-4-40000000000000000001111111100000000000000111111111111-1-1-1-1-1-1-1-1
χ344444-44444444-4-4-4-4000000000000000000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000000000−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321+i321−i321−i321−i321+i321+i321+i32
χ354444-44444444-4-4-4-4000000000000000000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000000000000−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321−i321+i321+i321+i321−i321−i321−i32
χ364444-444-4-4-4-44-4-444000000000000000000111111110000000000000011-1-1-1-111-1-1-1-1-1-1-111-111
χ374444-444-4-4-4-44-4-444000000000000000000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000000000−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ384444-444-4-4-4-44-4-444000000000000000000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000000000000−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ394444-4-4-444-4-44-44-440000000000000000001111111100000000000000-1-111-1-1-1-111-1-1-1-11-111-11
χ404444-4-4-444-4-44-44-44000000000000000000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000000001−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i321−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ414444-4-4-444-4-44-44-44000000000000000000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000000001+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i321+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ424444-4-4-4-4-4444-444-40000000000000000001111111100000000000000-1-1-1-111-1-1-1-111-1-111-111-1
χ434444-4-4-4-4-4444-444-4000000000000000000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000000001−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ444444-4-4-4-4-4444-444-4000000000000000000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000000001+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ4588-8-8000004-40000000004-400004-4000000222-2-22-2-20000000000000000002-200002-200000000
χ4688-8-8000004-40000000004-400004-4000000−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i3000000000000000000−1+i31−i30000−1−i31+i300000000
χ4788-8-8000004-40000000004-400004-4000000−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i3000000000000000000−1−i31+i30000−1+i31−i300000000
χ4888-8-800000-44000000000-4400004-4000000222-2-22-2-2000000000000000000-220000-2200000000
χ4988-8-800000-44000000000-4400004-4000000−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i30000000000000000001−i3−1+i300001+i3−1−i300000000
χ5088-8-800000-44000000000-4400004-4000000−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i30000000000000000001+i3−1−i300001−i3−1+i300000000
χ518-88-80004-40000000004-400004-40000000022-22-2-22-200000000000000002-200002-20000000000
χ528-88-80004-40000000004-400004-400000000−1+i3−1−i31−i3−1+i31−i31+i3−1−i31+i30000000000000000−1+i31−i30000−1−i31+i30000000000
χ538-88-80004-40000000004-400004-400000000−1−i3−1+i31+i3−1−i31+i31−i3−1+i31−i30000000000000000−1−i31+i30000−1+i31−i30000000000
χ548-88-8000-44000000000-4400004-40000000022-22-2-22-20000000000000000-220000-220000000000
χ558-88-8000-44000000000-4400004-400000000−1+i3−1−i31−i3−1+i31−i31+i3−1−i31+i300000000000000001−i3−1+i300001+i3−1−i30000000000
χ568-88-8000-44000000000-4400004-400000000−1−i3−1+i31+i3−1−i31+i31−i3−1+i31−i300000000000000001+i3−1−i300001−i3−1+i30000000000
χ578-8-8804-40000000004-400004-4000000000022-2-22-2-22000000000000002-200002-2000000000000
χ588-8-8804-40000000004-400004-40000000000−1+i3−1−i31−i31−i3−1+i31+i31+i3−1−i300000000000000−1+i31−i30000−1−i31+i3000000000000
χ598-8-8804-40000000004-400004-40000000000−1−i3−1+i31+i31+i3−1−i31−i31−i3−1+i300000000000000−1−i31+i30000−1+i31−i3000000000000
χ608-8-880-44000000000-4400004-4000000000022-2-22-2-2200000000000000-220000-22000000000000
χ618-8-880-44000000000-4400004-40000000000−1+i3−1−i31−i31−i3−1+i31+i31+i3−1−i3000000000000001−i3−1+i300001+i3−1−i3000000000000
χ628-8-880-44000000000-4400004-40000000000−1−i3−1+i31+i31+i3−1−i31−i31−i3−1+i3000000000000001+i3−1−i300001−i3−1+i3000000000000
χ631212121212000000-4-4000000000444444-4-4-4000000000000000000000000000000000000000000000
χ641212121212000000-4-400000000044-4-4-4-4-444000000000000000000000000000000000000000000000
χ651212121212000000-4-4000000000-4-444-4-44-44000000000000000000000000000000000000000000000
χ661212121212000000-4-4000000000-4-4-4-44444-4000000000000000000000000000000000000000000000
χ6712121212-12000000-44000444444000000000-4-4-4000000000000000000000000000000000000000000
χ6812121212-12000000-4400044-4-4-4-4000000000-444000000000000000000000000000000000000000000
χ6912121212-12000000-44000-4-444-4-40000000004-44000000000000000000000000000000000000000000
χ7012121212-12000000-44000-4-4-4-44400000000044-4000000000000000000000000000000000000000000
χ712424-24-240000012-12000000000-440000-44000000000000000000000000000000000000000000000000
χ722424-24-2400000-12120000000004-40000-44000000000000000000000000000000000000000000000000
χ7324-2424-2400012-12000000000-440000-4400000000000000000000000000000000000000000000000000
χ7424-2424-24000-12120000000004-40000-4400000000000000000000000000000000000000000000000000
χ7524-24-2424012-12000000000-440000-440000000000000000000000000000000000000000000000000000
χ7624-24-24240-12120000000004-40000-440000000000000000000000000000000000000000000000000000

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