Finite Group Databasebeta

← Group #72220575

Character table — Group #72220575

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122333344666666666688881212121212121212121212121212161616161616161616162424242432323232323232323232323248486464646464646464
order1222222222242222222222222222222222244444334466666644446666666666664466121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ31111111111111111111111111111111111111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ41111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-1-11-1-1
χ51111111111111111111111-1-1-1-111111111111111−1+i32−1−i32-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ61111111111111111111111-1-1-1-111111111111111−1−i32−1+i32-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ71111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ81111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321−i321−i321+i321+i321+i32
χ91111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321+i321+i321−i321−i321−i32
χ101111111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-111-111
χ111111111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32111−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ121111111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32111+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ131111-1-111111-111111111-1-111-1-1-1-1-1-111111-1-1-1-1-1111-111111111-1-1-1-111-1-1-1-111-1-11-111-11-1-11-1
χ141111-1-111111-111111111-1-111-1-1-1-1-1-111111-1-1-1-1-1−1+i32−1−i321-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-11−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i321-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ151111-1-111111-111111111-1-111-1-1-1-1-1-111111-1-1-1-1-1−1−i32−1+i321-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-11+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i321-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ161111-1-111111-111111111-1-1-1-111-1-1-1-111111-1-1-1-1-111-11111111-1-111-1-1-1-111-1-1-1-111-1111-1-11-1-11
χ171111-1-111111-111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1−1+i32−1−i32-11−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1111−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ181111-1-111111-111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1−1−i32−1+i32-11−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1111+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ191111-1-11111-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-11111111-1111111111-1-1-1-111-1-1-1-111-1-1-11-1-11-111-11
χ201111-1-11111-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-111111−1+i32−1−i32-11−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-11−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32-111−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ211111-1-11111-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-111111−1−i32−1+i32-11−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-11+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32-111+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ221111-1-11111-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1111111-1-111-1-1-1-111-1-1-1-1111-1-1-111-111-1
χ231111-1-11111-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-111111−1+i32−1−i321-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1111−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321-11−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ241111-1-11111-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-111111−1−i32−1+i321-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1111+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321-11+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ2522-2-200-22-22002222-2-2-2-200002-20000000000000022002-2-22-2-2002-200002-200002-20000000000
χ2622-2-200-22-22002222-2-2-2-200002-200000000000000−1+i3−1−i300−1+i31−i31−i3−1−i31+i31+i3002-20000−1+i31−i30000−1−i31+i30000000000
χ2722-2-200-22-22002222-2-2-2-200002-200000000000000−1−i3−1+i300−1−i31+i31+i3−1+i31−i31−i3002-20000−1−i31+i30000−1+i31−i30000000000
χ2822-2-200-22-22002222-2-2-2-20000-220000000000000022002-2-22-2-200-220000-220000-220000000000
χ2922-2-200-22-22002222-2-2-2-20000-2200000000000000−1+i3−1−i300−1+i31−i31−i3−1−i31+i31+i300-2200001−i3−1+i300001+i3−1−i30000000000
χ3022-2-200-22-22002222-2-2-2-20000-2200000000000000−1−i3−1+i300−1−i31+i31+i3−1+i31−i31−i300-2200001+i3−1−i300001−i3−1+i30000000000
χ312-22-200-2-2220022-2-222-2-2002-200000000000000002200-22-2-22-22-200002-200002-2000000000000
χ322-22-200-2-2220022-2-222-2-2002-20000000000000000−1+i3−1−i3001−i3−1+i31−i31+i3−1−i31+i32-20000−1+i31−i30000−1−i31+i3000000000000
χ332-22-200-2-2220022-2-222-2-2002-20000000000000000−1−i3−1+i3001+i3−1−i31+i31−i3−1+i31−i32-20000−1−i31+i30000−1+i31−i3000000000000
χ342-22-200-2-2220022-2-222-2-200-2200000000000000002200-22-2-22-2-220000-220000-22000000000000
χ352-22-200-2-2220022-2-222-2-200-220000000000000000−1+i3−1−i3001−i3−1+i31−i31+i3−1−i31+i3-2200001−i3−1+i300001+i3−1−i3000000000000
χ362-22-200-2-2220022-2-222-2-200-220000000000000000−1−i3−1+i3001+i3−1−i31+i31−i3−1+i31−i3-2200001+i3−1−i300001−i3−1+i3000000000000
χ372-2-222-22-2-220022-2-2-2-2222-2000022-2-200000000002200-2-22-2-2200002-200002-200000000000000
χ382-2-222-22-2-220022-2-2-2-2222-2000022-2-20000000000−1+i3−1−i3001−i31−i3−1+i31+i31+i3−1−i30000−1+i31−i30000−1−i31+i300000000000000
χ392-2-222-22-2-220022-2-2-2-2222-2000022-2-20000000000−1−i3−1+i3001+i31+i3−1−i31−i31−i3−1+i30000−1−i31+i30000−1+i31−i300000000000000
χ402-2-22-222-2-220022-2-2-2-222-220000-2-22200000000002200-2-22-2-220000-220000-2200000000000000
χ412-2-22-222-2-220022-2-2-2-222-220000-2-2220000000000−1+i3−1−i3001−i31−i3−1+i31+i31+i3−1−i300001−i3−1+i300001+i3−1−i300000000000000
χ422-2-22-222-2-220022-2-2-2-222-220000-2-2220000000000−1−i3−1+i3001+i31+i3−1−i31−i31−i3−1+i300001+i3−1−i300001−i3−1+i300000000000000
χ43333333333333-1-1-1-1-1-1-1-1333333-1-1-1-13-1-1-1-13-1-1-1-10033000000-1-1-1-1000000000000-1-100000000
χ44333333333333-1-1-1-1-1-1-1-133-3-3-3-3-1-1-1-13-1-1-1-13-1-1-1-100-3-300000011110000000000001100000000
χ453333333333-3-3-1-1-1-1-1-1-1-1333333-1-1-1-1-31111-3111100-3-3000000-1-1-1-10000000000001100000000
χ463333333333-3-3-1-1-1-1-1-1-1-133-3-3-3-3-1-1-1-1-31111-3111100330000001111000000000000-1-100000000
χ473333-3-333333-3-1-1-1-1-1-1-1-1-3-333-3-311113-1-1-1-1-31111003-3000000-1-111000000000000-1100000000
χ483333-3-333333-3-1-1-1-1-1-1-1-1-3-3-3-33311113-1-1-1-1-3111100-3300000011-1-10000000000001-100000000
χ493333-3-33333-33-1-1-1-1-1-1-1-1-3-333-3-31111-311113-1-1-1-100-33000000-1-1110000000000001-100000000
χ503333-3-33333-33-1-1-1-1-1-1-1-1-3-3-3-3331111-311113-1-1-1-1003-300000011-1-1000000000000-1100000000
χ51666666-2-2-2-2662-22-22-22-2-2-200002-22-2-222-2-2-222-2-2000000000000000000000000000000000000
χ52666666-2-2-2-266-22-22-22-22-2-20000-22-22-2-2-222-2-2-222000000000000000000000000000000000000
χ53666666-2-2-2-2-6-62-22-22-22-2-2-200002-22-22-2-2222-2-222000000000000000000000000000000000000
χ54666666-2-2-2-2-6-6-22-22-22-22-2-20000-22-22222-2-2222-2-2000000000000000000000000000000000000
χ556666-6-6-2-2-2-26-62-22-22-22-2220000-22-22-222-2-22-2-222000000000000000000000000000000000000
χ566666-6-6-2-2-2-26-6-22-22-22-222200002-22-2-2-2-222222-2-2000000000000000000000000000000000000
χ576666-6-6-2-2-2-2-662-22-22-22-2220000-22-222-2-222-222-2-2000000000000000000000000000000000000
χ586666-6-6-2-2-2-2-66-22-22-22-222200002-22-2222-2-2-2-2-222000000000000000000000000000000000000
χ5966-6-600-66-6600-2-2-2-2222200006-600000000000000000000000000-220000000000000000000000
χ6066-6-600-66-6600-2-2-2-222220000-66000000000000000000000000002-20000000000000000000000
χ616-66-600-6-66600-2-222-2-222006-600000000000000000000000000-22000000000000000000000000
χ626-66-600-6-66600-2-222-2-22200-66000000000000000000000000002-2000000000000000000000000
χ636-6-666-66-6-6600-2-22222-2-26-60000-2-2220000000000000000000000000000000000000000000000
χ646-6-666-6-222-2002-2-22-222-2-2200002-2-2204-40004-400000000000000000000000000000000000000
χ656-6-666-6-222-2002-2-22-222-2-2200002-2-220-44000-4400000000000000000000000000000000000000
χ666-6-666-6-222-200-222-22-2-22-220000-222-20004-40004-4000000000000000000000000000000000000
χ676-6-666-6-222-200-222-22-2-22-220000-222-2000-44000-44000000000000000000000000000000000000
χ686-6-66-666-6-6600-2-22222-2-2-66000022-2-20000000000000000000000000000000000000000000000
χ696-6-66-66-222-2002-2-22-222-22-20000-222-204-4000-4400000000000000000000000000000000000000
χ706-6-66-66-222-2002-2-22-222-22-20000-222-20-440004-400000000000000000000000000000000000000
χ716-6-66-66-222-200-222-22-2-222-200002-2-220004-4000-44000000000000000000000000000000000000
χ726-6-66-66-222-200-222-22-2-222-200002-2-22000-440004-4000000000000000000000000000000000000
χ731212-12-12004-44-4004-44-4-44-4400000000000000000000000000000000000000000000000000000000
χ741212-12-12004-44-400-44-444-44-400000000000000000000000000000000000000000000000000000000
χ7512-1212-120044-4-4004-4-444-4-4400000000000000000000000000000000000000000000000000000000
χ7612-1212-120044-4-400-444-4-444-400000000000000000000000000000000000000000000000000000000

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