Finite Group Databasebeta

← Group #11724283

Character table — Group #11724283

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112444488991212121218181818182424242411244448899121212121818181818242424241124444889912121212181818181824242424
order12433661212224444488881212121236123366121266121212121224242424121212123612336612126612121212122424242412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-11-1-1-1-111-1-11111111111111-1-11-1-1-1-111-1-11111111111111-1-11-1-1-1-111-1-1
χ311111111111-1-1111-1-1-1-1-1-11111111111111-1-1111-1-1-1-1-1-11111111111111-1-1111-1-1-1-1-1-111
χ411111111111-1-1-1-111111-1-1-1-111111111111-1-1-1-111111-1-1-1-111111111111-1-1-1-111111-1-1-1-1
χ511-11111-1-1-1-11-11-1111-1-11-11-111-11111-1-1-1-11-11-1111-1-11-11-111-11111-1-1-1-11-11-1111-1-11-11-1
χ611-11111-1-1-1-11-1-111-1-1111-1-1111-11111-1-1-1-11-1-111-1-1111-1-1111-11111-1-1-1-11-1-111-1-1111-1-11
χ711-11111-1-1-1-1-111-11-1-111-111-111-11111-1-1-1-1-111-11-1-111-111-111-11111-1-1-1-1-111-11-1-111-111-1
χ811-11111-1-1-1-1-11-11111-1-1-11-1111-11111-1-1-1-1-11-11111-1-1-11-1111-11111-1-1-1-1-11-11111-1-1-11-11
χ9222222222-2-20000-200000000222222222-2-20000-200000000222222222-2-20000-200000000
χ1022-22222-2-2220000-20000000022-22222-2-2220000-20000000022-22222-2-2220000-200000000
χ112-2022-2-2002-2000002−22−200002-2022-2-2002-2000002−22−200002-2022-2-2002-2000002−22−20000
χ122-2022-2-2002-200000−22−2200002-2022-2-2002-200000−22−2200002-2022-2-2002-200000−22−220000
χ132-2022-2-200-22000002−2−2200002-2022-2-200-22000002−2−2200002-2022-2-200-22000002−2−220000
χ142-2022-2-200-2200000−222−200002-2022-2-200-2200000−222−200002-2022-2-200-2200000−222−20000
χ154441-21-21-20000220000000-1-14441-21-21-20000220000000-1-14441-21-21-20000220000000-1-1
χ164441-21-21-20000-2-20000000114441-21-21-20000-2-20000000114441-21-21-20000-2-2000000011
χ17444-21-21-2100220000000-1-100444-21-21-2100220000000-1-100444-21-21-2100220000000-1-100
χ18444-21-21-2100-2-200000001100444-21-21-2100-2-200000001100444-21-21-2100-2-200000001100
χ1944-41-21-2-1200002-20000000-1144-41-21-2-1200002-20000000-1144-41-21-2-1200002-20000000-11
χ2044-41-21-2-120000-2200000001-144-41-21-2-120000-2200000001-144-41-21-2-120000-2200000001-1
χ2144-4-21-212-1002-20000000-110044-4-21-212-1002-20000000-110044-4-21-212-1002-20000000-1100
χ2244-4-21-212-100-2200000001-10044-4-21-212-100-2200000001-10044-4-21-212-100-2200000001-100
χ238-802-4-24000000000000000008-802-4-24000000000000000008-802-4-2400000000000000000
χ248-80-424-2000000000000000008-80-424-2000000000000000008-80-424-200000000000000000
χ25111111111111111111111111−1+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+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ261111111111111-1-11-1-1-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−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−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ2711111111111-1-1111-1-1-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−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−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ2811111111111-1-1-1-111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ2911-11111-1-1-1-11-11-1111-1-11-11-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32
χ3011-11111-1-1-1-11-1-111-1-1111-1-11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ3111-11111-1-1-1-1-111-11-1-111-111-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ3211-11111-1-1-1-1-11-11111-1-1-11-11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32
χ33222222222-2-20000-200000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i300001−i300000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i300001+i300000000
χ3422-22222-2-2220000-200000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i300001−i300000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i300001+i300000000
χ352-2022-2-2002-2000002−22−20000−1+i31−i30−1+i3−1+i31−i31−i300−1+i31−i300000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ230000−1−i31+i30−1−i3−1−i31+i31+i300−1−i31+i300000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ130000
χ362-2022-2-2002-200000−22−220000−1+i31−i30−1+i3−1+i31−i31−i300−1+i31−i300000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ230000−1−i31+i30−1−i3−1−i31+i31+i300−1−i31+i300000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ130000
χ372-2022-2-200-22000002−2−220000−1+i31−i30−1+i3−1+i31−i31−i3001−i3−1+i300000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ230000−1−i31+i30−1−i3−1−i31+i31+i3001+i3−1−i300000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ130000
χ382-2022-2-200-2200000−222−20000−1+i31−i30−1+i3−1+i31−i31−i3001−i3−1+i300000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ230000−1−i31+i30−1−i3−1−i31+i31+i3001+i3−1−i300000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ130000
χ394441-21-21-20000220000000-1-1−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i321−i30000−1+i3−1+i300000001−i321−i32−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i321+i30000−1−i3−1−i300000001+i321+i32
χ404441-21-21-20000-2-2000000011−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i321−i300001−i31−i30000000−1+i32−1+i32−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i321+i300001+i31+i30000000−1−i32−1−i32
χ41444-21-21-2100220000000-1-100−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i3−1+i3200−1+i3−1+i300000001−i321−i3200−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i3−1−i3200−1−i3−1−i300000001+i321+i3200
χ42444-21-21-2100-2-200000001100−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i3−1+i32001−i31−i30000000−1+i32−1+i3200−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i3−1−i32001+i31+i30000000−1−i32−1−i3200
χ4344-41-21-2-1200002-20000000-11−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i32−1+i30000−1+i31−i300000001−i32−1+i32−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i32−1−i30000−1−i31+i300000001+i32−1−i32
χ4444-41-21-2-120000-2200000001-1−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i32−1+i300001−i3−1+i30000000−1+i321−i32−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i32−1−i300001+i3−1−i30000000−1−i321+i32
χ4544-4-21-212-1002-20000000-1100−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i31−i3200−1+i31−i300000001−i32−1+i3200−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i31+i3200−1−i31+i300000001+i32−1−i3200
χ4644-4-21-212-100-2200000001-100−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i31−i32001−i3−1+i30000000−1+i321−i3200−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i31+i32001+i3−1−i30000000−1−i321+i3200
χ478-802-4-2400000000000000000−4+4i34−4i30−1+i32−2i31−i3−2+2i300000000000000000−4−4i34+4i30−1−i32+2i31+i3−2−2i300000000000000000
χ488-80-424-200000000000000000−4+4i34−4i302−2i3−1+i3−2+2i31−i300000000000000000−4−4i34+4i302+2i3−1−i3−2−2i31+i300000000000000000
χ49111111111111111111111111−1−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−i32−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ501111111111111-1-11-1-1-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+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+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32
χ5111111111111-1-1111-1-1-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+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+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ5211111111111-1-1-1-111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ5311-11111-1-1-1-11-11-1111-1-11-11-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32
χ5411-11111-1-1-1-11-1-111-1-1111-1-11−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32
χ5511-11111-1-1-1-1-111-11-1-111-111-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ5611-11111-1-1-1-1-11-11111-1-1-11-11−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i32
χ57222222222-2-20000-200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i300001+i300000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i300001−i300000000
χ5822-22222-2-2220000-200000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i300001+i300000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i300001−i300000000
χ592-2022-2-2002-2000002−22−20000−1−i31+i30−1−i3−1−i31+i31+i300−1−i31+i300000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ130000−1+i31−i30−1+i3−1+i31−i31−i300−1+i31−i300000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ230000
χ602-2022-2-2002-200000−22−220000−1−i31+i30−1−i3−1−i31+i31+i300−1−i31+i300000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ130000−1+i31−i30−1+i3−1+i31−i31−i300−1+i31−i300000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ230000
χ612-2022-2-200-22000002−2−220000−1−i31+i30−1−i3−1−i31+i31+i3001+i3−1−i300000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ130000−1+i31−i30−1+i3−1+i31−i31−i3001−i3−1+i300000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ230000
χ622-2022-2-200-2200000−222−20000−1−i31+i30−1−i3−1−i31+i31+i3001+i3−1−i300000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ130000−1+i31−i30−1+i3−1+i31−i31−i3001−i3−1+i300000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ230000
χ634441-21-21-20000220000000-1-1−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i321+i30000−1−i3−1−i300000001+i321+i32−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i321−i30000−1+i3−1+i300000001−i321−i32
χ644441-21-21-20000-2-2000000011−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i321+i300001+i31+i30000000−1−i32−1−i32−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i321−i300001−i31−i30000000−1+i32−1+i32
χ65444-21-21-2100220000000-1-100−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i3−1−i3200−1−i3−1−i300000001+i321+i3200−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i3−1+i3200−1+i3−1+i300000001−i321−i3200
χ66444-21-21-2100-2-200000001100−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i3−1−i32001+i31+i30000000−1−i32−1−i3200−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i3−1+i32001−i31−i30000000−1+i32−1+i3200
χ6744-41-21-2-1200002-20000000-11−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i32−1−i30000−1−i31+i300000001+i32−1−i32−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i32−1+i30000−1+i31−i300000001−i32−1+i32
χ6844-41-21-2-120000-2200000001-1−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i32−1−i300001+i3−1−i30000000−1−i321+i32−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i32−1+i300001−i3−1+i30000000−1+i321−i32
χ6944-4-21-212-1002-20000000-1100−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i31+i3200−1−i31+i300000001+i32−1−i3200−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i31−i3200−1+i31−i300000001−i32−1+i3200
χ7044-4-21-212-100-2200000001-100−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i31+i32001+i3−1−i30000000−1−i321+i3200−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i31−i32001−i3−1+i30000000−1+i321−i3200
χ718-802-4-2400000000000000000−4−4i34+4i30−1−i32+2i31+i3−2−2i300000000000000000−4+4i34−4i30−1+i32−2i31−i3−2+2i300000000000000000
χ728-80-424-200000000000000000−4−4i34+4i302+2i3−1−i3−2−2i31+i300000000000000000−4+4i34−4i302−2i3−1+i3−2+2i31−i300000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.