Finite Group Databasebeta

← Group #11923337

Character table — Group #11923337

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122244444466888888121212161616162244488888812121616161616162424243232323233666121212121212181824242424242436363648484848
order1248822336624121224242424448666636122424663366612121224242424121224666622488226666241212242424244486666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i32
χ31111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i32
χ411111-1-1111111111111-1-11-1-1-1-111111-1-1111111111111-1-11-1-1-1-111111-1-1111111111111-1-11-1-1-1-1
χ511111-1-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321+i321−i321−i3211111-1-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321+i321−i321−i3211111-1-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321+i321−i321−i32
χ611111-1-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321−i321+i321+i3211111-1-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321−i321+i321+i3211111-1-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321−i321+i321+i32
χ7111-1-11-111111111-1-1-1-11-1-11-11-1111-1-11-111111111-1-1-1-11-1-11-11-1111-1-11-111111111-1-1-1-11-1-11-11-1
χ8111-1-11-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i321-1-1−1−i321+i32−1+i321−i32111-1-11-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i321-1-1−1−i321+i32−1+i321−i32111-1-11-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i321-1-1−1−i321+i32−1+i321−i32
χ9111-1-11-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i321-1-1−1+i321−i32−1−i321+i32111-1-11-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i321-1-1−1+i321−i32−1−i321+i32111-1-11-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i321-1-1−1+i321−i32−1−i321+i32
χ10111-1-1-1111111111-1-1-1-1-11-1-11-11111-1-1-1111111111-1-1-1-1-11-1-11-11111-1-1-1111111111-1-1-1-1-11-1-11-11
χ11111-1-1-11−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i32-11-11+i32−1−i321−i32−1+i32111-1-1-11−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i32-11-11+i32−1−i321−i32−1+i32111-1-1-11−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i32-11-11+i32−1−i321−i32−1+i32
χ12111-1-1-11−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i32-11-11−i32−1+i321+i32−1−i32111-1-1-11−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i32-11-11−i32−1+i321+i32−1−i32111-1-1-11−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i32-11-11−i32−1+i321+i32−1−i32
χ1322-200002222-22-2-20000000000022-200002222-22-2-20000000000022-200002222-22-2-200000000000
χ1422-20000−1−i3−1+i3−1−i3−1+i3-221+i31−i30000000000022-20000−1−i3−1+i3−1−i3−1+i3-221+i31−i30000000000022-20000−1−i3−1+i3−1−i3−1+i3-221+i31−i300000000000
χ1522-20000−1+i3−1−i3−1+i3−1−i3-221−i31+i30000000000022-20000−1+i3−1−i3−1+i3−1−i3-221−i31+i30000000000022-20000−1+i3−1−i3−1+i3−1−i3-221−i31+i300000000000
χ1633333330000-1-1000000-1-1-1000033333330000-1-1000000-1-1-1000033333330000-1-1000000-1-1-10000
χ1733333-3-30000-1-100000011-1000033333-3-30000-1-100000011-1000033333-3-30000-1-100000011-10000
χ18333-3-33-30000-1-1000000-1110000333-3-33-30000-1-1000000-1110000333-3-33-30000-1-1000000-1110000
χ19333-3-3-330000-1-10000001-110000333-3-3-330000-1-10000001-110000333-3-3-330000-1-10000001-110000
χ204-4022−2200-2-22200002−22−200000004-4022−2200-2-22200002−22−200000004-4022−2200-2-22200002−22−20000000
χ214-4022−22001+i31−i3−1−i3−1+i30000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ2300000004-4022−22001+i31−i3−1−i3−1+i30000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ2300000004-4022−22001+i31−i3−1−i3−1+i30000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000
χ224-4022−22001−i31+i3−1+i3−1−i30000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ1300000004-4022−22001−i31+i3−1+i3−1−i30000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ1300000004-4022−22001−i31+i3−1+i3−1−i30000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000000
χ234-40−222200-2-2220000−22−2200000004-40−222200-2-2220000−22−2200000004-40−222200-2-2220000−22−220000000
χ244-40−2222001+i31−i3−1−i3−1+i30000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ2300000004-40−2222001+i31−i3−1−i3−1+i30000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ2300000004-40−2222001+i31−i3−1−i3−1+i30000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000
χ254-40−2222001−i31+i3−1+i3−1−i30000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ1300000004-40−2222001−i31+i3−1+i3−1−i30000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ1300000004-40−2222001−i31+i3−1+i3−1−i30000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000000
χ2666-6000000002-2000000000000066-6000000002-2000000000000066-6000000002-20000000000000
χ271111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ281111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-11+i321−i321+i321−i32-1-11+i321−i321+i321+i321−i321−i32-1-1-11+i321+i321−i321−i32
χ291111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-11−i321+i321−i321+i32-1-11−i321+i321−i321−i321+i321+i32-1-1-11−i321−i321+i321+i32
χ3011111-1-1111111111111-1-11-1-1-1-111111-1-1111111111111-1-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11111
χ3111111-1-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321+i321−i321−i3211111-1-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321+i321−i321−i32-1-1-1-1-1111+i321−i321+i321−i32-1-11+i321−i321+i321+i321−i321−i3211-1−1−i32−1−i32−1+i32−1+i32
χ3211111-1-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321−i321+i321+i3211111-1-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321−i321+i321+i32-1-1-1-1-1111−i321+i321−i321+i32-1-11−i321+i321−i321−i321+i321+i3211-1−1+i32−1+i32−1−i32−1−i32
χ33111-1-11-111111111-1-1-1-11-1-11-11-1111-1-11-111111111-1-1-1-11-1-11-11-1-1-1-111-11-1-1-1-1-1-1-1-11111-111-11-11
χ34111-1-11-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i321-1-1−1−i321+i32−1+i321−i32111-1-11-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i321-1-1−1−i321+i32−1+i321−i32-1-1-111-111+i321−i321+i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i32-1111+i32−1−i321−i32−1+i32
χ35111-1-11-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i321-1-1−1+i321−i32−1−i321+i32111-1-11-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i321-1-1−1+i321−i32−1−i321+i32-1-1-111-111−i321+i321−i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i32-1111−i32−1+i321+i32−1−i32
χ36111-1-1-1111111111-1-1-1-1-11-1-11-11111-1-1-1111111111-1-1-1-1-11-1-11-11-1-1-1111-1-1-1-1-1-1-1-1-111111-111-11-1
χ37111-1-1-11−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i32-11-11+i32−1−i321−i32−1+i32111-1-1-11−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i32-11-11+i32−1−i321−i32−1+i32-1-1-1111-11+i321−i321+i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i321-11−1−i321+i32−1+i321−i32
χ38111-1-1-11−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i32-11-11−i32−1+i321+i32−1−i32111-1-1-11−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i32-11-11−i32−1+i321+i32−1−i32-1-1-1111-11−i321+i321−i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i321-11−1+i321−i32−1−i321+i32
χ3922-200002222-22-2-20000000000022-200002222-22-2-200000000000-2-220000-2-2-2-22-22200000000000
χ4022-20000−1−i3−1+i3−1−i3−1+i3-221+i31−i30000000000022-20000−1−i3−1+i3−1−i3−1+i3-221+i31−i300000000000-2-2200001+i31−i31+i31−i32-2−1−i3−1+i300000000000
χ4122-20000−1+i3−1−i3−1+i3−1−i3-221−i31+i30000000000022-20000−1+i3−1−i3−1+i3−1−i3-221−i31+i300000000000-2-2200001−i31+i31−i31+i32-2−1+i3−1−i300000000000
χ4233333330000-1-1000000-1-1-1000033333330000-1-1000000-1-1-10000-3-3-3-3-3-3-30000110000001110000
χ4333333-3-30000-1-100000011-1000033333-3-30000-1-100000011-10000-3-3-3-3-333000011000000-1-110000
χ44333-3-33-30000-1-1000000-1110000333-3-33-30000-1-1000000-1110000-3-3-333-330000110000001-1-10000
χ45333-3-3-330000-1-10000001-110000333-3-3-330000-1-10000001-110000-3-3-3333-3000011000000-11-10000
χ464-4022−2200-2-22200002−22−200000004-4022−2200-2-22200002−22−20000000-440−22220022-2-20000−22−220000000
χ474-4022−22001+i31−i3−1−i3−1+i30000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ2300000004-4022−22001+i31−i3−1−i3−1+i30000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000-440−222200−1−i3−1+i31+i31−i30000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000
χ484-4022−22001−i31+i3−1+i3−1−i30000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ1300000004-4022−22001−i31+i3−1+i3−1−i30000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000000-440−222200−1+i3−1−i31−i31+i30000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000000
χ494-40−222200-2-2220000−22−2200000004-40−222200-2-2220000−22−220000000-44022−220022-2-200002−22−20000000
χ504-40−2222001+i31−i3−1−i3−1+i30000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ2300000004-40−2222001+i31−i3−1−i3−1+i30000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000-44022−2200−1−i3−1+i31+i31−i30000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000
χ514-40−2222001−i31+i3−1+i3−1−i30000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ1300000004-40−2222001−i31+i3−1+i3−1−i30000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000000-44022−2200−1+i3−1−i31−i31+i30000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000000
χ5266-6000000002-2000000000000066-6000000002-20000000000000-6-6600000000-220000000000000
χ5322222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ542222222−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3222−1−i3−1−i3−1+i3−1+i3-1-1-1-1-1-1-11+i321−i321+i321−i32-1-11+i321−i321+i321+i321−i321−i32-1-1-11+i321+i321−i321−i3200000000000000000000000000
χ552222222−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3222−1+i3−1+i3−1−i3−1−i3-1-1-1-1-1-1-11−i321+i321−i321+i32-1-11−i321+i321−i321−i321+i321+i32-1-1-11−i321−i321+i321+i3200000000000000000000000000
χ5622222-2-2222222222222-2-22-2-2-2-2-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1111100000000000000000000000000
χ5722222-2-2−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-221+i31+i31−i31−i3-1-1-1-1-1111+i321−i321+i321−i32-1-11+i321−i321+i321+i321−i321−i3211-1−1−i32−1−i32−1+i32−1+i3200000000000000000000000000
χ5822222-2-2−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-221−i31−i31+i31+i3-1-1-1-1-1111−i321+i321−i321+i32-1-11−i321+i321−i321−i321+i321+i3211-1−1+i32−1+i32−1−i32−1−i3200000000000000000000000000
χ59222-2-22-222222222-2-2-2-22-2-22-22-2-1-1-111-11-1-1-1-1-1-1-1-11111-111-11-1100000000000000000000000000
χ60222-2-22-2−1−i3−1+i3−1−i3−1+i322−1−i3−1+i31+i31+i31−i31−i32-2-2−1−i31+i3−1+i31−i3-1-1-111-111+i321−i321+i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i32-1111+i32−1−i321−i32−1+i3200000000000000000000000000
χ61222-2-22-2−1+i3−1−i3−1+i3−1−i322−1+i3−1−i31−i31−i31+i31+i32-2-2−1+i31−i3−1−i31+i3-1-1-111-111−i321+i321−i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i32-1111−i32−1+i321+i32−1−i3200000000000000000000000000
χ62222-2-2-2222222222-2-2-2-2-22-2-22-22-1-1-1111-1-1-1-1-1-1-1-1-111111-111-11-100000000000000000000000000
χ63222-2-2-22−1−i3−1+i3−1−i3−1+i322−1−i3−1+i31+i31+i31−i31−i3-22-21+i3−1−i31−i3−1+i3-1-1-1111-11+i321−i321+i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i321-11−1−i321+i32−1+i321−i3200000000000000000000000000
χ64222-2-2-22−1+i3−1−i3−1+i3−1−i322−1+i3−1−i31−i31−i31+i31+i3-22-21−i3−1+i31+i3−1−i3-1-1-1111-11−i321+i321−i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i321-11−1+i321−i32−1−i321+i3200000000000000000000000000
χ6544-400004444-44-4-400000000000-2-220000-2-2-2-22-2220000000000000000000000000000000000000
χ6644-40000−2−2i3−2+2i3−2−2i3−2+2i3-442+2i32−2i300000000000-2-2200001+i31−i31+i31−i32-2−1−i3−1+i30000000000000000000000000000000000000
χ6744-40000−2+2i3−2−2i3−2+2i3−2−2i3-442−2i32+2i300000000000-2-2200001−i31+i31−i31+i32-2−1+i3−1−i30000000000000000000000000000000000000
χ6866666660000-2-2000000-2-2-20000-3-3-3-3-3-3-3000011000000111000000000000000000000000000000
χ6966666-6-60000-2-200000022-20000-3-3-3-3-333000011000000-1-11000000000000000000000000000000
χ70666-6-66-60000-2-2000000-2220000-3-3-333-330000110000001-1-1000000000000000000000000000000
χ71666-6-6-660000-2-20000002-220000-3-3-3333-3000011000000-11-1000000000000000000000000000000
χ728-8042−4200-4-444000022−2222−220000000-440−22220022-2-20000−22−22000000000000000000000000000000000
χ738-8042−42002+2i32−2i3−2−2i3−2+2i30000−2ζ7+2ζ132ζ7−2ζ132ζ5−2ζ23−2ζ5+2ζ230000000-440−222200−1−i3−1+i31+i31−i30000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ23000000000000000000000000000000000
χ748-8042−42002−2i32+2i3−2+2i3−2−2i300002ζ5−2ζ23−2ζ5+2ζ23−2ζ7+2ζ132ζ7−2ζ130000000-440−222200−1+i3−1−i31−i31+i30000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ13000000000000000000000000000000000
χ758-80−424200-4-4440000−2222−22220000000-44022−220022-2-200002−22−2000000000000000000000000000000000
χ768-80−4242002+2i32−2i3−2−2i3−2+2i300002ζ7−2ζ13−2ζ7+2ζ13−2ζ5+2ζ232ζ5−2ζ230000000-44022−2200−1−i3−1+i31+i31−i30000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ23000000000000000000000000000000000
χ778-80−4242002−2i32+2i3−2+2i3−2−2i30000−2ζ5+2ζ232ζ5−2ζ232ζ7−2ζ13−2ζ7+2ζ130000000-44022−2200−1+i3−1−i31−i31+i30000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ13000000000000000000000000000000000
χ781212-12000000004-40000000000000-6-6600000000-22000000000000000000000000000000000000000

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