Finite Group Databasebeta

← Group #11923333

Character table — Group #11923333

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122244444466888888121212161616162244488888812121616161616162424243232323233666121212121212181824242424242436363648484848
order1248823346624121224242424248661212361224246331266612121224242424612246612122248826646624121224242424248661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i32
χ3111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i32
χ411111-111-11111111111-1-11-1-1-1-111111-111-11111111111-1-11-1-1-1-111111-111-11111111111-1-11-1-1-1-1
χ511111-1−1−i32−1+i32-1−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321−i321+i321−i3211111-1−1−i32−1+i32-1−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321−i321+i321−i3211111-1−1−i32−1+i32-1−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321−i321+i321−i32
χ611111-1−1+i32−1−i32-1−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321+i321−i321+i3211111-1−1+i32−1−i32-1−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321+i321−i321+i3211111-1−1+i32−1−i32-1−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321+i321−i321+i32
χ7111-1-1111-1111111-1-1-1-1-11-111-1-1111-1-1111-1111111-1-1-1-1-11-111-1-1111-1-1111-1111111-1-1-1-1-11-111-1-1
χ8111-1-11−1−i32−1+i32-1−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i32-11-1−1−i32−1+i321+i321−i32111-1-11−1−i32−1+i32-1−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i32-11-1−1−i32−1+i321+i321−i32111-1-11−1−i32−1+i32-1−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i32-11-1−1−i32−1+i321+i321−i32
χ9111-1-11−1+i32−1−i32-1−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i32-11-1−1+i32−1−i321−i321+i32111-1-11−1+i32−1−i32-1−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i32-11-1−1+i32−1−i321−i321+i32111-1-11−1+i32−1−i32-1−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i32-11-1−1+i32−1−i321−i321+i32
χ10111-1-1-1111111111-1-1-1-11-1-1-1-111111-1-1-1111111111-1-1-1-11-1-1-1-111111-1-1-1111111111-1-1-1-11-1-1-1-111
χ11111-1-1-1−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i321-1-11+i321−i32−1−i32−1+i32111-1-1-1−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i321-1-11+i321−i32−1−i32−1+i32111-1-1-1−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i321-1-11+i321−i32−1−i32−1+i32
χ12111-1-1-1−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i321-1-11−i321+i32−1+i32−1−i32111-1-1-1−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i321-1-11−i321+i32−1+i32−1−i32111-1-1-1−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i321-1-11−i321+i32−1+i32−1−i32
χ1322-200022022-22-2-20000000000022-200022022-22-2-20000000000022-200022022-22-2-200000000000
χ1422-2000−1−i3−1+i30−1−i3−1+i3-221+i31−i30000000000022-2000−1−i3−1+i30−1−i3−1+i3-221+i31−i30000000000022-2000−1−i3−1+i30−1−i3−1+i3-221+i31−i300000000000
χ1522-2000−1+i3−1−i30−1+i3−1−i3-221−i31+i30000000000022-2000−1+i3−1−i30−1+i3−1−i3-221−i31+i30000000000022-2000−1+i3−1−i30−1+i3−1−i3-221−i31+i300000000000
χ1633333300300-1-1000000-1-1-1000033333300300-1-1000000-1-1-1000033333300300-1-1000000-1-1-10000
χ1733333-300-300-1-100000011-1000033333-300-300-1-100000011-1000033333-300-300-1-100000011-10000
χ18333-3-3300-300-1-10000001-110000333-3-3300-300-1-10000001-110000333-3-3300-300-1-10000001-110000
χ19333-3-3-300300-1-1000000-1110000333-3-3-300300-1-1000000-1110000333-3-3-300300-1-1000000-1110000
χ204-40−2i22i20-2-20220000−i2i2−i2i200000004-40−2i22i20-2-20220000−i2i2−i2i200000004-40−2i22i20-2-20220000−i2i2−i2i20000000
χ214-40−2i22i201+i31−i30−1−i3−1+i30000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ2300000004-40−2i22i201+i31−i30−1−i3−1+i30000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ2300000004-40−2i22i201+i31−i30−1−i3−1+i30000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ230000000
χ224-40−2i22i201−i31+i30−1+i3−1−i30000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ1300000004-40−2i22i201−i31+i30−1+i3−1−i30000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ1300000004-40−2i22i201−i31+i30−1+i3−1−i30000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ130000000
χ234-402i2−2i20-2-20220000i2−i2i2−i200000004-402i2−2i20-2-20220000i2−i2i2−i200000004-402i2−2i20-2-20220000i2−i2i2−i20000000
χ244-402i2−2i201+i31−i30−1−i3−1+i30000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ2300000004-402i2−2i201+i31−i30−1−i3−1+i30000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ2300000004-402i2−2i201+i31−i30−1−i3−1+i30000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ230000000
χ254-402i2−2i201−i31+i30−1+i3−1−i30000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ1300000004-402i2−2i201−i31+i30−1+i3−1−i30000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ1300000004-402i2−2i201−i31+i30−1+i3−1−i30000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+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
χ28111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-11+i321−i32-11+i321−i32-1-11+i321−i321+i321+i321−i321−i32-1-1-11+i321−i321+i321−i32
χ29111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-11−i321+i32-11−i321+i32-1-11−i321+i321−i321−i321+i321+i32-1-1-11−i321+i321−i321+i32
χ3011111-111-11111111111-1-11-1-1-1-111111-111-11111111111-1-11-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111-11111
χ3111111-1−1−i32−1+i32-1−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321−i321+i321−i3211111-1−1−i32−1+i32-1−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321−i321+i321−i32-1-1-1-1-111+i321−i3211+i321−i32-1-11+i321−i321+i321+i321−i321−i3211-1−1−i32−1+i32−1−i32−1+i32
χ3211111-1−1+i32−1−i32-1−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321+i321−i321+i3211111-1−1+i32−1−i32-1−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321+i321−i321+i32-1-1-1-1-111−i321+i3211−i321+i32-1-11−i321+i321−i321−i321+i321+i3211-1−1+i32−1−i32−1+i32−1−i32
χ33111-1-1111-1111111-1-1-1-1-11-111-1-1111-1-1111-1111111-1-1-1-1-11-111-1-1-1-1-111-1-1-11-1-1-1-1-1-111111-11-1-111
χ34111-1-11−1−i32−1+i32-1−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i32-11-1−1−i32−1+i321+i321−i32111-1-11−1−i32−1+i32-1−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i32-11-1−1−i32−1+i321+i321−i32-1-1-111-11+i321−i3211+i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i321-111+i321−i32−1−i32−1+i32
χ35111-1-11−1+i32−1−i32-1−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i32-11-1−1+i32−1−i321−i321+i32111-1-11−1+i32−1−i32-1−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i32-11-1−1+i32−1−i321−i321+i32-1-1-111-11−i321+i3211−i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i321-111−i321+i32−1+i32−1−i32
χ36111-1-1-1111111111-1-1-1-11-1-1-1-111111-1-1-1111111111-1-1-1-11-1-1-1-111-1-1-1111-1-1-1-1-1-1-1-1-11111-11111-1-1
χ37111-1-1-1−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i321-1-11+i321−i32−1−i32−1+i32111-1-1-1−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321+i321+i321−i321−i321-1-11+i321−i32−1−i32−1+i32-1-1-11111+i321−i32-11+i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i32-111−1−i32−1+i321+i321−i32
χ38111-1-1-1−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i321-1-11−i321+i32−1+i32−1−i32111-1-1-1−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−i321−i321+i321+i321-1-11−i321+i32−1+i32−1−i32-1-1-11111−i321+i32-11−i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i32-111−1+i32−1−i321−i321+i32
χ3922-200022022-22-2-20000000000022-200022022-22-2-200000000000-2-22000-2-20-2-22-22200000000000
χ4022-2000−1−i3−1+i30−1−i3−1+i3-221+i31−i30000000000022-2000−1−i3−1+i30−1−i3−1+i3-221+i31−i300000000000-2-220001+i31−i301+i31−i32-2−1−i3−1+i300000000000
χ4122-2000−1+i3−1−i30−1+i3−1−i3-221−i31+i30000000000022-2000−1+i3−1−i30−1+i3−1−i3-221−i31+i300000000000-2-220001−i31+i301−i31+i32-2−1+i3−1−i300000000000
χ4233333300300-1-1000000-1-1-1000033333300300-1-1000000-1-1-10000-3-3-3-3-3-300-300110000001110000
χ4333333-300-300-1-100000011-1000033333-300-300-1-100000011-10000-3-3-3-3-330030011000000-1-110000
χ44333-3-3300-300-1-10000001-110000333-3-3300-300-1-10000001-110000-3-3-333-30030011000000-11-10000
χ45333-3-3-300300-1-1000000-1110000333-3-3-300300-1-1000000-1110000-3-3-333300-300110000001-1-10000
χ464-40−2i22i20-2-20220000−i2i2−i2i200000004-40−2i22i20-2-20220000−i2i2−i2i20000000-4402i2−2i20220-2-20000i2−i2i2−i20000000
χ474-40−2i22i201+i31−i30−1−i3−1+i30000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ2300000004-40−2i22i201+i31−i30−1−i3−1+i30000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ230000000-4402i2−2i20−1−i3−1+i301+i31−i30000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ230000000
χ484-40−2i22i201−i31+i30−1+i3−1−i30000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ1300000004-40−2i22i201−i31+i30−1+i3−1−i30000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ130000000-4402i2−2i20−1+i3−1−i301−i31+i30000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ130000000
χ494-402i2−2i20-2-20220000i2−i2i2−i200000004-402i2−2i20-2-20220000i2−i2i2−i20000000-440−2i22i20220-2-20000−i2i2−i2i20000000
χ504-402i2−2i201+i31−i30−1−i3−1+i30000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ2300000004-402i2−2i201+i31−i30−1−i3−1+i30000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ230000000-440−2i22i20−1−i3−1+i301+i31−i30000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ230000000
χ514-402i2−2i201−i31+i30−1+i3−1−i30000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ1300000004-402i2−2i201−i31+i30−1+i3−1−i30000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ130000000-440−2i22i20−1+i3−1−i301−i31+i30000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−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
χ54222222−1−i3−1+i32−1−i3−1+i322−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3222−1−i3−1+i3−1−i3−1+i3-1-1-1-1-1-11+i321−i32-11+i321−i32-1-11+i321−i321+i321+i321−i321−i32-1-1-11+i321−i321+i321−i3200000000000000000000000000
χ55222222−1+i3−1−i32−1+i3−1−i322−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3222−1+i3−1−i3−1+i3−1−i3-1-1-1-1-1-11−i321+i32-11−i321+i32-1-11−i321+i321−i321−i321+i321+i32-1-1-11−i321+i321−i321+i3200000000000000000000000000
χ5622222-222-22222222222-2-22-2-2-2-2-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111-1111100000000000000000000000000
χ5722222-2−1−i3−1+i3-2−1−i3−1+i322−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-221+i31−i31+i31−i3-1-1-1-1-111+i321−i3211+i321−i32-1-11+i321−i321+i321+i321−i321−i3211-1−1−i32−1+i32−1−i32−1+i3200000000000000000000000000
χ5822222-2−1+i3−1−i3-2−1+i3−1−i322−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-221−i31+i31−i31+i3-1-1-1-1-111−i321+i3211−i321+i32-1-11−i321+i321−i321−i321+i321+i3211-1−1+i32−1−i32−1+i32−1−i3200000000000000000000000000
χ59222-2-2222-2222222-2-2-2-2-22-222-2-2-1-1-111-1-1-11-1-1-1-1-1-111111-11-1-11100000000000000000000000000
χ60222-2-22−1−i3−1+i3-2−1−i3−1+i322−1−i3−1+i31+i31+i31−i31−i3-22-2−1−i3−1+i31+i31−i3-1-1-111-11+i321−i3211+i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i321-111+i321−i32−1−i32−1+i3200000000000000000000000000
χ61222-2-22−1+i3−1−i3-2−1+i3−1−i322−1+i3−1−i31−i31−i31+i31+i3-22-2−1+i3−1−i31−i31+i3-1-1-111-11−i321+i3211−i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i321-111−i321+i32−1+i32−1−i3200000000000000000000000000
χ62222-2-2-2222222222-2-2-2-22-2-2-2-222-1-1-1111-1-1-1-1-1-1-1-1-11111-11111-1-100000000000000000000000000
χ63222-2-2-2−1−i3−1+i32−1−i3−1+i322−1−i3−1+i31+i31+i31−i31−i32-2-21+i31−i3−1−i3−1+i3-1-1-11111+i321−i32-11+i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i32-111−1−i32−1+i321+i321−i3200000000000000000000000000
χ64222-2-2-2−1+i3−1−i32−1+i3−1−i322−1+i3−1−i31−i31−i31+i31+i32-2-21−i31+i3−1+i3−1−i3-1-1-11111−i321+i32-11−i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i32-111−1+i32−1−i321−i321+i3200000000000000000000000000
χ6544-400044044-44-4-400000000000-2-22000-2-20-2-22-2220000000000000000000000000000000000000
χ6644-4000−2−2i3−2+2i30−2−2i3−2+2i3-442+2i32−2i300000000000-2-220001+i31−i301+i31−i32-2−1−i3−1+i30000000000000000000000000000000000000
χ6744-4000−2+2i3−2−2i30−2+2i3−2−2i3-442−2i32+2i300000000000-2-220001−i31+i301−i31+i32-2−1+i3−1−i30000000000000000000000000000000000000
χ6866666600600-2-2000000-2-2-20000-3-3-3-3-3-300-30011000000111000000000000000000000000000000
χ6966666-600-600-2-200000022-20000-3-3-3-3-330030011000000-1-11000000000000000000000000000000
χ70666-6-6600-600-2-20000002-220000-3-3-333-30030011000000-11-1000000000000000000000000000000
χ71666-6-6-600600-2-2000000-2220000-3-3-333300-300110000001-1-1000000000000000000000000000000
χ728-80−4i24i20-4-40440000−2i22i2−2i22i20000000-4402i2−2i20220-2-20000i2−i2i2−i2000000000000000000000000000000000
χ738-80−4i24i202+2i32−2i30−2−2i3−2+2i300002ζ7+2ζ13−2ζ7−2ζ132ζ5+2ζ23−2ζ5−2ζ230000000-4402i2−2i20−1−i3−1+i301+i31−i30000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ23000000000000000000000000000000000
χ748-80−4i24i202−2i32+2i30−2+2i3−2−2i300002ζ5+2ζ23−2ζ5−2ζ232ζ7+2ζ13−2ζ7−2ζ130000000-4402i2−2i20−1+i3−1−i301−i31+i30000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ13000000000000000000000000000000000
χ758-804i2−4i20-4-404400002i2−2i22i2−2i20000000-440−2i22i20220-2-20000−i2i2−i2i2000000000000000000000000000000000
χ768-804i2−4i202+2i32−2i30−2−2i3−2+2i30000−2ζ7−2ζ132ζ7+2ζ13−2ζ5−2ζ232ζ5+2ζ230000000-440−2i22i20−1−i3−1+i301+i31−i30000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ23000000000000000000000000000000000
χ778-804i2−4i202−2i32+2i30−2+2i3−2−2i30000−2ζ5−2ζ232ζ5+2ζ23−2ζ7−2ζ132ζ7+2ζ130000000-440−2i22i20−1+i3−1−i301−i31+i30000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ13000000000000000000000000000000000
χ781212-12000000004-40000000000000-6-6600000000-22000000000000000000000000000000000000000

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