Finite Group Databasebeta

← Group #13166122

Character table — Group #13166122

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45
size12234661212121212121212121212121616242432323232363636484848486464727296969696108144144
order133236622461212121212121212336633332246666336126666466
χ1111111111111111111111111111111111111111111111
χ21111111111111111111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32
χ31111111111111111111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32
χ411111111-11111111111111-11111-1-111-11-111-111-11-1-1-1-1
χ511111111-11111111111−1−i32−1+i321-1−1−i32−1−i32−1+i32−1+i32-1-11−1−i321+i32−1+i321−i32−1−i32−1+i32-11−1−i321+i32−1+i321−i32-11+i321−i32
χ611111111-11111111111−1+i32−1−i321-1−1+i32−1+i32−1−i32−1−i32-1-11−1+i321−i32−1−i321+i32−1+i32−1−i32-11−1+i321−i32−1−i321+i32-11−i321+i32
χ71111111-11111111111111-1111111-1-1-11-11111-1-11-11-1-1-1
χ81111111-111111111111−1−i32−1+i32-11−1−i32−1−i32−1+i32−1+i321-1-11+i32−1−i321−i32−1+i32−1−i32−1+i321-11+i32−1−i321−i32−1+i32-11+i321−i32
χ91111111-111111111111−1+i32−1−i32-11−1+i32−1+i32−1−i32−1−i321-1-11−i32−1+i321+i32−1−i32−1+i32−1−i321-11−i32−1+i321+i32−1−i32-11−i321+i32
χ101111111-1-1111111111111-1-11111-11-1-1-1-1-111-1-1-1-1-1-1111
χ111111111-1-11111111111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32-11-11+i321+i321−i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32
χ121111111-1-11111111111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32-11-11−i321−i321+i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32
χ1322-12-1-12022-1-1-122-1-1-1-1220-12-12-12000202-1-1-100-10-1000
χ1422-12-1-12022-1-1-122-1-1-1-1−1−i3−1+i30-1−1−i31+i32−1+i31−i322000−1−i30−1+i31+i321−i32-1001+i3201−i32000
χ1522-12-1-12022-1-1-122-1-1-1-1−1+i3−1−i30-1−1+i31−i32−1−i31+i322000−1+i30−1−i31−i321+i32-1001−i3201+i32000
χ1622-12-1-120-22-1-1-122-1-1-1-122012-12-1-2000-20-2-1-1100101000
χ1722-12-1-120-22-1-1-122-1-1-1-1−1−i3−1+i301−1−i31+i32−1+i31−i32-20001+i301−i31+i321−i32100−1−i320−1+i32000
χ1822-12-1-120-22-1-1-122-1-1-1-1−1+i3−1−i301−1+i31−i32−1−i31+i32-20001−i301+i31−i321+i32100−1+i320−1−i32000
χ192-122-12-1202-122-1-1-1-1-1-122-10-12-120022020-1-10-1-10-10000
χ202-122-12-1202-122-1-1-1-1-1-1−1−i3−1+i3-101+i32−1−i31−i32−1+i3002−1−i30−1+i301+i321−i320-11+i3201−i320000
χ212-122-12-1202-122-1-1-1-1-1-1−1+i3−1−i3-101−i32−1+i31+i32−1−i3002−1+i30−1−i301−i321+i320-11−i3201+i320000
χ222-122-12-1-202-122-1-1-1-1-1-12210-12-1200-2-20-20-1-1011010000
χ232-122-12-1-202-122-1-1-1-1-1-1−1−i3−1+i3101+i32−1−i31−i32−1+i300-21+i301−i301+i321−i3201−1−i320−1+i320000
χ242-122-12-1-202-122-1-1-1-1-1-1−1+i3−1−i3101−i32−1+i31+i32−1−i300-21−i301+i301−i321+i3201−1+i320−1−i320000
χ25333333333-13-1-1-1-1-1-1-1-100330000-13-1000000-1-10000-100
χ2633333333-3-13-1-1-1-1-1-1-1-1003-300001-3-10000001-10000100
χ273333333-33-13-1-1-1-1-1-1-1-100-330000-1-31000000-110000100
χ283333333-3-3-13-1-1-1-1-1-1-1-100-3-30000131000000110000-100
χ294-2-241-2-20041-2-2-2-211114400-2-2-2-2000000011000000000
χ304-2-241-2-20041-2-2-2-21111−2−2i3−2+2i3001+i31+i31−i31−i30000000−1−i32−1+i32000000000
χ314-2-241-2-20041-2-2-2-21111−2+2i3−2−2i3001−i31−i31+i31+i30000000−1+i32−1−i32000000000
χ3266-36-3-3606-2-311-2-21111000-30000-200000000100000000
χ3366-36-3-360-6-2-311-2-2111100030000200000000-100000000
χ346-366-36-360-2-3-2-211111100-30000000-2000000010000000
χ356-366-36-3-60-2-3-2-2111111003000000020000000-10000000
χ36121212-412-4-4000-40000000000000000000000000000000000
χ371212-6-4-62-40002−2i32i300−2i3−2i32i32i300000000000000000000000000
χ381212-6-4-62-400022i3−2i3002i32i3−2i3−2i300000000000000000000000000
χ3912-612-4-6-4200020023−2323−2323−2300000000000000000000000000
χ4012-612-4-6-42000200−2323−2323−232300000000000000000000000000
χ4112-6-6123-6-600-432222-1-1-1-100000000000000000000000000
χ4212-6-6-4322000-1−2i32i323−23ζ2−2ζ7−ζ10−4ζ11ζ2+2ζ7−ζ10+4ζ11−ζ2+4ζ7+ζ10+2ζ11−ζ2−4ζ7+ζ10−2ζ1100000000000000000000000000
χ4312-6-6-4322000-1−2i32i3−2323ζ2+2ζ7−ζ10+4ζ11ζ2−2ζ7−ζ10−4ζ11−ζ2−4ζ7+ζ10−2ζ11−ζ2+4ζ7+ζ10+2ζ1100000000000000000000000000
χ4412-6-6-4322000-12i3−2i323−23−ζ2+4ζ7+ζ10+2ζ11−ζ2−4ζ7+ζ10−2ζ11ζ2−2ζ7−ζ10−4ζ11ζ2+2ζ7−ζ10+4ζ1100000000000000000000000000
χ4512-6-6-4322000-12i3−2i3−2323−ζ2−4ζ7+ζ10−2ζ11−ζ2+4ζ7+ζ10+2ζ11ζ2+2ζ7−ζ10+4ζ11ζ2−2ζ7−ζ10−4ζ1100000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.