Finite Group Databasebeta

← Group #13146937

Character table — Group #13146937

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1122233334444666666661212121212121212121212121212121212242424242424363636363636484848484848484848727272727272727272
order12346336626612246612121212466666121212121212121212121233366644121212126666661212122668824242424
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1
χ3111111111-1-1-1111111111-1111-1-11-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1111-1-1-11-111-1-1
χ4111111111-1-1-1111111111-1111-1-11-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-111
χ511111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ611111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321−i321+i321−i32
χ711111−1−i32−1+i32−1−i32−1+i32-1-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11−1−i32−1+i321+i321−i321-1-1−1−i32−1+i321+i321+i321+i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-11+i321−i321-1−1−i32−1+i321+i321−i32
χ811111−1−i32−1+i32−1−i32−1+i32-1-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11−1−i32−1+i321+i321−i321-1-1−1−i32−1+i321+i321+i321+i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-111+i321−i32−1−i32−1+i32
χ911111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ1011111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321+i321−i321+i32
χ1111111−1+i32−1−i32−1+i32−1−i32-1-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−1+i32−1−i321−i321+i321-1-1−1+i32−1−i321−i321−i321−i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-11−i321+i321-1−1+i32−1−i321−i321+i32
χ1211111−1+i32−1−i32−1+i32−1−i32-1-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−1+i32−1−i321−i321+i321-1-1−1+i32−1−i321−i321−i321−i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-111−i321+i32−1+i32−1−i32
χ1322222222222222222222222222222222222222-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1000000000
χ14222222222-2-2-2222222222-2222-2-22-2-222-2-2-2-2-2-2-1-1-1-1-1-1000000111111-1-1-1000000000
χ1522222−1−i3−1+i3−1−i3−1+i3222222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322−1−i3−1+i3−1−i3−1+i3222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-11+i321−i32-11+i321−i32000000-1-11+i321+i321−i321−i32-11+i321−i32000000000
χ1622222−1−i3−1+i3−1−i3−1+i3-2-2-2222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-22−1−i3−1+i31+i31−i32-2-2−1−i3−1+i31+i31+i31+i31−i31−i31−i3-11+i321−i32-11+i321−i3200000011−1−i32−1−i32−1+i32−1+i32-11+i321−i32000000000
χ1722222−1+i3−1−i3−1+i3−1−i3222222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322−1+i3−1−i3−1+i3−1−i3222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-11−i321+i32-11−i321+i32000000-1-11−i321−i321+i321+i32-11−i321+i32000000000
χ1822222−1+i3−1−i3−1+i3−1−i3-2-2-2222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-22−1+i3−1−i31−i31+i32-2-2−1+i3−1−i31−i31−i31−i31+i31+i31+i3-11−i321+i32-11−i321+i3200000011−1+i32−1+i32−1−i32−1−i32-11−i321+i32000000000
χ19222-222222000-2-22-2-22-22-20-2-2-20020022000000222222000000000000-2-2-2000000000
χ20222-222222000-2-22-2-22-22-20-2-2-20020022000000-1-1-1-1-1-1000000−i3i3−i3i3−i3i3111000000000
χ21222-222222000-2-22-2-22-22-20-2-2-20020022000000-1-1-1-1-1-1000000i3−i3i3−i3i3−i3111000000000
χ22222-22−1−i3−1+i3−1−i3−1+i3000-2-221+i31−i3−1−i31+i3−1+i31−i30-21+i31−i300200−1−i3−1+i30000002−1−i3−1+i32−1−i3−1+i3000000000000-21+i31−i3000000000
χ23222-22−1−i3−1+i3−1−i3−1+i3000-2-221+i31−i3−1−i31+i3−1+i31−i30-21+i31−i300200−1−i3−1+i3000000-11+i321−i32-11+i321−i32000000−i3i3−3+i323−i323+i32−3−i321−1−i32−1+i32000000000
χ24222-22−1−i3−1+i3−1−i3−1+i3000-2-221+i31−i3−1−i31+i3−1+i31−i30-21+i31−i300200−1−i3−1+i3000000-11+i321−i32-11+i321−i32000000i3−i33−i32−3+i32−3−i323+i321−1−i32−1+i32000000000
χ25222-22−1+i3−1−i3−1+i3−1−i3000-2-221−i31+i3−1+i31−i3−1−i31+i30-21−i31+i300200−1+i3−1−i30000002−1+i3−1−i32−1+i3−1−i3000000000000-21−i31+i3000000000
χ26222-22−1+i3−1−i3−1+i3−1−i3000-2-221−i31+i3−1+i31−i3−1−i31+i30-21−i31+i300200−1+i3−1−i3000000-11−i321+i32-11−i321+i32000000−i3i33+i32−3−i32−3+i323−i321−1+i32−1−i32000000000
χ27222-22−1+i3−1−i3−1+i3−1−i3000-2-221−i31+i3−1+i31−i3−1−i31+i30-21−i31+i300200−1+i3−1−i3000000-11−i321+i32-11−i321+i32000000i3−i3−3−i323+i323−i32−3+i321−1+i32−1−i32000000000
χ283333333333333-1-1-1-1-13-13-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1000000111111000000000-1-1-1-11-1-111
χ293333333333333-1-1-1-1-13-13-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-10000000001111-111-1-1
χ30333333333-3-3-33-1-1-1-1-13-131-1-1-1-3-3-111-1-1111111000000111111000000000111-1-1-1-1-1-1
χ31333333333-3-3-33-1-1-1-1-13-131-1-1-1-3-3-111-1-1111111000000-1-1-1-1-1-1000000000-1-1-1111111
χ3233333−3−3i32−3+3i32−3−3i32−3+3i323333-1-11+i321−i321+i32−3−3i321−i32−3+3i32-1-11+i321−i32−3−3i32−3+3i32-1-1-11+i321−i321+i321+i321+i321−i321−i321−i3200000011−1−i32−1−i32−1+i32−1+i32000000000-11+i321−i32-111+i321−i32−1−i32−1+i32
χ3333333−3−3i32−3+3i32−3−3i32−3+3i323333-1-11+i321−i321+i32−3−3i321−i32−3+3i32-1-11+i321−i32−3−3i32−3+3i32-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32000000-1-11+i321+i321−i321−i320000000001−1−i32−1+i321-1−1−i32−1+i321+i321−i32
χ3433333−3−3i32−3+3i32−3−3i32−3+3i32-3-3-33-1-11+i321−i321+i32−3−3i321−i32−3+3i321-11+i321−i323+3i323−3i32-1111+i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000011−1−i32−1−i32−1+i32−1+i320000000001−1−i32−1+i32-1-11+i321−i321+i321−i32
χ3533333−3−3i32−3+3i32−3−3i32−3+3i32-3-3-33-1-11+i321−i321+i32−3−3i321−i32−3+3i321-11+i321−i323+3i323−3i32-1111+i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000-1-11+i321+i321−i321−i32000000000-11+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ3633333−3+3i32−3−3i32−3+3i32−3−3i323333-1-11−i321+i321−i32−3+3i321+i32−3−3i32-1-11−i321+i32−3+3i32−3−3i32-1-1-11−i321+i321−i321−i321−i321+i321+i321+i3200000011−1+i32−1+i32−1−i32−1−i32000000000-11−i321+i32-111−i321+i32−1+i32−1−i32
χ3733333−3+3i32−3−3i32−3+3i32−3−3i323333-1-11−i321+i321−i32−3+3i321+i32−3−3i32-1-11−i321+i32−3+3i32−3−3i32-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32000000-1-11−i321−i321+i321+i320000000001−1+i32−1−i321-1−1+i32−1−i321−i321+i32
χ3833333−3+3i32−3−3i32−3+3i32−3−3i32-3-3-33-1-11−i321+i321−i32−3+3i321+i32−3−3i321-11−i321+i323−3i323+3i32-1111−i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000011−1+i32−1+i32−1−i32−1−i320000000001−1+i32−1−i32-1-11−i321+i321−i321+i32
χ3933333−3+3i32−3−3i32−3+3i32−3−3i32-3-3-33-1-11−i321+i321−i32−3+3i321+i32−3−3i321-11−i321+i323−3i323+3i32-1111−i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000-1-11−i321−i321+i321+i32000000000-11−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ404-440-444-4-400000000000000000000000000000-2-2-22222i−2i2i−2i2i−2i000000000000000000
χ414-440-444-4-400000000000000000000000000000-2-2-2222−2i2i−2i2i−2i2i000000000000000000
χ424-440-4−2−2i3−2+2i32+2i32−2i300000000000000000000000000000-21+i31−i32−1−i3−1+i32i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000000
χ434-440-4−2−2i3−2+2i32+2i32−2i300000000000000000000000000000-21+i31−i32−1−i3−1+i3−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000000
χ444-440-4−2+2i3−2−2i32−2i32+2i300000000000000000000000000000-21−i31+i32−1+i3−1−i32i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000000
χ454-440-4−2+2i3−2−2i32−2i32+2i300000000000000000000000000000-21−i31+i32−1+i3−1−i3−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000000
χ46666-666666000-62-222-2-6-2-6022200-200-2-2000000000000000000000000000000000000
χ47666-66−3−3i3−3+3i3−3−3i3−3+3i3000-62-2−1−i3−1+i31+i33+3i31−i33−3i302−1−i3−1+i300-2001+i31−i3000000000000000000000000000000000000
χ48666-66−3+3i3−3−3i3−3+3i3−3−3i3000-62-2−1+i3−1−i31−i33−3i31+i33+3i302−1+i3−1−i300-2001−i31+i3000000000000000000000000000000000000
χ4966-36-300006-3-3-3660000006-30000-3-3-300000000000000000000000000000000000000
χ5066-36-300006-3-3-3-2-2444040-21-2-200111-2-24-2-24-2-2000000000000000000000000000000
χ5166-36-300006-3-3-3-2-2−2−2i3−2+2i3−2−2i30−2+2i30-211+i31−i3001111+i31−i3−2−2i31+i31+i3−2+2i31−i31−i3000000000000000000000000000000
χ5266-36-300006-3-3-3-2-2−2+2i3−2−2i3−2+2i30−2−2i30-211−i31+i3001111−i31+i3−2+2i31−i31−i3−2−2i31+i31+i3000000000000000000000000000000
χ5366-36-30000-633-366000000-6-30000-33300000000000000000000000000000000000000
χ5466-36-30000-633-3-2-244404021-2-2001-1-1-2-2-422-422000000000000000000000000000000
χ5566-36-30000-633-3-2-2−2−2i3−2+2i3−2−2i30−2+2i30211+i31−i3001-1-11+i31−i32+2i3−1−i3−1−i32−2i3−1+i3−1+i3000000000000000000000000000000
χ5666-36-30000-633-3-2-2−2+2i3−2−2i3−2+2i30−2−2i30211−i31+i3001-1-11−i31+i32−2i3−1+i3−1+i32+2i3−1−i3−1−i3000000000000000000000000000000
χ5766-3-6-300000−3i33i332-2-4-440400-122001−i3i3-2-20−2i32i30−2i32i3000000000000000000000000000000
χ5866-3-6-300000−3i33i332-22+2i32−2i3−2−2i30−2+2i300-1−1−i3−1+i3001−i3i31+i31−i30−3+i33−i303+i3−3−i3000000000000000000000000000000
χ5966-3-6-300000−3i33i332-22−2i32+2i3−2+2i30−2−2i300-1−1+i3−1−i3001−i3i31−i31+i303+i3−3−i30−3+i33−i3000000000000000000000000000000
χ6066-3-6-300000−3i33i33-66000000030000-33i3−3i300000000000000000000000000000000000000
χ6166-3-6-3000003i3−3i332-2-4-440400-122001i3−i3-2-202i3−2i302i3−2i3000000000000000000000000000000
χ6266-3-6-3000003i3−3i332-22+2i32−2i3−2−2i30−2+2i300-1−1−i3−1+i3001i3−i31+i31−i303−i3−3+i30−3−i33+i3000000000000000000000000000000
χ6366-3-6-3000003i3−3i332-22−2i32+2i3−2+2i30−2−2i300-1−1+i3−1−i3001i3−i31−i31+i30−3−i33+i303−i3−3+i3000000000000000000000000000000
χ6466-3-6-3000003i3−3i33-66000000030000-3−3i33i300000000000000000000000000000000000000
χ658-880-888-8-800000000000000000000000000000222-2-2-2000000000000000000000000
χ668-880-8−4−4i3−4+4i34+4i34−4i3000000000000000000000000000002−1−i3−1+i3-21+i31−i3000000000000000000000000
χ678-880-8−4+4i3−4−4i34−4i34+4i3000000000000000000000000000002−1+i3−1−i3-21−i31+i3000000000000000000000000
χ6824-24-12012000000000000000000000000000000000000000000000000000000000000000

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