Finite Group Databasebeta

← Group #13164640

Character table — Group #13164640

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222444666666991212121212121212121212121212121212121212121212181818242424242424242424243636363648484848484854545454727272727272
order1222346661223444644336666666612121212121212121212121212244336666661212121212126666121222246612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111−1−i32−1+i32111111−1−i32−1+i321111111111111111−1−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+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ3111111111111111111−1+i32−1−i32111111−1+i32−1−i321111111111111111−1+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−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ41111111111111111-1-111111111111111111111111-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ51111111111111111-1-1−1−i32−1+i32111111−1−i32−1+i321111111111111-1-1-1−1−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−i32−1+i32-1-1-1-11+i321−i321+i321+i321−i321−i32
χ61111111111111111-1-1−1+i32−1−i32111111−1+i32−1−i321111111111111-1-1-1−1+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+i32−1−i32-1-1-1-11−i321+i321−i321−i321+i321+i32
χ7111-11-111-1-1-1111-111111-11-1-1-1-11111-1111111-1-1-1-1-11-1111-11-111-1-111111-11-1-1-111-1-1-1-11-11-1
χ8111-11-111-1-1-1111-1111−1−i32−1+i32-11-1-1-1-1−1−i32−1+i3211-1111111-1-1-1-1-11-1−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i321+i321−i3211-1-11+i321−i32−1−i321+i32−1+i321−i32
χ9111-11-111-1-1-1111-1111−1+i32−1−i32-11-1-1-1-1−1+i32−1−i3211-1111111-1-1-1-1-11-1−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−i321+i3211-1-11−i321+i32−1+i321−i32−1−i321+i32
χ10111-11-111-1-1-1111-11-1-111-11-1-1-1-11111-1111111-1-1-1-11-11111-11-111-1-1-1-1-1-11-11-1-1-1-1-11111-11-11
χ11111-11-111-1-1-1111-11-1-1−1−i32−1+i32-11-1-1-1-1−1−i32−1+i3211-1111111-1-1-1-11-11−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i321+i32−1+i321−i321+i321−i32-1-111−1−i32−1+i321+i32−1−i321−i32−1+i32
χ12111-11-111-1-1-1111-11-1-1−1+i32−1−i32-11-1-1-1-1−1+i32−1−i3211-1111111-1-1-1-11-11−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i321−i32−1−i321+i321−i321+i32-1-111−1+i32−1−i321−i32−1+i321+i32−1−i32
χ1311-111-11-11-1-111-1111111-1-11-1-1-1111-11111-1-1-1111-1-1-1111-11-1111-1-11111-11-11-1-11-11-1-1-1-11-11
χ1411-111-11-11-1-111-11111−1−i32−1+i32-1-11-1-1-1−1−i32−1+i321-11111-1-1-1111-1-1-11−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i321+i321−i321-11-11+i321−i321+i32−1−i321−i32−1+i32
χ1511-111-11-11-1-111-11111−1+i32−1−i32-1-11-1-1-1−1+i32−1−i321-11111-1-1-1111-1-1-11−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i321−i321+i321-11-11−i321+i321−i32−1+i321+i32−1−i32
χ1611-111-11-11-1-111-111-1-111-1-11-1-1-1111-11111-1-1-1111-111-111-11-1111-1-1-1-1-1-1-11-11-1-1-11-11111-11-1
χ1711-111-11-11-1-111-111-1-1−1−i32−1+i32-1-11-1-1-1−1−i32−1+i321-11111-1-1-1111-111-1−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i321+i32−1−i321−i32−1+i321+i321−i32-11-11−1−i32−1+i32−1−i321+i32−1+i321−i32
χ1811-111-11-11-1-111-111-1-1−1+i32−1−i32-1-11-1-1-1−1+i32−1−i321-11111-1-1-1111-111-1−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i321−i32−1+i321+i32−1−i321−i321+i32-11-11−1+i32−1−i32−1+i321−i32−1−i321+i32
χ1911-1-1111-1-11111-1-1111111-1-1111111-1-1111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1111-1-1111-1-1-1-1
χ2011-1-1111-1-11111-1-1111−1−i32−1+i321-1-1111−1−i32−1+i321-1-1111-1-1-1-1-1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1-11−1−i32−1+i321+i321+i321−i321−i32
χ2111-1-1111-1-11111-1-1111−1+i32−1−i321-1-1111−1+i32−1−i321-1-1111-1-1-1-1-1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i321-1-11−1+i32−1−i321−i321−i321+i321+i32
χ2211-1-1111-1-11111-1-11-1-1111-1-1111111-1-1111-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-11111
χ2311-1-1111-1-11111-1-11-1-1−1−i32−1+i321-1-1111−1−i32−1+i321-1-1111-1-1-1-1-1-11-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32-111-11+i321−i32−1−i32−1−i32−1+i32−1+i32
χ2411-1-1111-1-11111-1-11-1-1−1+i32−1−i321-1-1111−1+i32−1−i321-1-1111-1-1-1-1-1-11-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32-111-11−i321+i32−1+i32−1+i32−1−i32−1−i32
χ2522222222222-1222-100222-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1000-1-12222-1-1220000-1-1-1-1-1-10000000000
χ2622222222222-1222-100−1−i3−1+i32-1-1-1-1-1−1−i3−1+i3222-1-1-1-1-1-1-1-1-1-10001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i300001+i321+i321−i321−i321+i321−i320000000000
χ2722222222222-1222-100−1+i3−1−i32-1-1-1-1-1−1+i3−1−i3222-1-1-1-1-1-1-1-1-1-10001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i300001−i321−i321+i321+i321−i321+i320000000000
χ28222-22-222-2-2-2-122-2-10022-2-111112222-2-1-1-1-1-1-11111000-1-12-22-2-1-1-2-20000-11-11110000000000
χ29222-22-222-2-2-2-122-2-100−1−i3−1+i3-2-11111−1−i3−1+i322-2-1-1-1-1-1-111110001+i321−i32−1−i31+i3−1+i31−i31+i321−i321+i31−i300001+i32−1−i321−i32−1+i32−1−i32−1+i320000000000
χ30222-22-222-2-2-2-122-2-100−1+i3−1−i3-2-11111−1+i3−1−i322-2-1-1-1-1-1-111110001−i321+i32−1+i31−i3−1−i31+i31−i321+i321−i31+i300001−i32−1+i321+i32−1−i32−1+i32−1−i320000000000
χ3122-222-22-22-2-2-12-22-10022-21-1111222-22-1-1-1111-1-1-11000-1-1-22-22-1-1-2-200001-11-1110000000000
χ3222-222-22-22-2-2-12-22-100−1−i3−1+i3-21-1111−1−i3−1+i32-22-1-1-1111-1-1-110001+i321−i321+i3−1−i31−i3−1+i31+i321−i321+i31−i30000−1−i321+i32−1+i321−i32−1−i32−1+i320000000000
χ3322-222-22-22-2-2-12-22-100−1+i3−1−i3-21-1111−1+i3−1−i32-22-1-1-1111-1-1-110001−i321+i321−i3−1+i31+i3−1−i31−i321+i321−i31+i30000−1+i321−i32−1−i321+i32−1+i32−1−i320000000000
χ3422-2-2222-2-222-12-2-2-10022211-1-1-1222-2-2-1-1-1111111-1000-1-1-2-2-2-2-1-12200001111-1-10000000000
χ3522-2-2222-2-222-12-2-2-100−1−i3−1+i3211-1-1-1−1−i3−1+i32-2-2-1-1-1111111-10001+i321−i321+i31+i31−i31−i31+i321−i32−1−i3−1+i30000−1−i32−1−i32−1+i32−1+i321+i321−i320000000000
χ3622-2-2222-2-222-12-2-2-100−1+i3−1−i3211-1-1-1−1+i3−1−i32-2-2-1-1-1111111-10001−i321+i321−i31−i31+i31+i31−i321+i32−1+i3−1−i30000−1+i32−1+i32−1−i32−1−i321−i321+i320000000000
χ373333333333-13-1-1-133300-133-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1333300000000000000000000-1-1-1-1000000
χ383333333333-13-1-1-13-3-300-133-1-1-100-1-1-1-1-1-1-1-1-1-1-1-13-3-3-3000000000000000000001111000000
χ39333-33-333-3-313-1-113330013-311100-1-11-1-1-1-1-1-1111-3-33-300000000000000000000-1-111000000
χ40333-33-333-3-313-1-113-3-30013-311100-1-11-1-1-1-1-1-1111-33-330000000000000000000011-1-1000000
χ4133-333-33-33-313-11-1333001-3311100-11-1-1-1-1111-1-1-1-3-3-3300000000000000000000-11-11000000
χ4233-333-33-33-313-11-13-3-3001-3311100-11-1-1-1-1111-1-1-1-333-3000000000000000000001-11-1000000
χ4333-3-3333-3-33-13-11133300-1-3-3-1-1-100-111-1-1-111111133-3-300000000000000000000-111-1000000
χ4433-3-3333-3-33-13-1113-3-300-1-3-3-1-1-100-111-1-1-11111113-333000000000000000000001-1-11000000
χ454-40040-400004000-44i−4i-2-2000000220000000000000000-2-2000022002i−2i2i−2i0000000000000000
χ464-40040-400004000-44i−4i1+i31−i3000000−1−i3−1+i300000000000000001+i31−i30000−1−i3−1+i3002ζ11−2ζ112ζ7−2ζ70000000000000000
χ474-40040-400004000-44i−4i1−i31+i3000000−1+i3−1−i300000000000000001−i31+i30000−1+i3−1−i3002ζ7−2ζ72ζ11−2ζ110000000000000000
χ484-40040-400004000-4−4i4i-2-2000000220000000000000000-2-200002200−2i2i−2i2i0000000000000000
χ494-40040-400004000-4−4i4i1+i31−i3000000−1−i3−1+i300000000000000001+i31−i30000−1−i3−1+i300−2ζ112ζ11−2ζ72ζ70000000000000000
χ504-40040-400004000-4−4i4i1−i31+i3000000−1+i3−1−i300000000000000001−i31+i30000−1+i3−1−i300−2ζ72ζ7−2ζ112ζ110000000000000000
χ516666666666-2-3-2-2-2-30000-2-3-311100-2-2-2111111111-3000000000000000000000000000000000
χ526666-36-3-3-3-36066600000-30000000-3-3-30000000000000000000000000000000000000000000
χ536666-36-3-3-3-3-20-2-2-2000001004-2-2001114-2-24-2-24-2-20000000000000000000000000000000000
χ546666-36-3-3-3-3-20-2-2-200000100-24-200111-24-2-24-2-24-20000000000000000000000000000000000
χ556666-36-3-3-3-3-20-2-2-200000100-2-2400111-2-24-2-24-2-240000000000000000000000000000000000
χ56666-66-666-6-62-3-2-22-300002-33-1-1-100-2-22111111-1-1-13000000000000000000000000000000000
χ57666-6-3-6-3-33320-2-2200000-10022-40011-1-2-24-2-2422-40000000000000000000000000000000000
χ58666-6-3-6-3-33320-2-2200000-1002-420011-1-24-2-24-22-420000000000000000000000000000000000
χ59666-6-3-6-3-33320-2-2200000-100-4220011-14-2-24-2-2-4220000000000000000000000000000000000
χ60666-6-3-6-3-333-6066-60000030000000-3-330000000000000000000000000000000000000000000
χ6166-666-66-66-62-3-22-2-3000023-3-1-1-100-22-2111-1-1-11113000000000000000000000000000000000
χ6266-66-3-6-33-3320-22-200000-10022-4001-11-2-2422-4-2-240000000000000000000000000000000000
χ6366-66-3-6-33-3320-22-200000-1002-42001-11-24-22-42-24-20000000000000000000000000000000000
χ6466-66-3-6-33-3320-22-200000-100-422001-114-2-2-4224-2-20000000000000000000000000000000000
χ6566-66-3-6-33-33-606-660000030000000-33-30000000000000000000000000000000000000000000
χ6666-6-6666-6-66-2-3-222-30000-23311100-222111-1-1-1-1-1-1-3000000000000000000000000000000000
χ6766-6-6-36-333-3606-6-600000-30000000-3330000000000000000000000000000000000000000000
χ6866-6-6-36-333-3-20-222000001004-2-2001-1-14-2-2-422-4220000000000000000000000000000000000
χ6966-6-6-36-333-3-20-22200000100-24-2001-1-1-24-22-422-420000000000000000000000000000000000
χ7066-6-6-36-333-3-20-22200000100-2-24001-1-1-2-2422-422-40000000000000000000000000000000000
χ718-80080-80000-4000400-4-4000000440000000000000000220000-2-20000000000000000000000
χ728-80080-80000-40004002+2i32−2i3000000−2−2i3−2+2i30000000000000000−1−i3−1+i300001+i31−i30000000000000000000000
χ738-80080-80000-40004002−2i32+2i3000000−2+2i3−2−2i30000000000000000−1+i3−1−i300001−i31+i30000000000000000000000
χ7424-2400-120120000000000000000000000000000000000000000000000000000000000000000000

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