Finite Group Databasebeta

← Group #13164614

Character table — Group #13164614

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1122222334446666666666666991212121212121212121212121212121212121218181824242424242424242424272736363636484848484848545454727272727272
order12223462266122234666666666443366666666666612121212122443366666612124412121212666612122446612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111−1−i32−1+i321111111111−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ3111111111111111111111111111−1+i32−1−i321111111111−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ41111111111111111111111111-1-11111111111111111111-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111-1-1−1−i32−1+i321111111111−1−i32−1+i3211111-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321+i321−i321−i32
χ61111111111111111111111111-1-1−1+i32−1−i321111111111−1+i32−1−i3211111-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321−i321+i321+i32
χ7111-11-11111-1-11-11-111111111111111-11111-1-1-1-111-1-1-1-1-1-11-1111-11-111-1-11111111-11-1-1-1-11-1-1-11-11-1
χ8111-11-11111-1-11-11-111111111111−1−i32−1+i321-11111-1-1-1-1−1−i32−1+i32-1-1-1-1-1-11-1−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i321+i321−i32-11-11+i321−i32−1−i321+i32−1+i321−i32
χ9111-11-11111-1-11-11-111111111111−1+i32−1−i321-11111-1-1-1-1−1+i32−1−i32-1-1-1-1-1-11-1−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−i321+i32-11-11−i321+i32−1+i321−i32−1−i321+i32
χ10111-11-11111-1-11-11-1111111111-1-1111-11111-1-1-1-111-1-1-1-1-11-11111-11-111-1-1-1-1-1-1-1-11-11-1-1-11-1111-11-11
χ11111-11-11111-1-11-11-1111111111-1-1−1−i32−1+i321-11111-1-1-1-1−1−i32−1+i32-1-1-1-1-11-11−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32−1−i321+i32−1+i321−i321+i321−i321-11−1−i32−1+i321+i32−1−i321−i32−1+i32
χ12111-11-11111-1-11-11-1111111111-1-1−1+i32−1−i321-11111-1-1-1-1−1+i32−1−i32-1-1-1-1-11-11−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32−1+i321−i32−1−i321+i321−i321+i321-11−1+i32−1−i321−i32−1+i321+i32−1−i32
χ1311-111-1111-11-1-111-11111111111111-11-1-1-1-1111111-1-1-1-1-1-1-1111-11-1111-1-1111111-11-11-1-1-1-11-1-1-11-11
χ1411-111-1111-11-1-111-111111111111−1−i32−1+i32-11-1-1-1-11111−1−i32−1+i32-1-1-1-1-1-1-11−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i321+i321−i32-1-111+i321−i321+i32−1−i321−i32−1+i32
χ1511-111-1111-11-1-111-111111111111−1+i32−1−i32-11-1-1-1-11111−1+i32−1−i32-1-1-1-1-1-1-11−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i321−i321+i32-1-111−i321+i321−i32−1+i321+i32−1−i32
χ1611-111-1111-11-1-111-1111111111-1-111-11-1-1-1-1111111-1-1-1-1-111-111-11-1111-1-1-1-1-1-1-1-1-11-11-1-111-1111-11-1
χ1711-111-1111-11-1-111-1111111111-1-1−1−i32−1+i32-11-1-1-1-11111−1−i32−1+i32-1-1-1-1-111-1−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321+i32−1−i321−i32−1+i321+i321−i3211-1−1−i32−1+i32−1−i321+i32−1+i321−i32
χ1811-111-1111-11-1-111-1111111111-1-1−1+i32−1−i32-11-1-1-1-11111−1+i32−1−i32-1-1-1-1-111-1−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−i32−1+i321+i32−1−i321−i321+i3211-1−1+i32−1−i32−1+i321−i32−1−i321+i32
χ1911-1-111111-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111111111-1-1-1-1111-1-111-1-1-1-1
χ2011-1-111111-1-11-1-11111111111111−1−i32−1+i32-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32111111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i32
χ2111-1-111111-1-11-1-11111111111111−1+i32−1−i32-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32111111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i321-1-1−1+i32−1−i321−i321−i321+i321+i32
χ2211-1-111111-1-11-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ2311-1-111111-1-11-1-111111111111-1-1−1−i32−1+i32-1-1-1-1-1-1-1-1-1-1−1−i32−1+i3211111-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32-1111+i321−i32−1−i32−1−i32−1+i32−1+i32
χ2411-1-111111-1-11-1-111111111111-1-1−1+i32−1−i32-1-1-1-1-1-1-1-1-1-1−1+i32−1−i3211111-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32-1111−i321+i32−1+i32−1+i32−1−i32−1−i32
χ2522222222222222-1222-1-1-1-1-1-1-1002222-1-1-1-1-1-1-1-1222-1-1-1-1000-1-12222-1-122000000-1-1-1-1-1-1000000000
χ2622222222222222-1222-1-1-1-1-1-1-100−1−i3−1+i322-1-1-1-1-1-1-1-1−1−i3−1+i32-1-1-1-10001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i30000001+i321+i321−i321−i321+i321−i32000000000
χ2722222222222222-1222-1-1-1-1-1-1-100−1+i3−1−i322-1-1-1-1-1-1-1-1−1+i3−1−i32-1-1-1-10001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i30000001−i321−i321+i321+i321−i321+i32000000000
χ28222-22-22222-2-22-2-1-222-1-1-1-1-1-1-100222-2-1-1-1-1111122-21111000-1-12-22-2-1-1-2-2000000-11-1111000000000
χ29222-22-22222-2-22-2-1-222-1-1-1-1-1-1-100−1−i3−1+i32-2-1-1-1-11111−1−i3−1+i3-211110001+i321−i32−1−i31+i3−1+i31−i31+i321−i321+i31−i30000001+i32−1−i321−i32−1+i32−1−i32−1+i32000000000
χ30222-22-22222-2-22-2-1-222-1-1-1-1-1-1-100−1+i3−1−i32-2-1-1-1-11111−1+i3−1−i3-211110001−i321+i32−1+i31−i3−1−i31+i31−i321+i321−i31+i30000001−i32−1+i321+i32−1−i32−1+i32−1−i32000000000
χ3122-222-2222-22-2-22-1-222-1-1-1-1-1-1-10022-221111-1-1-1-122-21111000-1-1-22-22-1-1-2-20000001-11-111000000000
χ3222-222-2222-22-2-22-1-222-1-1-1-1-1-1-100−1−i3−1+i3-221111-1-1-1-1−1−i3−1+i3-211110001+i321−i321+i3−1−i31−i3−1+i31+i321−i321+i31−i3000000−1−i321+i32−1+i321−i32−1−i32−1+i32000000000
χ3322-222-2222-22-2-22-1-222-1-1-1-1-1-1-100−1+i3−1−i3-221111-1-1-1-1−1+i3−1−i3-211110001−i321+i321−i3−1+i31+i3−1−i31−i321+i321−i31+i3000000−1+i321−i32−1−i321+i32−1+i32−1−i32000000000
χ3422-2-222222-2-22-2-2-1222-1-1-1-1-1-1-10022-2-211111111222-1-1-1-1000-1-1-2-2-2-2-1-1220000001111-1-1000000000
χ3522-2-222222-2-22-2-2-1222-1-1-1-1-1-1-100−1−i3−1+i3-2-211111111−1−i3−1+i32-1-1-1-10001+i321−i321+i31+i31−i31−i31+i321−i32−1−i3−1+i3000000−1−i32−1−i32−1+i32−1+i321+i321−i32000000000
χ3622-2-222222-2-22-2-2-1222-1-1-1-1-1-1-100−1+i3−1−i3-2-211111111−1+i3−1−i32-1-1-1-10001−i321+i321−i31−i31+i31+i31−i321+i32−1+i3−1−i3000000−1+i32−1+i32−1−i32−1−i321−i321+i32000000000
χ372-20020-22-200000202-2222-2-2-2-22i−2i220000000000-2-200000000220000-2-2002i−2i2i−2i2i−2i000000000000000
χ382-20020-22-200000202-2222-2-2-2-22i−2i−1−i3−1+i300000000001+i31−i300000000−1−i3−1+i300001+i31−i3002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000
χ392-20020-22-200000202-2222-2-2-2-22i−2i−1+i3−1−i300000000001−i31+i300000000−1+i3−1−i300001−i31+i3002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000
χ402-20020-22-200000202-2222-2-2-2-2−2i2i220000000000-2-200000000220000-2-200−2i2i−2i2i−2i2i000000000000000
χ412-20020-22-200000202-2222-2-2-2-2−2i2i−1−i3−1+i300000000001+i31−i300000000−1−i3−1+i300001+i31−i300−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000
χ422-20020-22-200000202-2222-2-2-2-2−2i2i−1+i3−1−i300000000001−i31+i300000000−1+i3−1−i300001−i31+i300−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000
χ433333333-1-1333-1-13-1-1-1-1-1-1-1-1-133300-1-13-1-1-13-1-1-100-13-1-1-13330000000000-1-10000000000-1-1-1000000
χ443333333-1-1333-1-13-1-1-1-1-1-1-1-1-13-3-300-1-13-1-1-13-1-1-100-13-1-1-1-3-3-30000000000110000000000111000000
χ45333-33-33-1-13-3-3-1131-1-1-1-1-1-1-1-133300-113-1-1-1-3111001-3111-33-30000000000-1-100000000001-11000000
χ46333-33-33-1-13-3-3-1131-1-1-1-1-1-1-1-13-3-300-113-1-1-1-3111001-31113-330000000000110000000000-11-1000000
χ4733-333-33-1-1-33-31-131-1-1-1-1-1-1-1-1333001-1-31113-1-1-1001-3111-3-330000000000-1-1000000000011-1000000
χ4833-333-33-1-1-33-31-131-1-1-1-1-1-1-1-13-3-3001-1-31113-1-1-1001-311133-30000000000110000000000-1-11000000
χ4933-3-3333-1-1-3-33113-1-1-1-1-1-1-1-1-13330011-3111-311100-13-1-1-13-3-30000000000-1-10000000000-111000000
χ5033-3-3333-1-1-3-33113-1-1-1-1-1-1-1-1-13-3-30011-3111-311100-13-1-1-1-33300000000001100000000001-1-1000000
χ514-40040-44-400000-204-4-2-2-2222200440000000000-4-400000000-2-200002200000000000000000000000
χ524-40040-44-400000-204-4-2-2-2222200−2−2i3−2+2i300000000002+2i32−2i3000000001+i31−i30000−1−i3−1+i300000000000000000000000
χ534-40040-44-400000-204-4-2-2-2222200−2+2i3−2−2i300000000002−2i32+2i3000000001−i31+i30000−1+i3−1−i300000000000000000000000
χ546666666-2-2666-2-2-3-2-2-2111111-30000-2-2-3111-311100-2-31110000000000000000000000000000000000
χ556666-36-366-3-3-36606-3-300000000000-3-30000000000-300000000000000000000000000000000000000
χ566666-36-3-2-2-3-3-3-2-20-2114-2-24-2-2000001104-2-204-2-200104-2-20000000000000000000000000000000000
χ576666-36-3-2-2-3-3-3-2-20-211-24-2-24-200000110-24-20-24-20010-24-20000000000000000000000000000000000
χ586666-36-3-2-2-3-3-3-2-20-211-2-24-2-2400000110-2-240-2-240010-2-240000000000000000000000000000000000
χ59666-66-66-2-26-6-6-22-32-2-2111111-30000-22-31113-1-1-10023-1-1-10000000000000000000000000000000000
χ60666-6-3-6-366-3336-60-6-3-300000000000-330000000000300000000000000000000000000000000000000
χ61666-6-3-6-3-2-2-333-2202114-2-24-2-2000001-104-2-20-42200-10-4220000000000000000000000000000000000
χ62666-6-3-6-3-2-2-333-220211-24-2-24-2000001-10-24-202-4200-102-420000000000000000000000000000000000
χ63666-6-3-6-3-2-2-333-220211-2-24-2-24000001-10-2-24022-400-1022-40000000000000000000000000000000000
χ6466-666-66-2-2-66-62-2-32-2-2111111-300002-23-1-1-1-31110023-1-1-10000000000000000000000000000000000
χ6566-66-3-6-3663-33-660-6-3-3000000000003-30000000000300000000000000000000000000000000000000
χ6666-66-3-6-3-2-23-332-202114-2-24-2-200000-110-42204-2-200-10-4220000000000000000000000000000000000
χ6766-66-3-6-3-2-23-332-20211-24-2-24-200000-1102-420-24-200-102-420000000000000000000000000000000000
χ6866-66-3-6-3-2-23-332-20211-2-24-2-2400000-11022-40-2-2400-1022-40000000000000000000000000000000000
χ6966-6-6666-2-2-6-6622-3-2-2-2111111-30000223-1-1-13-1-1-100-2-31110000000000000000000000000000000000
χ7066-6-6-36-36633-3-6-606-3-300000000000330000000000-300000000000000000000000000000000000000
χ7166-6-6-36-3-2-233-3220-2114-2-24-2-200000-1-10-4220-42200104-2-20000000000000000000000000000000000
χ7266-6-6-36-3-2-233-3220-211-24-2-24-200000-1-102-4202-420010-24-20000000000000000000000000000000000
χ7366-6-6-36-3-2-233-3220-211-2-24-2-2400000-1-1022-4022-40010-2-240000000000000000000000000000000000
χ746-60060-6-220000060-22-2-2-2222-66i−6i00000000000000000000000000000000−2i2i0000000000000000000
χ756-60060-6-220000060-22-2-2-2222-6−6i6i000000000000000000000000000000002i−2i0000000000000000000
χ7612-1200120-12-4400000-60-44222-2-2-260000000000000000000000000000000000000000000000000000000
χ7712-1200-60612-120000000-6600000000000000000000000000000000000000000000000000000000000000
χ7812-1200-606-4400000002-28-4-4-84400000000000000000000000000000000000000000000000000000000
χ7912-1200-606-4400000002-2-48-44-8400000000000000000000000000000000000000000000000000000000
χ8012-1200-606-4400000002-2-4-4844-800000000000000000000000000000000000000000000000000000000

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