Finite Group Databasebeta

← Group #13164624

Character table — Group #13164624

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1122222334446666666666666991212121212121212121212121212121212121218181824242424242424242424272736363636484848484848545454727272727272
order123444622121212344466666666644336612121212121212121212121212121222233661212121212124412121212121212121212222666666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111−1−i32−1+i32−1−i32−1+i32111111111111111111−1−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−i32−1+i32−1−i32111111111111111111−1+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+i32−1−i32−1+i32111111111111111-1-1-1−1−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−i32−1+i32−1−i32111111111111111-1-1-1−1+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
χ71111-1-11111-1-111-1-11111111111111111-1-11111-1-1-1-1-1-1-1-11-1-111111-1-11-1-11111111-1-11-1-11-1-11-1-11-1-1
χ81111-1-11111-1-111-1-111111111111−1−i32−1+i32−1−i32−1+i321-1-11111-1-1-1-1-1-1-1-11-1-1−1−i32−1+i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i321+i321+i32−1+i321−i321−i321-1-1−1−i321+i321+i32−1+i321−i321−i32
χ91111-1-11111-1-111-1-111111111111−1+i32−1−i32−1+i32−1−i321-1-11111-1-1-1-1-1-1-1-11-1-1−1+i32−1−i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i321−i321−i32−1−i321+i321+i321-1-1−1+i321−i321−i32−1−i321+i321+i32
χ101111-1-11111-1-111-1-1111111111-1-111111-1-11111-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-11-1-11-1-1-111-111-111
χ111111-1-11111-1-111-1-1111111111-1-1−1−i32−1+i32−1−i32−1+i321-1-11111-1-1-1-1-1-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32-1-11+i321+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32-1111+i32−1−i32−1−i321−i32−1+i32−1+i32
χ121111-1-11111-1-111-1-1111111111-1-1−1+i32−1−i32−1+i32−1−i321-1-11111-1-1-1-1-1-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32-1-11−i321−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32-1111−i32−1+i32−1+i321+i32−1−i32−1−i32
χ13111-11-1111-11-11-11-1111111111111111-11-1-1-1-1-11111-1-1-1-1-11-11111-11-1-11-1111111-11-1-11-1-11-1-11-1-11-1
χ14111-11-1111-11-11-11-111111111111−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1-11111-1-1-1-1-11-1−1−i32−1+i32−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i3211−1−i32−1−i32−1+i32−1+i321+i32−1−i321+i321−i32−1+i321−i32-11-11+i32−1−i321+i321−i32−1+i321−i32
χ15111-11-1111-11-11-11-111111111111−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1-11111-1-1-1-1-11-1−1+i32−1−i32−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i3211−1+i32−1+i32−1−i32−1−i321−i32−1+i321−i321+i32−1−i321+i32-11-11−i32−1+i321−i321+i32−1−i321+i32
χ16111-11-1111-11-11-11-1111111111-1-11111-11-1-1-1-1-11111-1-1-1-11-111111-11-1-11-1-1-1-1-1-1-1-11-1-11-11-111-111-11
χ17111-11-1111-11-11-11-1111111111-1-1−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1-11111-1-1-1-11-11−1−i32−1+i32−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32-1-11+i321+i321−i321−i321+i32−1−i321+i321−i32−1+i321−i321-11−1−i321+i32−1−i32−1+i321−i32−1+i32
χ18111-11-1111-11-11-11-1111111111-1-1−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1-11111-1-1-1-11-11−1+i32−1−i32−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32-1-11−i321−i321+i321+i321−i32−1+i321−i321+i32−1−i321+i321-11−1+i321−i32−1+i32−1−i321+i32−1−i32
χ19111-1-11111-1-111-1-11111111111111111-1-11-1-1-1-1-1-1-1-11111-1-111111-1-11-1-11111111-1-11-1-11-1-11-1-11-1-11
χ20111-1-11111-1-111-1-1111111111111−1−i32−1+i32−1−i32−1+i32-1-11-1-1-1-1-1-1-1-11111-1-11−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i321−i321−i32−1+i32-1-111+i321+i32−1−i321−i321−i32−1+i32
χ21111-1-11111-1-111-1-1111111111111−1+i32−1−i32−1+i32−1−i32-1-11-1-1-1-1-1-1-1-11111-1-11−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i321+i321+i32−1−i32-1-111−i321−i32−1+i321+i321+i32−1−i32
χ22111-1-11111-1-111-1-11111111111-1-11111-1-11-1-1-1-1-1-1-1-1111111-11111-1-11-1-11-1-1-1-1-1-1-1-11-1-1111-111-111-1
χ23111-1-11111-1-111-1-11111111111-1-1−1−i32−1+i32−1−i32−1+i32-1-11-1-1-1-1-1-1-1-1111111-1−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32-1-11+i321+i321−i321−i321+i321+i32−1−i321−i321−i32−1+i3211-1−1−i32−1−i321+i32−1+i32−1+i321−i32
χ24111-1-11111-1-111-1-11111111111-1-1−1+i32−1−i32−1+i32−1−i32-1-11-1-1-1-1-1-1-1-1111111-1−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32-1-11−i321−i321+i321+i321−i321−i32−1+i321+i321+i32−1−i3211-1−1+i32−1+i321−i32−1−i32−1−i321+i32
χ25222222222222-122222-1-1-1-1-1-1-1002222222-1-1-1-1-1-1-1-1-1-1-1-1000-1-1-1-1222222000000-1-1-1-1-1-1000000000
χ26222222222222-122222-1-1-1-1-1-1-100−1−i3−1+i3−1−i3−1+i3222-1-1-1-1-1-1-1-1-1-1-1-10001+i321−i321+i321−i32−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30000001+i321+i321+i321−i321−i321−i32000000000
χ27222222222222-122222-1-1-1-1-1-1-100−1+i3−1−i3−1+i3−1−i3222-1-1-1-1-1-1-1-1-1-1-1-10001−i321+i321−i321+i32−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30000001−i321−i321−i321+i321+i321+i32000000000
χ282222-2-22222-2-2-12-2-222-1-1-1-1-1-1-10022222-2-2-1-1-1-111111111000-1-1-1-12-2-22-2-2000000-111-111000000000
χ292222-2-22222-2-2-12-2-222-1-1-1-1-1-1-100−1−i3−1+i3−1−i3−1+i32-2-2-1-1-1-1111111110001+i321−i321+i321−i32−1−i31+i31+i3−1+i31−i31−i30000001+i32−1−i32−1−i321−i32−1+i32−1+i32000000000
χ302222-2-22222-2-2-12-2-222-1-1-1-1-1-1-100−1+i3−1−i3−1+i3−1−i32-2-2-1-1-1-1111111110001−i321+i321−i321+i32−1+i31−i31−i3−1−i31+i31+i30000001−i32−1+i32−1+i321+i32−1−i32−1−i32000000000
χ31222-22-2222-22-2-1-22-222-1-1-1-1-1-1-1002222-22-21111-1-1-1-11111000-1-1-1-1-22-2-22-20000001-111-11000000000
χ32222-22-2222-22-2-1-22-222-1-1-1-1-1-1-100−1−i3−1+i3−1−i3−1+i3-22-21111-1-1-1-111110001+i321−i321+i321−i321+i3−1−i31+i31−i3−1+i31−i3000000−1−i321+i32−1−i32−1+i321−i32−1+i32000000000
χ33222-22-2222-22-2-1-22-222-1-1-1-1-1-1-100−1+i3−1−i3−1+i3−1−i3-22-21111-1-1-1-111110001−i321+i321−i321+i321−i3−1+i31−i31+i3−1−i31+i3000000−1+i321−i32−1+i32−1−i321+i32−1−i32000000000
χ34222-2-22222-2-22-1-2-2222-1-1-1-1-1-1-1002222-2-2211111111-1-1-1-1000-1-1-1-1-2-22-2-2200000011-111-1000000000
χ35222-2-22222-2-22-1-2-2222-1-1-1-1-1-1-100−1−i3−1+i3−1−i3−1+i3-2-2211111111-1-1-1-10001+i321−i321+i321−i321+i31+i3−1−i31−i31−i3−1+i3000000−1−i32−1−i321+i32−1+i32−1+i321−i32000000000
χ36222-2-22222-2-22-1-2-2222-1-1-1-1-1-1-100−1+i3−1−i3−1+i3−1−i3-2-2211111111-1-1-1-10001−i321+i321−i321+i321−i31−i3−1+i31+i31+i3−1−i3000000−1+i32−1+i321−i32−1−i32−1−i321+i32000000000
χ372-22000-22-200020002-2222-2-2-2-22i−2i22-2-200000000000000000022-2-20000002i−2i2i−2i2i−2i000000000000000
χ382-22000-22-200020002-2222-2-2-2-22i−2i−1−i3−1+i31+i31−i3000000000000000000−1−i3−1+i31+i31−i30000002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000
χ392-22000-22-200020002-2222-2-2-2-22i−2i−1+i3−1−i31−i31+i3000000000000000000−1+i3−1−i31−i31+i30000002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000
χ402-22000-22-200020002-2222-2-2-2-2−2i2i22-2-200000000000000000022-2-2000000−2i2i−2i2i−2i2i000000000000000
χ412-22000-22-200020002-2222-2-2-2-2−2i2i−1−i3−1+i31+i31−i3000000000000000000−1−i3−1+i31+i31−i3000000−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000
χ422-22000-22-200020002-2222-2-2-2-2−2i2i−1+i3−1−i31−i31+i3000000000000000000−1+i3−1−i31−i31+i3000000−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000
χ433333333-1-13333-1-1-1-1-1-1-1-1-1-1-13330000-1-1-13-1-1-13-1-1-13-1-1-13330000000000-1-10000000000-1-1-1000000
χ443333333-1-13333-1-1-1-1-1-1-1-1-1-1-13-3-30000-1-1-13-1-1-13-1-1-13-1-1-1-3-3-30000000000110000000000111000000
χ453333-3-33-1-13-3-33-111-1-1-1-1-1-1-1-13330000-1113-1-1-1-3111-31113-3-30000000000-1-10000000000-111000000
χ463333-3-33-1-13-3-33-111-1-1-1-1-1-1-1-13-3-30000-1113-1-1-1-3111-3111-33300000000001100000000001-1-1000000
χ47333-33-33-1-1-33-331-11-1-1-1-1-1-1-1-133300001-11-31113-1-1-1-3111-33-30000000000-1-100000000001-11000000
χ48333-33-33-1-1-33-331-11-1-1-1-1-1-1-1-13-3-300001-11-31113-1-1-1-31113-330000000000110000000000-11-1000000
χ49333-3-333-1-1-3-33311-1-1-1-1-1-1-1-1-1333000011-1-3111-31113-1-1-1-3-330000000000-1-1000000000011-1000000
χ50333-3-333-1-1-3-33311-1-1-1-1-1-1-1-1-13-3-3000011-1-3111-31113-1-1-133-30000000000110000000000-1-11000000
χ514-44000-44-4000-20004-4-2-2-222220044-4-4000000000000000000-2-222000000000000000000000000000
χ524-44000-44-4000-20004-4-2-2-2222200−2−2i3−2+2i32+2i32−2i30000000000000000001+i31−i3−1−i3−1+i3000000000000000000000000000
χ534-44000-44-4000-20004-4-2-2-2222200−2+2i3−2−2i32−2i32+2i30000000000000000001−i31+i3−1+i3−1−i3000000000000000000000000000
χ546666666-2-2666-3-2-2-2-2-2111111-3000000-2-2-2-3111-3111-31110000000000000000000000000000000000
χ556666-6-66-2-26-6-6-3-222-2-2111111-3000000-222-31113-1-1-13-1-1-10000000000000000000000000000000000
χ56666-66-66-2-2-66-6-32-22-2-2111111-30000002-223-1-1-1-31113-1-1-10000000000000000000000000000000000
χ57666-6-666-2-2-6-66-322-2-2-2111111-300000022-23-1-1-13-1-1-1-31110000000000000000000000000000000000
χ5866-3666-366-3-3-30666-3-30000000000000-3-3-30000000000000000000000000000000000000000000000
χ5966-3666-3-2-2-3-3-30-2-2-2114-2-24-2-2000000011104-2-204-2-204-2-20000000000000000000000000000000000
χ6066-3666-3-2-2-3-3-30-2-2-211-24-2-24-200000001110-24-20-24-20-24-20000000000000000000000000000000000
χ6166-3666-3-2-2-3-3-30-2-2-211-2-24-2-2400000001110-2-240-2-240-2-240000000000000000000000000000000000
χ6266-36-6-6-366-33306-6-6-3-30000000000000-3330000000000000000000000000000000000000000000000
χ6366-36-6-6-3-2-2-3330-222114-2-24-2-200000001-1-104-2-20-4220-4220000000000000000000000000000000000
χ6466-36-6-6-3-2-2-3330-22211-24-2-24-200000001-1-10-24-202-4202-420000000000000000000000000000000000
χ6566-36-6-6-3-2-2-3330-22211-2-24-2-2400000001-1-10-2-24022-4022-40000000000000000000000000000000000
χ6666-3-66-6-3663-330-66-6-3-300000000000003-330000000000000000000000000000000000000000000000
χ6766-3-66-6-3-2-23-3302-22114-2-24-2-20000000-11-10-42204-2-20-4220000000000000000000000000000000000
χ6866-3-66-6-3-2-23-3302-2211-24-2-24-20000000-11-102-420-24-202-420000000000000000000000000000000000
χ6966-3-66-6-3-2-23-3302-2211-2-24-2-240000000-11-1022-40-2-24022-40000000000000000000000000000000000
χ7066-3-6-66-36633-30-6-66-3-3000000000000033-30000000000000000000000000000000000000000000000
χ7166-3-6-66-3-2-233-3022-2114-2-24-2-20000000-1-110-4220-42204-2-20000000000000000000000000000000000
χ7266-3-6-66-3-2-233-3022-211-24-2-24-20000000-1-1102-4202-420-24-20000000000000000000000000000000000
χ7366-3-6-66-3-2-233-3022-211-2-24-2-240000000-1-11022-4022-40-2-240000000000000000000000000000000000
χ746-66000-6-220006000-22-2-2-2222-66i−6i00000000000000000000000000000000−2i2i0000000000000000000
χ756-66000-6-220006000-22-2-2-2222-6−6i6i000000000000000000000000000000002i−2i0000000000000000000
χ7612-1212000-12-44000-6000-44222-2-2-260000000000000000000000000000000000000000000000000000000
χ7712-12-6000612-120000000-6600000000000000000000000000000000000000000000000000000000000000
χ7812-12-60006-4400000002-28-4-4-84400000000000000000000000000000000000000000000000000000000
χ7912-12-60006-4400000002-2-48-44-8400000000000000000000000000000000000000000000000000000000
χ8012-12-60006-4400000002-2-4-4844-800000000000000000000000000000000000000000000000000000000

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