Finite Group Databasebeta

← Group #13178480

Character table — Group #13178480

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222224444444444444444448888888888888888888888816161616161616161616181818181818181818183636363636363636363636363636367272727272727272
order1233346662333334666668121212242466612121212121212122424242424242424242424246666612121212122224448812122444446668812122424612121212122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-11-1-1111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-11-1-11-1-1-1-1-1-1-111-1-11-1-11-11-1-1-1-1-111-1-11-1
χ4111111111111111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-111-11-1-11-11-1-1-1-1-1-111-11
χ5111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111111-1-111-111-11-1111-1-111-1-1-111-11-1-1-1
χ6111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11-1-11-1-1-1-111-11-11-11-1-1111-1-1-1-1-11-11-1111
χ7111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-11-111-1-11-11-1-111-1-1-111-1111-11-1-11-11
χ8111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11-1-1111-1-11-1-111-1-11-11-1-11111-1-111-11-1
χ9111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1-11-11111-1-111-1-11-1-11-11-1-1
χ10111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1111-11-11-1-1-1111-1-1-1-11-11-11-111
χ11111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-11-111-1-1-11-111-11-1-1-111-111-11-111-1-11
χ12111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1111-1-1-111-1-11-11-11-1-1111-111-1-111-1
χ13111111111-111111-111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111111-1-1-1-1-1-111
χ14111111111-111111-111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11111-1-11-1-1-1-111-1-11111-1-1
χ15111111111-111111-111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111-1-1111-1-11-11-1-1-111-1-1111-1
χ16111111111-111111-111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-11-1-11-11-1-11111-1-1-11
χ1722222-22220222220222220-2-2-200000000-2-2-2-2-2000000000000000000000022-2-2-2200-2-20000002-2200-220000000000
χ1822222-22220222220222220-2-2-200000000-2-2-2-2-200000000000000000000002-22-22-200-2-2000000-222002-20000000000
χ1922222-22220222220222220-2-2-200000000-2-2-2-2-20000000000000000000000-2222-2-2002200000022-200-2-20000000000
χ2022222-22220222220222220-2-2-200000000-2-2-2-2-20000000000000000000000-2-2-22220022000000-2-2-200220000000000
χ212222-12-12222-1-1-1-122-1-1-1-12-122-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-120020022-1-122000000-10000-1-1-1-1000000
χ222222-12-12222-1-1-1-122-1-1-1-12-122-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-1-200-200-2-211-2-2000000100001111000000
χ232222-12-12222-1-1-1-1-22-1-1-1-1-2-1221122-11-2-22-1-1-1-1-2-2-2-2111111112-1-1-1-1-21111200200-2-2-1-1-22000000-10000111-1000000
χ242222-12-12222-1-1-1-1-22-1-1-1-1-2-1221122-11-2-22-1-1-1-1-2-2-2-2111111112-1-1-1-1-21111-200-20022112-200000010000-1-1-11000000
χ252222-12-122-22-1-1-1-122-1-1-1-1-2-12211-2-21-1222-1-1-1-1-2-2-2-211111111-211112-1-1-1-1200200-2-2-1-12-2000000-1000011-11000000
χ262222-12-122-22-1-1-1-122-1-1-1-1-2-12211-2-21-1222-1-1-1-1-2-2-2-211111111-211112-1-1-1-1-200-2002211-2200000010000-1-11-1000000
χ272222-12-122-22-1-1-1-1-22-1-1-1-12-122-1-1-2-211-2-22-1-1-1-12222-1-1-1-1-1-1-1-1-21111-2111120020022-1-1-2-2000000-10000-1-111000000
χ282222-12-122-22-1-1-1-1-22-1-1-1-12-122-1-1-2-211-2-22-1-1-1-12222-1-1-1-1-1-1-1-1-21111-21111-200-200-2-211220000001000011-1-1000000
χ29222-12222-12-12-1-1-12-12-1-1-1222-1222-1222-1-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-100200200000000220-10020-1000000-1-10-1
χ30222-12222-12-12-1-1-12-12-1-1-1222-1222-1222-1-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-100-200-200000000-2-20100-2010000001101
χ31222-12222-12-12-1-1-1-2-12-1-1-1-222-1-2-22-12-2-21-12-1-1-1-2111-2-2111111-12-1-1-11-2111002002000000002-20-100-20-1000000-1101
χ32222-12222-12-12-1-1-1-2-12-1-1-1-222-1-2-22-12-2-21-12-1-1-1-2111-2-2111111-12-1-1-11-211100-200-200000000-2201002010000001-10-1
χ33222-12222-1-2-12-1-1-12-12-1-1-1-222-1-2-2-21-222-1-12-1-1-1-2111-2-21111111-2111-12-1-1-100200200000000-220-100-20-10000001-101
χ34222-12222-1-2-12-1-1-12-12-1-1-1-222-1-2-2-21-222-1-12-1-1-1-2111-2-21111111-2111-12-1-1-100-200-2000000002-20100201000000-110-1
χ35222-12222-1-2-12-1-1-1-2-12-1-1-1222-122-21-2-2-21-12-1-1-12-1-1-122-1-1-1-1-1-11-21111-211100200200000000-2-20-10020-1000000110-1
χ36222-12222-1-2-12-1-1-1-2-12-1-1-1222-122-21-2-2-21-12-1-1-12-1-1-122-1-1-1-1-1-11-21111-211100-200-200000000220100-201000000-1-101
χ3722-12222-122-1-12-1-12-1-12-1-122-1222-1222-12-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-10200200000002200-10020-100000-1-100-10
χ3822-12222-122-1-12-1-12-1-12-1-122-1222-1222-12-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-10-200-20000000-2-200100-20100000110010
χ3922-12222-122-1-12-1-1-2-1-12-1-1-22-12-2-2-122-21-2-1-12-1-11-21111-2-21111-1-12-1-111-2110200200000002-200-100-20-100000-110010
χ4022-12222-122-1-12-1-1-2-1-12-1-1-22-12-2-2-122-21-2-1-12-1-11-21111-2-21111-1-12-1-111-2110-200-20000000-2200100201000001-100-10
χ4122-12222-12-2-1-12-1-12-1-12-1-1-22-12-2-21-2-22-12-1-12-1-11-21111-2-2111111-211-1-12-1-1020020000000-2200-100-20-1000001-10010
χ4222-12222-12-2-1-12-1-12-1-12-1-1-22-12-2-21-2-22-12-1-12-1-11-21111-2-2111111-211-1-12-1-10-200-200000002-20010020100000-1100-10
χ4322-12222-12-2-1-12-1-1-2-1-12-1-122-12221-2-2-21-2-1-12-1-1-12-1-1-1-122-1-1-1-111-21111-211020020000000-2-200-10020-1000001100-10
χ4422-12222-12-2-1-12-1-1-2-1-12-1-122-12221-2-2-21-2-1-12-1-1-12-1-1-1-122-1-1-1-111-21111-2110-200-200000002200100-20100000-1-10010
χ454444-2-4-24404-2-2-2-204-2-2-2-202-4-400000000-422220000000000000000000000400-400002200000000-200000000000000
χ464444-2-4-24404-2-2-2-204-2-2-2-202-4-400000000-422220000000000000000000000-40040000-2-200000000200000000000000
χ47444-24-444-20-24-2-2-20-24-2-2-20-4-42000000002-4222000000000000000000000000400-400000000000-2000020000000000
χ48444-24-444-20-24-2-2-20-24-2-2-20-4-42000000002-4222000000000000000000000000-40040000000000020000-20000000000
χ49444-2-24-24-24-2-21114-2-21114-24-2-2-24-2-2-24-2-2-21114-2-2-2-2-2111111-2-2111-2-2111000000000000000000000000000000000
χ50444-2-24-24-24-2-2111-4-2-2111-4-24-2224-2-22-42-2-2111-422222-1-1-1-1-1-1-2-211122-1-1-1000000000000000000000000000000000
χ51444-2-24-24-2-4-2-21114-2-2111-4-24-222-422-24-2-2-2111-422222-1-1-1-1-1-122-1-1-1-2-2111000000000000000000000000000000000
χ52444-2-24-24-2-4-2-2111-4-2-21114-24-2-2-2-4222-42-2-21114-2-2-2-2-211111122-1-1-122-1-1-1000000000000000000000000000000000
χ5344-244-44-240-2-24-2-20-2-24-2-20-42-40000000022-42200000000000000000000000400-400000000000-20000200000000000
χ5444-244-44-240-2-24-2-20-2-24-2-20-42-40000000022-42200000000000000000000000-40040000000000020000-200000000000
χ5544-24-24-2-244-21-2114-21-2114-2-24-2-2-24-2-2-24-21-211-24-2-211-2-21111-21-211-21-211000000000000000000000000000000000
χ5644-24-24-2-244-21-211-4-21-211-4-2-2422-24-222-4-21-2112-422-1-122-1-1-1-1-21-2112-12-1-1000000000000000000000000000000000
χ5744-24-24-2-24-4-21-2114-21-211-4-2-24222-42-2-24-21-2112-422-1-122-1-1-1-12-12-1-1-21-211000000000000000000000000000000000
χ5844-24-24-2-24-4-21-211-4-21-2114-2-24-2-22-4222-4-21-211-24-2-211-2-211112-12-1-12-12-1-1000000000000000000000000000000000
χ5944-2-2444-2-241-2-21141-2-21144-2-244-2-244-2-21-2-211-2-211-2-2-2-211111-2-2111-2-211000000000000000000000000000000000
χ6044-2-2444-2-241-2-211-41-2-211-44-2-2-4-4-2-24-4221-2-21122-1-12222-1-1-1-11-2-211-122-1-1000000000000000000000000000000000
χ6144-2-2444-2-2-41-2-21141-2-211-44-2-2-4-422-44-2-21-2-21122-1-12222-1-1-1-1-122-1-11-2-211000000000000000000000000000000000
χ6244-2-2444-2-2-41-2-211-41-2-21144-2-24422-4-4221-2-211-2-211-2-2-2-21111-122-1-1-122-1-1000000000000000000000000000000000
χ6344-2-2-24-2-2-24111−1−3i32−1+3i324111−1−3i32−1+3i324-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32000000000000000000000000000000000
χ6444-2-2-24-2-2-24111−1−3i32−1+3i32-4111−1−3i32−1+3i32-4-2-2-222-2-2-2222111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i32-1-1-11+3i321−3i32000000000000000000000000000000000
χ6544-2-2-24-2-2-24111−1+3i32−1−3i324111−1+3i32−1−3i324-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i32000000000000000000000000000000000
χ6644-2-2-24-2-2-24111−1+3i32−1−3i32-4111−1+3i32−1−3i32-4-2-2-222-2-2-2222111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i32-1-1-11−3i321+3i32000000000000000000000000000000000
χ6744-2-2-24-2-2-2-4111−1−3i32−1+3i324111−1−3i32−1+3i32-4-2-2-222222-2-2-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-11+3i321−3i32111−1−3i32−1+3i32000000000000000000000000000000000
χ6844-2-2-24-2-2-2-4111−1−3i32−1+3i32-4111−1−3i32−1+3i324-2-2-2-2-2222222111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-1-1-11+3i321−3i32-1-1-11+3i321−3i32000000000000000000000000000000000
χ6944-2-2-24-2-2-2-4111−1+3i32−1−3i324111−1+3i32−1−3i32-4-2-2-222222-2-2-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-11−3i321+3i32111−1+3i32−1−3i32000000000000000000000000000000000
χ7044-2-2-24-2-2-2-4111−1+3i32−1−3i32-4111−1+3i32−1−3i324-2-2-2-2-2222222111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-1-1-11−3i321+3i32-1-1-11−3i321+3i32000000000000000000000000000000000
χ714-44440-4-4-40444440-4-4-4-4-400000000000000000000000000000000000000000000022−2200000000000000022−2200000000
χ724-44440-4-4-40444440-4-4-4-4-4000000000000000000000000000000000000000000000−2222000000000000000−222200000000
χ734-444-202-4-404-2-2-2-20-4222200006−60000000000000006−66−66−66−6000000000000000022−2223−230000000000000−2200000000
χ744-444-202-4-404-2-2-2-20-4222200006−60000000000000006−66−66−66−60000000000000000−2222−232300000000000002−200000000
χ754-444-202-4-404-2-2-2-20-422220000−66000000000000000−66−66−66−66000000000000000022−22−23230000000000000−2200000000
χ764-444-202-4-404-2-2-2-20-422220000−66000000000000000−66−66−66−660000000000000000−222223−2300000000000002−200000000
χ77888-4-4-8-48-40-4-42220-4-422204-840000000044-2-2-20000000000000000000000000000000000000000000000000000000
χ7888-48-4-8-4-480-42-4220-42-422044-8000000004-24-2-20000000000000000000000000000000000000000000000000000000
χ7988-4-48-88-4-402-4-42202-4-4220-84400000000-244-2-20000000000000000000000000000000000000000000000000000000
χ8088-4-4-4-8-4-4-40222−1−3i3−1+3i30222−1−3i3−1+3i3044400000000-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000
χ8188-4-4-4-8-4-4-40222−1+3i3−1−3i30222−1+3i3−1−3i3044400000000-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000
χ828-88-480-8-840-48-4-4-404-8444000000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-4-404-840-4-4222044-2-2-2000026−2600000000000000026−26−66−66−660000000000000000000000000000000000000000000
χ848-88-4-404-840-4-4222044-2-2-20000−2626000000000000000−26266−66−66−60000000000000000000000000000000000000000000
χ858-8-4880-84-80-4-48-4-4044-844000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-48-4044-80-42-42204-24-2-2000026−26000000000000000−6626−26−66−660000000000000000000000000000000000000000000
χ878-8-48-4044-80-42-42204-24-2-20000−26260000000000000006−6−26266−66−60000000000000000000000000000000000000000000
χ888-8-4-480-84402-4-4220-244-2-20000000000000000000−3i23i20000−3i23i23i2−3i20000000000000000000000000000000000000000000
χ898-8-4-480-84402-4-4220-244-2-200000000000000000003i2−3i200003i2−3i2−3i23i20000000000000000000000000000000000000000000
χ908-8-4-4-404440222−1−3i3−1+3i30-2-2-21+3i31−3i3000026−2600000000000003i2−3i2−66−66−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ232ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ230000000000000000000000000000000000000000000
χ918-8-4-4-404440222−1−3i3−1+3i30-2-2-21+3i31−3i30000−26260000000000000−3i23i26−66−6ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ23−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ230000000000000000000000000000000000000000000
χ928-8-4-4-404440222−1+3i3−1−3i30-2-2-21−3i31+3i3000026−260000000000000−3i23i2−66−662ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ23−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ230000000000000000000000000000000000000000000
χ938-8-4-4-404440222−1+3i3−1−3i30-2-2-21−3i31+3i30000−262600000000000003i2−3i26−66−6−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ23ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ230000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.