Finite Group Databasebeta

← Group #13178479

Character table — Group #13178479

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222224444444444444444448888888888888888888888816161616161616161616181818181818181818183636363636363636363636363636367272727272727272
order123334666233333466666812121224246661212121212121212242424242424242424242424666661212121212222444881212222224666881212242466666122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-11-1-111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-11-1-1
χ3111111111111111111111111111111111111111111111111111111111111-11-1-11-1-1-1-1-1-111-1-1-1-11-11-11-1-1-1-111-1-1-11-1
χ4111111111111111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-111-1-1-11-11-11-1-1-1-1-111-1-11
χ5111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111111-1-111-11-11-11111-1-111-1-1-11-11-11-1-1
χ6111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11-1-11-1-1-1-111-1-11-1111-1-111-1-1-1-1-1-11-11111
χ7111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-11-111-1-111-1-11-1-11-1-111-11111-1-11-1-11
χ8111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11-1-1111-1-11-111-1-1-1-111-1-11111-111-1-11-1
χ9111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-11-11-1111-1-111-1-11-11-11-1-1-1
χ10111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-1-11111-11-1-11-1-111-1-1-1-111-11-1-111
χ11111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-11-111-1-1-1-111-11-11-1-111-111-1-111-11-11
χ12111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1111-1-1-11-1-111-1-111-1-1111-11-1-1111-1
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
χ14111111111-111111-111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-11111-11-1-1-1-1-1-111-11111-1-1-1
χ15111111111-111111-111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-11-1-1111-11-11-11-1-1-11-1-11111-1
χ16111111111-111111-111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111-1-11-1-11-11-11-1-1111-1-11-11
χ1722222-22220222220222220-2-2-200000000-2-2-2-2-2000000000000000000000022-2-2-2200-2-200000022-200-220000000000
χ1822222-22220222220222220-2-2-200000000-2-2-2-2-200000000000000000000002-22-22-200-2-20000002-22002-20000000000
χ1922222-22220222220222220-2-2-200000000-2-2-2-2-20000000000000000000000-2222-2-20022000000-22200-2-20000000000
χ2022222-22220222220222220-2-2-200000000-2-2-2-2-20000000000000000000000-2-2-22220022000000-2-2-200220000000000
χ212222-122-1222-1-1-1-122-1-1-1-122-122222-12-122-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-1002002000000022000-1020-100000-1-100-1
χ222222-122-1222-1-1-1-122-1-1-1-122-122222-12-122-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-100-200-20000000-2-200010-2010000011001
χ232222-122-1222-1-1-1-1-22-1-1-1-1-22-12-2-222-1-21-22-1-1-1-1-21-2-2111111112-1-1-1-1-2111100200200000002-2000-10-20-100000-11001
χ242222-122-1222-1-1-1-1-22-1-1-1-1-22-12-2-222-1-21-22-1-1-1-1-21-2-2111111112-1-1-1-1-2111100-200-20000000-2200010201000001-100-1
χ252222-122-12-22-1-1-1-122-1-1-1-1-22-12-2-2-2-212-122-1-1-1-1-21-2-211111111-211112-1-1-1-10020020000000-22000-10-20-1000001-1001
χ262222-122-12-22-1-1-1-122-1-1-1-1-22-12-2-2-2-212-122-1-1-1-1-21-2-211111111-211112-1-1-1-100-200-200000002-20001020100000-1100-1
χ272222-122-12-22-1-1-1-1-22-1-1-1-122-1222-2-21-21-22-1-1-1-12-122-1-1-1-1-1-1-1-1-21111-211110020020000000-2-2000-1020-1000001100-1
χ282222-122-12-22-1-1-1-1-22-1-1-1-122-1222-2-21-21-22-1-1-1-12-122-1-1-1-1-1-1-1-1-21111-2111100-200-200000002200010-20100000-1-1001
χ29222-122-1222-12-1-1-12-12-1-1-12-122222-12-122-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-102002000000220000-1020-10000-1-1000-10
χ30222-122-1222-12-1-1-12-12-1-1-12-122222-12-122-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-10-200-2000000-2-2000010-20100001100010
χ31222-122-1222-12-1-1-1-2-12-1-1-1-2-122-2-22-121-2-2-12-1-1-11-211-2-2111111-12-1-1-11-2111020020000002-20000-10-20-10000-1100010
χ32222-122-1222-12-1-1-1-2-12-1-1-1-2-122-2-22-121-2-2-12-1-1-11-211-2-2111111-12-1-1-11-21110-200-2000000-2200001020100001-1000-10
χ33222-122-122-2-12-1-1-12-12-1-1-1-2-122-2-2-21-2-122-12-1-1-11-211-2-21111111-2111-12-1-1-102002000000-220000-10-20-100001-100010
χ34222-122-122-2-12-1-1-12-12-1-1-1-2-122-2-2-21-2-122-12-1-1-11-211-2-21111111-2111-12-1-1-10-200-20000002-20000102010000-11000-10
χ35222-122-122-2-12-1-1-1-2-12-1-1-12-12222-21-21-2-2-12-1-1-1-12-1-122-1-1-1-1-1-11-21111-211102002000000-2-20000-1020-1000011000-10
χ36222-122-122-2-12-1-1-1-2-12-1-1-12-12222-21-21-2-2-12-1-1-1-12-1-122-1-1-1-1-1-11-21111-21110-200-200000022000010-2010000-1-100010
χ3722-122222-12-1-12-1-12-1-12-1-1222-1-1-1-12222-1-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-120020022-1-1200002-1000000-1-1-10000-100
χ3822-122222-12-1-12-1-12-1-12-1-1222-1-1-1-12222-1-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-1-200-200-2-211-20000-210000001110000100
χ3922-122222-12-1-12-1-1-2-1-12-1-1-222-111-122-2-21-1-12-1-1-2-21111-2-21111-1-12-1-111-211200200-2-2-1-1-200002-10000001110000-100
χ4022-122222-12-1-12-1-1-2-1-12-1-1-222-111-122-2-21-1-12-1-1-2-21111-2-21111-1-12-1-111-211-200-200221120000-21000000-1-1-10000100
χ4122-122222-1-2-1-12-1-12-1-12-1-1-222-1111-2-222-1-1-12-1-1-2-21111-2-2111111-211-1-12-1-1200200-2-2-1-120000-2-100000011-10000100
χ4222-122222-1-2-1-12-1-12-1-12-1-1-222-1111-2-222-1-1-12-1-1-2-21111-2-2111111-211-1-12-1-1-200-2002211-2000021000000-1-110000-100
χ4322-122222-1-2-1-12-1-1-2-1-12-1-1222-1-1-11-2-2-2-21-1-12-1-122-1-1-1-122-1-1-1-111-21111-21120020022-1-1-20000-2-1000000-1-110000100
χ4422-122222-1-2-1-12-1-1-2-1-12-1-1222-1-1-11-2-2-2-21-1-12-1-122-1-1-1-122-1-1-1-111-21111-211-200-200-2-211200002100000011-10000-100
χ454444-2-44-2404-2-2-2-204-2-2-2-20-42-400000000-42222000000000000000000000000400-4000000000000-200020000000000
χ464444-2-44-2404-2-2-2-204-2-2-2-20-42-400000000-42222000000000000000000000000-40040000000000002000-20000000000
χ47444-24-4-2440-24-2-2-20-24-2-2-202-4-4000000002-422200000000000000000000000400-4000000000000-2000200000000000
χ48444-24-4-2440-24-2-2-20-24-2-2-202-4-4000000002-422200000000000000000000000-40040000000000002000-200000000000
χ49444-2-24-2-244-2-21114-2-21114-2-24444-2-2-2-24-2-2111-2-2-2-2-2-2111111-2-2111-2-2111000000000000000000000000000000000
χ50444-2-24-2-244-2-2111-4-2-2111-4-2-24-4-44-2-222-4-2-2111222222-1-1-1-1-1-1-2-211122-1-1-1000000000000000000000000000000000
χ51444-2-24-2-24-4-2-21114-2-2111-4-2-24-4-4-422-2-24-2-2111222222-1-1-1-1-1-122-1-1-1-2-2111000000000000000000000000000000000
χ52444-2-24-2-24-4-2-2111-4-2-21114-2-2444-42222-4-2-2111-2-2-2-2-2-211111122-1-1-122-1-1-1000000000000000000000000000000000
χ5344-244-444-20-2-24-2-20-2-24-2-20-4-420000000022-4220000000000000000000000400-4000022000000-20000000000000000
χ5444-244-444-20-2-24-2-20-2-24-2-20-4-420000000022-4220000000000000000000000-40040000-2-200000020000000000000000
χ5544-24-244-2-24-21-2114-21-21144-2-2-2-2-24-24-2-2-21-2114-2-2-211-2-21111-21-211-21-211000000000000000000000000000000000
χ5644-24-244-2-24-21-211-4-21-211-44-2-222-24-2-422-21-211-4222-1-122-1-1-1-1-21-2112-12-1-1000000000000000000000000000000000
χ5744-24-244-2-2-4-21-2114-21-211-44-2-2222-424-2-2-21-211-4222-1-122-1-1-1-12-12-1-1-21-211000000000000000000000000000000000
χ5844-24-244-2-2-4-21-211-4-21-21144-2-2-2-22-42-422-21-2114-2-2-211-2-211112-12-1-12-12-1-1000000000000000000000000000000000
χ5944-2-244-24-241-2-21141-2-2114-24-2-2-2-2-24-24-21-2-211-2411-2-2-2-211111-2-2111-2-211000000000000000000000000000000000
χ6044-2-244-24-241-2-211-41-2-211-4-24-222-2-242-421-2-2112-4-1-12222-1-1-1-11-2-211-122-1-1000000000000000000000000000000000
χ6144-2-244-24-2-41-2-21141-2-211-4-24-22222-4-24-21-2-2112-4-1-12222-1-1-1-1-122-1-11-2-211000000000000000000000000000000000
χ6244-2-244-24-2-41-2-211-41-2-2114-24-2-2-222-42-421-2-211-2411-2-2-2-21111-122-1-1-122-1-1000000000000000000000000000000000
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
χ734-4-2440-4-420-2-24-2-2022-42200006−600000000000006−66−6006−66−6000000000000000022−2223−230000000000000−2200000000
χ744-4-2440-4-420-2-24-2-2022-42200006−600000000000006−66−6006−66−60000000000000000−2222−232300000000000002−200000000
χ754-4-2440-4-420-2-24-2-2022-4220000−660000000000000−66−6600−66−66000000000000000022−22−23230000000000000−2200000000
χ764-4-2440-4-420-2-24-2-2022-4220000−660000000000000−66−6600−66−660000000000000000−222223−2300000000000002−200000000
χ77888-4-4-8-4-480-4-42220-4-4222044-80000000044-2-2-20000000000000000000000000000000000000000000000000000000
χ7888-48-4-88-4-40-42-4220-42-4220-844000000004-24-2-20000000000000000000000000000000000000000000000000000000
χ7988-4-48-8-48-402-4-42202-4-42204-8400000000-244-2-20000000000000000000000000000000000000000000000000000000
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
χ828-888-40-84-808-4-4-4-40-84444000000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-4804-8-80-48-4-4-404-8444000000000000000000000000000000000000000000000000000000000000000000000000
χ848-88-4-4044-80-4-4222044-2-2-200000000000000000000000−3i23i2−3i23i23i2−3i20000000000000000000000000000000000000000000
χ858-88-4-4044-80-4-4222044-2-2-2000000000000000000000003i2−3i23i2−3i2−3i23i20000000000000000000000000000000000000000000
χ868-8-48-40-8440-42-42204-24-2-2000026−26000000000000026−26−6600−66−660000000000000000000000000000000000000000000
χ878-8-48-40-8440-42-42204-24-2-20000−26260000000000000−26266−6006−66−60000000000000000000000000000000000000000000
χ888-8-4-4804-8402-4-4220-244-2-2000026−260000000000000−6626−2600−66−660000000000000000000000000000000000000000000
χ898-8-4-4804-8402-4-4220-244-2-20000−262600000000000006−6−2626006−66−60000000000000000000000000000000000000000000
χ908-8-4-4-404440222−1−3i3−1+3i30-2-2-21+3i31−3i3000026−260000000000000−66−663i2−3i2−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+3i31−3i30000−262600000000000006−66−6−3i23i2ζ5+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+3i3000026−260000000000000−66−66−3i23i22ζ5+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+3i30000−262600000000000006−66−63i2−3i2−2ζ5−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.