Finite Group Databasebeta

← Group #13178478

Character table — Group #13178478

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222224444444444444444448888888888888888888888816161616161616161616181818181818181818183636363636363636363636363636367272727272727272
order1233346662333334666668121212242466612121212121212122424242424242424242424246666612121212122224446688222444668812121224246661212122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-11-1-111111-1-11-1-1-1-1-1-1-11-1111-1-11-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-11-1-11-1-1-1-1-1-111-1-1-1-111-11-1-1-1-1-111-1-1-11-1
χ4111111111111111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1111-1-11-1-11-1-1-1-1-1-111-11
χ5111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111111111-1-111-1-11-111-1-1111-1-111-1-11-1-1-1
χ6111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11-1-11-1-111-1-11-11-1-11-1-111-11-1-1-11-11-1-1111
χ7111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-11-1-1-111-11-11-11-11-111-1-111-11-11-11-11
χ8111111111111111-111111-1111-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11-1-11-1-111-1-1111-11-11-1-1-1111-1-1111-11-1
χ9111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-111-1111-1-1111-1-1-1-111-11-1-1
χ10111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111-1-1-11-111-1-1-111-11-1-1-1-11-111-111
χ11111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-1-1111-11-11-1-11-111-1-1111-11-11-1-11
χ12111111111-111111111111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11-1-11111-1-1-111-11-1-1-111111-1-1-111-1
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
χ14111111111-111111-111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-111-111-1-1-1-1-11-111-111-111-1-1
χ15111111111-111111-111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-11-1-1111-111-11-1-1-1-11-1-11111-1
χ16111111111-111111-111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-11-1-11-1-11-1-11111-1-1-11
χ1722222-22220222220222220-2-2-200000000-2-2-2-2-2000000000000000000000022-2-2-222200000000-2200-2-220000000000
χ1822222-22220222220222220-2-2-200000000-2-2-2-2-200000000000000000000002-22-22-222000000002-2002-2-20000000000
χ1922222-22220222220222220-2-2-200000000-2-2-2-2-20000000000000000000000-2222-2-2-2-2000000002200-22-20000000000
χ2022222-22220222220222220-2-2-200000000-2-2-2-2-20000000000000000000000-2-2-2222-2-200000000-2-2002220000000000
χ212222-12-12222-1-1-1-122-1-1-1-12-1222222-1-1222-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-102002000000220000-120-100000-1-1000-10
χ222222-12-12222-1-1-1-122-1-1-1-12-1222222-1-1222-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-10-200-2000000-2-200001-201000001100010
χ232222-12-12222-1-1-1-1-22-1-1-1-1-2-122-2-222-11-2-22-1-1-1-1-21-2-2111111112-1-1-1-1-21111020020000002-20000-1-20-100000-1100010
χ242222-12-12222-1-1-1-1-22-1-1-1-1-2-122-2-222-11-2-22-1-1-1-1-21-2-2111111112-1-1-1-1-211110-200-2000000-2200001201000001-1000-10
χ252222-12-122-22-1-1-1-122-1-1-1-1-2-122-2-2-2-21-1222-1-1-1-1-21-2-211111111-211112-1-1-1-102002000000-220000-1-20-1000001-100010
χ262222-12-122-22-1-1-1-122-1-1-1-1-2-122-2-2-2-21-1222-1-1-1-1-21-2-211111111-211112-1-1-1-10-200-20000002-20000120100000-11000-10
χ272222-12-122-22-1-1-1-1-22-1-1-1-12-12222-2-211-2-22-1-1-1-12-122-1-1-1-1-1-1-1-1-21111-2111102002000000-2-20000-120-10000011000-10
χ282222-12-122-22-1-1-1-1-22-1-1-1-12-12222-2-211-2-22-1-1-1-12-122-1-1-1-1-1-1-1-1-21111-211110-200-20000002200001-20100000-1-100010
χ29222-1222-122-12-1-1-12-12-1-1-122-12-1-12-122-12-12-1-1-122-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-1200200-1-12220020000000-10-1-1-100-10000
χ30222-1222-122-12-1-1-12-12-1-1-122-12-1-12-122-12-12-1-1-122-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-1-200-20011-2-2-200-20000000101110010000
χ31222-1222-122-12-1-1-1-2-12-1-1-1-22-12112-12-21-2-12-1-1-1-2-211-2-2111111-12-1-1-11-2111200200-1-1-2-2200-20000000-1011-10010000
χ32222-1222-122-12-1-1-1-2-12-1-1-1-22-12112-12-21-2-12-1-1-1-2-211-2-2111111-12-1-1-11-2111-200-2001122-2002000000010-1-1100-10000
χ33222-1222-12-2-12-1-1-12-12-1-1-1-22-1211-21-22-12-12-1-1-1-2-211-2-21111111-2111-12-1-1-1200200-1-1-2-2-20020000000-1011100-10000
χ34222-1222-12-2-12-1-1-12-12-1-1-1-22-1211-21-22-12-12-1-1-1-2-211-2-21111111-2111-12-1-1-1-200-2001122200-2000000010-1-1-10010000
χ35222-1222-12-2-12-1-1-1-2-12-1-1-122-12-1-1-21-2-21-2-12-1-1-122-1-122-1-1-1-1-1-11-21111-2111200200-1-122-200-20000000-10-1-110010000
χ36222-1222-12-2-12-1-1-1-2-12-1-1-122-12-1-1-21-2-21-2-12-1-1-122-1-122-1-1-1-1-1-11-21111-2111-200-20011-2-2200200000001011-100-10000
χ3722-122222-12-1-12-1-12-1-12-1-1222-122-12222-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-10020020000000022-100200-1000000-1-10-1
χ3822-122222-12-1-12-1-12-1-12-1-1222-122-12222-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-100-200-200000000-2-2100-20010000001101
χ3922-122222-12-1-12-1-1-2-1-12-1-1-222-1-2-2-122-2-21-1-12-1-11-21111-2-21111-1-12-1-111-211002002000000002-2-100-200-1000000-1101
χ4022-122222-12-1-12-1-1-2-1-12-1-1-222-1-2-2-122-2-21-1-12-1-11-21111-2-21111-1-12-1-111-21100-200-200000000-2210020010000001-10-1
χ4122-122222-1-2-1-12-1-12-1-12-1-1-222-1-2-21-2-222-1-1-12-1-11-21111-2-2111111-211-1-12-1-100200200000000-22-100-200-10000001-101
χ4222-122222-1-2-1-12-1-12-1-12-1-1-222-1-2-21-2-222-1-1-12-1-11-21111-2-2111111-211-1-12-1-100-200-2000000002-21002001000000-110-1
χ4322-122222-1-2-1-12-1-1-2-1-12-1-1222-1221-2-2-2-21-1-12-1-1-12-1-1-1-122-1-1-1-111-21111-21100200200000000-2-2-100200-1000000110-1
χ4422-122222-1-2-1-12-1-1-2-1-12-1-1222-1221-2-2-2-21-1-12-1-1-12-1-1-1-122-1-1-1-111-21111-21100-200-20000000022100-2001000000-1-101
χ454444-2-4-24404-2-2-2-204-2-2-2-202-4-400000000-4222200000000000000000000000400-4000000000000-2002000000000000
χ464444-2-4-24404-2-2-2-204-2-2-2-202-4-400000000-4222200000000000000000000000-4004000000000000200-2000000000000
χ47444-24-44-240-24-2-2-20-24-2-2-20-42-4000000002-42220000000000000000000000400-400-2-20000000000000200000000000
χ48444-24-44-240-24-2-2-20-24-2-2-20-42-4000000002-42220000000000000000000000-400400220000000000000-200000000000
χ49444-2-24-2-244-2-21114-2-21114-2-24-2-24-2-2-2-24-2-21114-2-2-2-2-2111111-2-2111-2-2111000000000000000000000000000000000
χ50444-2-24-2-244-2-2111-4-2-2111-4-2-24224-2-222-4-2-2111-422222-1-1-1-1-1-1-2-211122-1-1-1000000000000000000000000000000000
χ51444-2-24-2-24-4-2-21114-2-2111-4-2-2422-422-2-24-2-2111-422222-1-1-1-1-1-122-1-1-1-2-2111000000000000000000000000000000000
χ52444-2-24-2-24-4-2-2111-4-2-21114-2-24-2-2-42222-4-2-21114-2-2-2-2-211111122-1-1-122-1-1-1000000000000000000000000000000000
χ5344-244-444-20-2-24-2-20-2-24-2-20-4-420000000022-422000000000000000000000000400-40000000000-20000020000000000
χ5444-244-444-20-2-24-2-20-2-24-2-20-4-420000000022-422000000000000000000000000-40040000000000200000-20000000000
χ5544-24-24-24-24-21-2114-21-2114-24-244-24-2-24-2-21-211-2-2-2-211-2-21111-21-211-21-211000000000000000000000000000000000
χ5644-24-24-24-24-21-211-4-21-211-4-24-2-4-4-24-22-42-21-2112222-1-122-1-1-1-1-21-2112-12-1-1000000000000000000000000000000000
χ5744-24-24-24-2-4-21-2114-21-211-4-24-2-4-42-42-24-2-21-2112222-1-122-1-1-1-12-12-1-1-21-211000000000000000000000000000000000
χ5844-24-24-24-2-4-21-211-4-21-2114-24-2442-422-42-21-211-2-2-2-211-2-211112-12-1-12-12-1-1000000000000000000000000000000000
χ5944-2-2444-2-241-2-21141-2-21144-2-2-2-2-2-244-2-21-2-211-2411-2-2-2-211111-2-2111-2-211000000000000000000000000000000000
χ6044-2-2444-2-241-2-211-41-2-211-44-2-222-2-24-4221-2-2112-4-1-12222-1-1-1-11-2-211-122-1-1000000000000000000000000000000000
χ6144-2-2444-2-2-41-2-21141-2-211-44-2-22222-44-2-21-2-2112-4-1-12222-1-1-1-1-122-1-11-2-211000000000000000000000000000000000
χ6244-2-2444-2-2-41-2-211-41-2-21144-2-2-2-222-4-4221-2-211-2411-2-2-2-21111-122-1-1-122-1-1000000000000000000000000000000000
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
χ714-44440-4-4-40444440-4-4-4-4-400000000000000000000000000000000000000000000000−2i22i20000000000000−2i22i200000000
χ724-44440-4-4-40444440-4-4-4-4-4000000000000000000000000000000000000000000000002i2−2i200000000000002i2−2i200000000
χ734-44-240-42-40-24-2-2-202-422200006−600000000000006−6006−66−66−60000000000000000−2i32i3−2i22i20000000000000i2−i200000000
χ744-44-240-42-40-24-2-2-202-422200006−600000000000006−6006−66−66−600000000000000002i3−2i32i2−2i20000000000000−i2i200000000
χ754-44-240-42-40-24-2-2-202-42220000−660000000000000−6600−66−66−660000000000000000−2i32i32i2−2i20000000000000−i2i200000000
χ764-44-240-42-40-24-2-2-202-42220000−660000000000000−6600−66−66−6600000000000000002i3−2i3−2i22i20000000000000i2−i200000000
χ77888-4-4-8-4-480-4-42220-4-4222044-80000000044-2-2-20000000000000000000000000000000000000000000000000000000
χ7888-48-4-8-48-40-42-4220-42-42204-84000000004-24-2-20000000000000000000000000000000000000000000000000000000
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
χ828-888-404-8-808-4-4-4-40-84444000000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-4-4044-80-4-4222044-2-2-2000026−26000000000000026−2600−66−66−660000000000000000000000000000000000000000000
χ848-88-4-4044-80-4-4222044-2-2-20000−26260000000000000−2626006−66−66−60000000000000000000000000000000000000000000
χ858-8-4880-8-840-4-48-4-4044-844000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-48-404-840-42-42204-24-2-2000000000000000000000−3i23i200−3i23i23i2−3i20000000000000000000000000000000000000000000
χ878-8-48-404-840-42-42204-24-2-20000000000000000000003i2−3i2003i2−3i2−3i23i20000000000000000000000000000000000000000000
χ888-8-4-480-84402-4-4220-244-2-2000026−260000000000000−660026−26−66−660000000000000000000000000000000000000000000
χ898-8-4-480-84402-4-4220-244-2-20000−262600000000000006−600−26266−66−60000000000000000000000000000000000000000000
χ908-8-4-4-404440222−1−3i3−1+3i30-2-2-21+3i31−3i3000026−260000000000000−663i2−3i2−66−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+3i31−3i30000−262600000000000006−6−3i23i26−6ζ5+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+3i3000026−260000000000000−66−3i23i2−662ζ5+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+3i30000−262600000000000006−63i2−3i26−6−2ζ5−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.