Finite Group Databasebeta

← Group #13171583

Character table — Group #13171583

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222224444444444446666888888888881212121212121212121212121212121212121212161616161818242424242424242424242424242436363636363636363648545472727272108
order1233346662333666661212122244366666661212122446666812121212121212121212121266612246666121212121212242424242246881212126886624244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1111111-1111111111111111111-1-111111111-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-1
χ31111111111111111111111-11-11111111111111-11-11-111-1111-1-1-111-1-11111-1-1111-11-111-1-111111-1-1-11-1-1-1-11-1-11-11-1-1
χ41111111111111111111111-11-111111111111-11-11-11-1-11-1111-1-1-111-1-11111-1-1-1-11-11-111-1-1-1-1-1-1-11-1-1-11-1-1-1-111-11-111
χ5111111111111111111111-11-11111111111111-11-11-111-11-1-1-1111-1-1111111-1-111-11-11-1-1111111-11-1-1-11-1-1-11-1-1-11-11-1
χ6111111111111111111111-11-1111111111111-1-11-11-11-1-11-1-1-1111-1-1111111-1-1-1-1-11-11-1-111-1-1-1-11-1-1-11-1-1-1-1-1111-11-11
χ7111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11
χ8111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ9111111111-1111-1-111111111111-1-1-1-1-1-111111-1-11111-1111-1-11-1-11111-1-1-11111111-1-1-1-1-1-1-1-1-1-111-11-1-11-1-11-1-111-1-11
χ10111111111-1111-1-111111111111-1-1-1-1-1-11111-1-1-111111111-1-11-1-11111-1-1-1111-1-111-1-1-1-1-1-11111-1-1-11111-1-1-111-1-111-1
χ11111111111-1111-1-11111111-11-11-1-1-1-1-1-111111-111-11-1-11-11-1-1-11111-1-1-1-1-11-1-1111-1-11-1-111-1-1-1-11-11-1-11-1111111-1-11-1
χ12111111111-1111-1-11111111-11-11-1-1-1-1-1-11111-1-111-11-111-11-1-1-11111-1-1-1-1-11-1-1-1-11-1-11-1-1111111-111-11-1-111-1-1-1-111-11
χ13111111111-1111-1-1111111-11-111-1-1-1-1-1-1111111-1-11-11-1-11-1111-1-1-1-111-1-1-11-1-111-111-111-1-1-1-1-1-1-111-11-1-111111-111-1-1
χ14111111111-1111-1-1111111-11-111-1-1-1-1-1-11111-11-1-11-111-11-1111-1-1-1-111-1-1-11-1-1-1-1-111-111-1-111111-11-1-11-111-1-1-11-1-111
χ15111111111-1111-1-1111111-1-1-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-1-11111-1-11-1-1-1-1111
χ16111111111-1111-1-1111111-1-1-1-11-1-1-1-1-1-11111-111-1-1-1-11-1-1-111-111-1-1-1-1-1-1-1111-1-1-1-1111111111111-11-1-11-1-1-11111-1-1-1
χ1722222-2222022200222-2-2-222-2-220000002-2-2-200022220-2-2-200-200-2-2-2-2000-2-2200220000000000000-20020000000000
χ1822222-2222022200222-2-2-22-2-2220000002-2-2-20002-22-20-22-200200-2-222000-22-2002-20000000000000200-20000000000
χ1922222-2222022200222-2-2-2-222-220000002-2-2-2000-22-2202-2200-20022-2-2000-22-200-220000000000000200-20000000000
χ2022222-2222022200222-2-2-2-2-22220000002-2-2-2000-2-2-2-20222002002222000-2-2200-2-20000000000000-20020000000000
χ212222-122-1222-1-122-12-122-10202-12-122-1-1-12-1-1202020-120-100022200-1-1-1-1-1-1002-10-10-100-1-12-1-1-1020002000-1000-10-10
χ222222-122-1222-1-122-12-122-10202-12-122-1-1-12-1-1-202020-1-20-100022200-1-1-1-1-1-100-210-10-100-1-1-21110-2000-200010001010
χ232222-122-1222-1-122-12-122-10-20-2-12-122-1-1-12-1-120-20-201201000-2-2-20011-1-1-1-1002-1010100112-1-1-10-2000-2000-10001010
χ242222-122-1222-1-122-12-122-10-20-2-12-122-1-1-12-1-1-20-20-201-201000-2-2-20011-1-1-1-100-2101010011-21110200020001000-10-10
χ252222-122-12-22-1-1-2-2-12-122-10202-1-21-2-211-12-1-120-2020-1-20-10002-2-200-1-1111-1002-10-1010011-211102000-2000-1000-1010
χ262222-122-12-22-1-1-2-2-12-122-10202-1-21-2-211-12-1-1-20-2020-120-10002-2-200-1-1111-100-210-10100112-1-1-10-20002000100010-10
χ272222-122-12-22-1-1-2-2-12-122-10-20-2-1-21-2-211-12-1-12020-201-201000-2220011111-1002-1010-100-1-1-21110-20002000-100010-10
χ282222-122-12-22-1-1-2-2-12-122-10-20-2-1-21-2-211-12-1-1-2020-201201000-2220011111-100-21010-100-1-12-1-1-102000-20001000-1010
χ29222-122-1222-12-122-1-122-122020-1-12-1-122-1-12-122020-102-10222000-1-100-1-1-1-100-12-10-10-1-100-12-1-1200020000-100-10-100
χ30222-122-1222-12-122-1-122-122020-1-12-1-122-1-12-1-22020-10-2-10222000-1-100-1-1-1-1001-2-10-10-1-1001-211-2000-2000010010100
χ31222-122-1222-12-122-1-122-12-20-20-1-12-1-122-1-12-12-20-2010210-2-2-20001100-1-1-1-100-1210101100-12-1-1-2000-20000-10010100
χ32222-122-1222-12-122-1-122-12-20-20-1-12-1-122-1-12-1-2-20-2010-210-2-2-20001100-1-1-1-1001-2101011001-211200020000100-10-100
χ33222-122-122-2-12-1-2-2-1-122-122020-11-211-2-2-1-12-12-2020-10-2-102-2-2000-1-100111-100-12-101011001-2112000-20000-100-10100
χ34222-122-122-2-12-1-2-2-1-122-122020-11-211-2-2-1-12-1-2-2020-102-102-2-2000-1-100111-1001-2-10101100-12-1-1-20002000010010-100
χ35222-122-122-2-12-1-2-2-1-122-12-20-20-11-211-2-2-1-12-1220-2010-210-2220001100111-100-1210-10-1-1001-211-200020000-10010-100
χ36222-122-122-2-12-1-2-2-1-122-12-20-20-11-211-2-2-1-12-1-220-2010210-2220001100111-1001-210-10-1-100-12-1-12000-20000100-10100
χ3722-122222-12-1-12-1-12-1-1-1222222-122-1-1-1-1-1-1-12022-1-122022-1-1-1-1-1-1-1-1-1-12-1-1-12200-1-122-1-1-1-10000002-100-1-1-100000000
χ3822-122222-12-1-12-1-12-1-1-1222-22-2-122-1-1-1-1-1-1-1202-2-112-202-2-1-1-1111-1-1112-1-1-1-2-200-112-2-1-111000000-210011100000000
χ3922-122222-12-1-12-1-12-1-1-122-22-22-122-1-1-1-1-1-1-120-221-1-220-22111-1-1-111-1-12-1-1-1-2-2001-1-2211-1-1000000-210011100000000
χ4022-122222-12-1-12-1-12-1-1-122-2-2-2-2-122-1-1-1-1-1-1-120-2-211-2-20-2-211111111112-1-1-1220011-2-211110000002-100-1-1-100000000
χ4122-122222-1-2-1-12112-1-1-1222222-1-2-21111-1-1-120-2-2-1-122022-111-111-1-1-1-1-211-12200-1-1-2-21111000000-2-100-11100000000
χ4222-122222-1-2-1-12112-1-1-1222-22-2-1-2-21111-1-1-120-22-112-202-2-1111-1-1-1-111-211-1-2-200-11-2211-1-100000021001-1-100000000
χ4322-122222-1-2-1-12112-1-1-122-22-22-1-2-21111-1-1-1202-21-1-220-221-1-1-11111-1-1-211-1-2-2001-12-2-1-11100000021001-1-100000000
χ4422-122222-1-2-1-12112-1-1-122-2-2-2-2-1-2-21111-1-1-1202211-2-20-2-21-1-11-1-11111-211-122001122-1-1-1-1000000-2-100-11100000000
χ4522-122-222-10-1-12−i3i32-1-11-2-222-2-2-100−i3i3−i3i3-111-2000-1-1220-2-21−i3i31−i3i311110−i3i31-2200-1-100−i3i3−i3i30000000100-1−i3i300000000
χ4622-122-222-10-1-12−i3i32-1-11-2-22-2-22-100−i3i3−i3i3-111-2000-112-20-221−i3i3-1i3−i311-1-10−i3i312-200-1100−i3i3i3−i30000000-1001i3−i300000000
χ4722-122-222-10-1-12−i3i32-1-11-2-2-222-2-100−i3i3−i3i3-111-20001-1-2202-2-1i3−i31−i3i3-1-1110−i3i312-2001-100i3−i3−i3i30000000-1001i3−i300000000
χ4822-122-222-10-1-12−i3i32-1-11-2-2-2-222-100−i3i3−i3i3-111-200011-2-2022-1i3−i3-1i3−i3-1-1-1-10−i3i31-22001100i3−i3i3−i30000000100-1−i3i300000000
χ4922-122-222-10-1-12i3−i32-1-11-2-222-2-2-100i3−i3i3−i3-111-2000-1-1220-2-21i3−i31i3−i311110i3−i31-2200-1-100i3−i3i3−i30000000100-1i3−i300000000
χ5022-122-222-10-1-12i3−i32-1-11-2-22-2-22-100i3−i3i3−i3-111-2000-112-20-221i3−i3-1−i3i311-1-10i3−i312-200-1100i3−i3−i3i30000000-1001−i3i300000000
χ5122-122-222-10-1-12i3−i32-1-11-2-2-222-2-100i3−i3i3−i3-111-20001-1-2202-2-1−i3i31i3−i3-1-1110i3−i312-2001-100−i3i3i3−i30000000-1001−i3i300000000
χ5222-122-222-10-1-12i3−i32-1-11-2-2-2-222-100i3−i3i3−i3-111-200011-2-2022-1−i3i3-1−i3i3-1-1-1-10i3−i31-22001100−i3i3−i3i30000000100-1i3−i300000000
χ534444-2-44-2404-2-200-24-2-4-42040-4-2000000-2-422000040-2002000-4000022000200000-2000000000000000000000000000
χ544444-2-44-2404-2-200-24-2-4-420-404-2000000-2-4220000-40200-200040000-2-20002000002000000000000000000000000000
χ55444-24-4-2440-24-200-2-24-42-440-40-2000000-22-4200040-20020-400000220000020000-20000000000000000000000000000
χ56444-24-4-2440-24-200-2-24-42-4-4040-2000000-22-42000-40200-20400000-2-2000002000020000000000000000000000000000
χ57444-2-24-2-244-2-21441-2-24-2-200001-2-2-2-2-2-21-2-2140000004000000000000111100-2-200000000-2-21100000000010000000
χ58444-2-24-2-244-2-21441-2-24-2-200001-2-2-2-2-2-21-2-21-4000000-4000000000000111100220000000022-1-1000000000-10000000
χ59444-2-24-2-24-4-2-21-4-41-2-24-2-2000012222221-2-214000000-4000000000000-1-1-1100-2-20000000022-1-100000000010000000
χ60444-2-24-2-24-4-2-21-4-41-2-24-2-2000012222221-2-21-40000004000000000000-1-1-11002200000000-2-211000000000-10000000
χ6144-24-244-2-24-21-2-2-2-2-21-24-2040414-2-2-2111-21-20040-20-200-2000-2-2-20011-21110000010-20011000000000000000000000
χ6244-24-244-2-24-21-2-2-2-2-21-24-20-40-414-2-2-2111-21-200-4020200200022200-1-1-211100000-10200-1-1000000000000000000000
χ6344-24-244-2-2-4-21-222-2-21-24-204041-4222-1-11-21-200-40-20-200-2000-22200112-1-110000010200-1-1000000000000000000000
χ6444-24-244-2-2-4-21-222-2-21-24-20-40-41-4222-1-11-21-200402020020002-2-200-1-12-1-1100000-10-20011000000000000000000000
χ6544-24-2-44-2-20-21-2−2i32i3-2-212-42040-4100−2i32i3i3−i312-120000-20-20020002−2i32i300-1-10i3−i3-10000010000i3−i3000000000000000000000
χ6644-24-2-44-2-20-21-2−2i32i3-2-212-420-404100−2i32i3i3−i312-12000020200-2000-22i3−2i300110i3−i3-100000-10000−i3i3000000000000000000000
χ6744-24-2-44-2-20-21-22i3−2i3-2-212-42040-41002i3−2i3−i3i312-120000-20-200200022i3−2i300-1-10−i3i3-10000010000−i3i3000000000000000000000
χ6844-24-2-44-2-20-21-22i3−2i3-2-212-420-4041002i3−2i3−i3i312-12000020200-2000-2−2i32i300110−i3i3-100000-10000i3−i3000000000000000000000
χ6944-2-244-24-241-2-2-2-2-21-2-2-2440401-2411-2-211-2-2040-20-200-20-2-2-20001100-2111000010-201100000000000000000000000
χ7044-2-244-24-241-2-2-2-2-21-2-2-24-40-401-2411-2-211-2-20-402020020222000-1-100-21110000-1020-1-100000000000000000000000
χ7144-2-244-24-2-41-2-222-21-2-2-24404012-4-1-12211-2-20-40-20-200-20-22200011002-1-1100001020-1-100000000000000000000000
χ7244-2-244-24-2-41-2-222-21-2-2-24-40-4012-4-1-12211-2-204020200202-2-2000-1-1002-1-110000-10-201100000000000000000000000
χ7344-2-24-4-24-201-2-2−2i32i3-21-222-440-40100i3−i3−2i32i31-122000-20-200202−2i32i3000-1-1000i3−i3-100001000i3−i300000000000000000000000
χ7444-2-24-4-24-201-2-2−2i32i3-21-222-4-4040100i3−i3−2i32i31-12200020200-20-22i3−2i300011000i3−i3-10000-1000−i3i300000000000000000000000
χ7544-2-24-4-24-201-2-22i3−2i3-21-222-440-40100−i3i32i3−2i31-122000-20-2002022i3−2i3000-1-1000−i3i3-100001000−i3i300000000000000000000000
χ7644-2-24-4-24-201-2-22i3−2i3-21-222-4-4040100−i3i32i3−2i31-12200020200-20-2−2i32i300011000−i3i3-10000-1000i3−i300000000000000000000000
χ774-44440-4-4-4044400-4-4-400000004000000-400000000000000000000000000000000000000000000000000000−2i22i200000
χ784-44440-4-4-4044400-4-4-400000004000000-4000000000000000000000000000000000000000000000000000002i2−2i200000
χ79888-4-4-8-4-480-4-42002-4-4-84400002000000244-200000000000000000000000-2000000000000000000000000000000000
χ8088-4-4-48-4-4-48222-4-4222-4-4-40000-1-4-42222-1222000000000000000000002-1-1-1000000000000000000000000000000000
χ8188-4-4-48-4-4-4-822244222-4-4-40000-144-2-2-2-2-122200000000000000000000-211-1000000000000000000000000000000000
χ8288-4-4-4-8-4-4-40222−4i34i32224440000-1002i3−2i32i3−2i3-1-2-2-2000000000000000000000−i3i31000000000000000000000000000000000
χ8388-4-4-4-8-4-4-402224i3−4i32224440000-100−2i32i3−2i32i3-1-2-2-2000000000000000000000i3−i31000000000000000000000000000000000
χ848-888-40-84-808-4-4004-840000000-40000004000000000000000000000000000000000000000000000000000000000000
χ858-88-4804-8-80-48-40044-80000000-40000004000000000000000000000000000000000000000000000000000000000000
χ868-88-4-4044-80-4-4200-24400000002000000-20000000000000000000000000000000000000000032−3200000000000000000
χ878-88-4-4044-80-4-4200-24400000002000000-200000000000000000000000000000000000000000−323200000000000000000
χ888-8-4880-8-840-4-4800-8440000000-40000004000000000000000000000000000000000000000000000000000000000000
χ898-8-48-40-8440-42-40044-200000002000000-20000000000000000000006i−6i0000000000000000000000000000000000000
χ908-8-48-40-8440-42-40044-200000002000000-2000000000000000000000−6i6i0000000000000000000000000000000000000
χ918-8-4-4804-8402-4-4004-2400000002000000-200000000000000000006i−6i000000000000000000000000000000000000000
χ928-8-4-4804-8402-4-4004-2400000002000000-20000000000000000000−6i6i000000000000000000000000000000000000000
χ9316-16-8-8-80888044400-4-4-40000000-20000002000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).