Finite Group Databasebeta

← Group #13156371

Character table — Group #13156371

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222222444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636363636363636363636363636108108
order1222333446666666663336666666661212121212123666121212121212121212124444441212121212121212121212121212121212121212121212124888812121212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-11-1111111-1-111-1-111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1111-1-11111-1-1111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111111111111111111111111-1-11111-1-111-1-1111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1
χ711111111111111111111111111111111111111111111111111-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-111
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2002200000000000000000000000000-2000022-2-20000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200-2-20000000000000000000000000020000-2-2220000000000
χ11222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100222200220022-1-1-1-10000-1-1-1-1-1-1-1-120000-1-1-1-10000000000
χ12222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-10022-2-200-2-200-2-2111100001111111120000-1-1-1-10000000000
χ13222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-22-2002200-2-2-1-1110000-1-1-1-11111-2000011110000000000
χ14222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-2-2200-2-2002211-1-100001111-1-1-1-1-2000011110000000000
χ15222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100220000000000−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3-20000-1-1110000000000
χ16222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100220000000000i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3-20000-1-1110000000000
χ17222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100-2-20000000000−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i32000011-1-10000000000
χ18222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100-2-20000000000i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i32000011-1-10000000000
χ1922222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1220020-1-1-1-122002200-1-1-1-1-1-1-1-10000022000000-1-1-1-1000000
χ2022222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-12200-20-1-1112200-2-200-1-1-1-1111100000-2-20000001111000000
χ2122222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2002011-1-1-2-20022001111-1-1-1-100000-2-20000001111000000
χ2222222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-200-201111-2-200-2-200111111110000022000000-1-1-1-1000000
χ232222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-12200022200-1-1-1-10022-1-1-1-10000-1-1-1-10002200000000-1-1-1-100
χ242222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-122000-22200-1-11100-2-2-1-1-1-100001111000-2-200000000111100
χ252222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-20002-2-20011-1-1002211110000-1-1-1-1000-2-200000000111100
χ262222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-2000-2-2-200111100-2-21111000011110002200000000-1-1-1-100
χ272-22-222200-2-2-2-22-222-2222-2-22-2-2-222-200000022-2-20000000000002i−2i000000000000000000000000000−i2i22−22i−2i00−i2−i2i2i222−2−200
χ282-22-222200-2-2-2-22-222-2222-2-22-2-2-222-200000022-2-20000000000002i−2i000000000000000000000000000i2−i2−222i−2i00i2i2−i2−i2−2−22200
χ292-22-222200-2-2-2-22-222-2222-2-22-2-2-222-200000022-2-2000000000000−2i2i000000000000000000000000000−i2i2−22−2i2i00−i2−i2i2i2−2−22200
χ302-22-222200-2-2-2-22-222-2222-2-22-2-2-222-200000022-2-2000000000000−2i2i000000000000000000000000000i2−i22−2−2i2i00i2i2−i2−i222−2−200
χ312-2-222222-2-2222-2-2-2-2-2222-2-2-2222-2-2-2222-2-2-22-2-222-22-22-222-2-2000000000000000000000000000000000000000000000002-2
χ322-2-222222-2-2222-2-2-2-2-2222-2-2-2222-2-2-2222-2-2-22-2-222-22-22-222-2-200000000000000000000000000000000000000000000000-22
χ332-2-22222-22-2222-2-2-2-2-2222-2-2-2222-2-2-2-2-2-22222-2-22-22-22-22-2-2222i−2i00002i−2i002i−2i0000002i2i−2i−2i000000000000000000000000000
χ342-2-22222-22-2222-2-2-2-2-2222-2-2-2222-2-2-2-2-2-22222-2-22-22-22-22-2-222−2i2i0000−2i2i00−2i2i000000−2i−2i2i2i000000000000000000000000000
χ352-2-222-12-22-22-1211-2-2-2-12-11-21-12-11-21-21-222-1-111-11-1-221-111-1-12i−2i0000−ii3−32i−2i000000−i−iii3−33−30000000000000−i3i3−i3i3000000
χ362-2-222-12-22-22-1211-2-2-2-12-11-21-12-11-21-21-222-1-111-11-1-221-111-1-12i−2i0000−ii−332i−2i000000−i−iii−33−330000000000000i3−i3i3−i3000000
χ372-2-222-12-22-22-1211-2-2-2-12-11-21-12-11-21-21-222-1-111-11-1-221-111-1-1−2i2i0000i−i3−3−2i2i000000ii−i−i3−33−30000000000000i3−i3i3−i3000000
χ382-2-222-12-22-22-1211-2-2-2-12-11-21-12-11-21-21-222-1-111-11-1-221-111-1-1−2i2i0000i−i−33−2i2i000000ii−i−i−33−330000000000000−i3i3−i3i3000000
χ392-2-22-122-221-122-2-21-2-2-1-1211-2-1-1211-21-2-22-12-111-11-11-1-2211-1-12i−2i00002i−2i00−ii3−30000−i−iii00003−33−30000000000000−i3i3−i3i300
χ402-2-22-122-221-122-2-21-2-2-1-1211-2-1-1211-21-2-22-12-111-11-11-1-2211-1-12i−2i00002i−2i00−ii−330000−i−iii0000−33−330000000000000i3−i3i3−i300
χ412-2-22-122-221-122-2-21-2-2-1-1211-2-1-1211-21-2-22-12-111-11-11-1-2211-1-1−2i2i0000−2i2i00i−i3−30000ii−i−i00003−33−30000000000000i3−i3i3−i300
χ422-2-22-122-221-122-2-21-2-2-1-1211-2-1-1211-21-2-22-12-111-11-11-1-2211-1-1−2i2i0000−2i2i00i−i−330000ii−i−i0000−33−330000000000000−i3i3−i3i300
χ4344444-24-4-444-24-2-2444-24-2-24-2-24-2-24-2-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000
χ4444444-2-24444-2-2-2-24-2-2-2-21-2-21-2-21-2-214-2-2-24-21111-2-2-2-211111100004000-2-20000-2-2000000111100000000000000000000000
χ4544444-2-24444-2-2-2-24-2-2-2-21-2-21-2-21-2-214-2-2-24-21111-2-2-2-21111110000-400022000022000000-1-1-1-100000000000000000000000
χ4644444-2-2-4-444-2-2-2-24-2-2-2-21-2-21-2-21-2-21-4222-4211112222-1-1-1-1-1-100000000000000−2i32i3000000i3i3−i3−i300000000000000000000000
χ4744444-2-2-4-444-2-2-2-24-2-2-2-21-2-21-2-21-2-21-4222-4211112222-1-1-1-1-1-1000000000000002i3−2i3000000−i3−i3i3i300000000000000000000000
χ484444-244-4-4-2-24444-244-2-24-2-24-2-24-2-242-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000000
χ494444-24-244-2-24-244-2-2-2-21-2-21-2-21-2-21-2-24-2-2-241111-2-211-2-21111000004000000-2-200-2-20000000011110000000000000000000
χ504444-24-244-2-24-244-2-2-2-21-2-21-2-21-2-21-2-24-2-2-241111-2-211-2-2111100000-400000022002200000000-1-1-1-10000000000000000000
χ514444-24-2-4-4-2-24-244-2-2-2-21-2-21-2-21-2-21-22-4222-4111122-1-122-1-1-1-10000000000000000−2i32i300000000i3i3−i3−i30000000000000000000
χ524444-24-2-4-4-2-24-244-2-2-2-21-2-21-2-21-2-21-22-4222-4111122-1-122-1-1-1-100000000000000002i3−2i300000000−i3−i3i3i30000000000000000000
χ534444-2-2444-2-2-24-2-2-2441-2-21-2-21-2-21-2-2-2-244-2-2111111-2-2-2-21111440000-2-200-2-20000001111000000000000000000000000000
χ544444-2-2444-2-2-24-2-2-2441-2-21-2-21-2-21-2-2-2-244-2-2111111-2-2-2-21111-4-40000220022000000-1-1-1-1000000000000000000000000000
χ554444-2-24-4-4-2-2-24-2-2-2441-2-21-2-21-2-21-2-222-4-4221111-1-12222-1-1-1-10000000000000000003-33-3000000000000000000000000000
χ564444-2-24-4-4-2-2-24-2-2-2441-2-21-2-21-2-21-2-222-4-4221111-1-12222-1-1-1-1000000000000000000-33-33000000000000000000000000000
χ5744-4-4444004-4-4-4-44-4-4444444-4-4-4-4-4-440000004-44-400000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2004-4-42-44-42-24-2-24-22-422-42-2000000-22-220000000000000000000000000000000000000000000000023−230000000000
χ5944-4-444-2004-4-42-44-42-24-2-24-22-422-42-2000000-22-2200000000000000000000000000000000000000000000000−23230000000000
χ6044-4-44-24004-42-42-2-4-44-24-2-2422-422-4-2000000-22-2200000000000000000000000000000000000000000000000006−6−66000000
χ6144-4-44-24004-42-42-2-4-44-24-2-2422-422-4-2000000-22-220000000000000000000000000000000000000000000000000−666−6000000
χ6244-4-4-24400-22-4-4-442-44-2-24-2-2-422-4224000000-22-2200000000000000000000000000000000000000000000000000000i6−i6−i6i600
χ6344-4-4-24400-22-4-4-442-44-2-24-2-2-422-4224000000-22-2200000000000000000000000000000000000000000000000000000−i6i6i6−i600
χ644-44-444-200-4-4-424-44-224-2-2-42-2-4224-22000000-2-2220000000000004i−4i0000000000000000000000000000000−2i2i000000000000
χ654-44-444-200-4-4-424-44-224-2-2-42-2-4224-22000000-2-222000000000000−4i4i00000000000000000000000000000002i−2i000000000000
χ664-44-44-2400-4-42-4-2244-4-24-22-4-22-42-242000000-2-22200000000000000000000000000000000000000000−2i22i2000000i2i2−i2−i2000000
χ674-44-44-2400-4-42-4-2244-4-24-22-4-22-42-242000000-2-222000000000000000000000000000000000000000002i2−2i2000000−i2−i2i2i2000000
χ684-44-4-2440022-4-44-4-24-4-2-2422422-4-2-2-4000000-2-222000000000000000000000000000000000000000000022−2200000000−2−22200
χ694-44-4-2440022-4-44-4-24-4-2-2422422-4-2-2-4000000-2-2220000000000000000000000000000000000000000000−22220000000022−2−200
χ704-4-4444-24-4-444-2-4-4-4224-2-2-4224-2-2-42244-22-4-4-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000000
χ714-4-4444-2-44-444-2-4-4-4224-2-2-4224-2-2-422-4-42-244-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000
χ724-4-444-244-4-44-2422-4-4-4-24-22-42-24-22-424-24-4-42-222-2-224-4-22-2-2220000000000000000000000000000000000000000000000000
χ734-4-444-2-24-4-44-2-222-422-2-2122-1-2-2122-14-2-22-421-1-11-22-221-111-1-100000000000000000000003i−3i−3i3i00000000000000000000000
χ744-4-444-2-24-4-44-2-222-422-2-2122-1-2-2122-14-2-22-421-1-11-22-221-111-1-10000000000000000000000−3i3i3i−3i00000000000000000000000
χ754-4-444-2-2-44-44-2-222-422-2-2122-1-2-2122-1-422-24-21-1-112-22-2-11-1-1110000000023−23000000000000−33−3300000000000000000000000
χ764-4-444-2-2-44-44-2-222-422-2-2122-1-2-2122-1-422-24-21-1-112-22-2-11-1-11100000000−23230000000000003−33−300000000000000000000000
χ774-4-44-2444-42-244-4-42-4-4-2-2422-4-2-2422-4-244-42-4-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000
χ784-4-44-24-24-42-24-2-4-4222-21-22-12-21-22-12-24-222-41-1-11-221-1-2211-1-1000000000000000000000000003i−3i−3i3i0000000000000000000
χ794-4-44-24-24-42-24-2-4-4222-21-22-12-21-22-12-24-222-41-1-11-221-1-2211-1-100000000000000000000000000−3i3i3i−3i0000000000000000000
χ804-4-44-24-2-442-24-2-4-4222-21-22-12-21-22-122-42-2-241-1-112-2-112-2-1-11100000000000023−23000000000000−33−330000000000000000000
χ814-4-44-24-2-442-24-2-4-4222-21-22-12-21-22-122-42-2-241-1-112-2-112-2-1-111000000000000−23230000000000003−33−30000000000000000000
χ824-4-44-2-244-42-2-24222-4-41-2-2-1221-2-2-122-2-24-4221-1-111-1-22-2211-1-10000000000000000003i−3i−3i3i000000000000000000000000000
χ834-4-44-2-244-42-2-24222-4-41-2-2-1221-2-2-122-2-24-4221-1-111-1-22-2211-1-1000000000000000000−3i3i3i−3i000000000000000000000000000
χ844-4-44-2-24-442-2-24222-4-41-2-2-1221-2-2-12222-44-2-21-1-11-112-22-2-1-1114i−4i0000−2i2i00−2i2i000000ii−i−i000000000000000000000000000
χ854-4-44-2-24-442-2-24222-4-41-2-2-1221-2-2-12222-44-2-21-1-11-112-22-2-1-111−4i4i00002i−2i002i−2i000000−i−iii000000000000000000000000000
χ868888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000
χ878888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000
χ8888-8-88-4-4008-8444-4-84-4-4-42-4-4-244-24420000002-22-200000000000000000000000000000000000000000000000000000000000
χ8988-8-8-48-400-44-84-8844-4-42-4-4244-244-2-40000002-22-200000000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-4800-444-84-44-882-4-42-44-244-24-40000002-22-200000000000000000000000000000000000000000000000000000000000
χ9188-8-8-4-4-400-44444-444-422222-2-2-2-2-2-22000000-11-1100000033−3333−330000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-400-44444-444-422222-2-2-2-2-2-22000000-11-11000000−3333−33330000000000000000000000000000000000000000000000000
χ938-88-88-4-400-8-844-448-44-4-4244244-2-4-4-200000022-2-200000000000000000000000000000000000000000000000000000000000
χ948-88-8-48-40044-848-8-4-44-42-44-2-44-24-42400000022-2-200000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-4800444-8-44-48-82-4-4-24-4-2442-4400000022-2-200000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4004444-44-4-44222-2-22-2-2-222-2000000-1-11100000033−33−33330000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4004444-44-4-44222-2-22-2-2-222-2000000-1-111000000−333333−330000000000000000000000000000000000000000000000000
χ988-8-88-4-4-48-84-4-4-444444222-2-2-2222-2-2-2-4-4-4444-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000
χ998-8-88-4-4-4-884-4-4-444444222-2-2-2222-2-2-2444-4-4-4-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000

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