Finite Group Databasebeta

← Group #13156306

Character table — Group #13156306

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222222444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636363636363636363636363636108108
order1222333446666666663336666666661212121212123666121212121212121212124444441212121212121212121212121212121212121212121212124888812121212242424242424242422
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111
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
χ41111111111111111111111111111111111111111111111111111-1-1-111111-1-111-1-1111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
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
χ711111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
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
χ11222222-12222-12222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100222200002222-1-1-1-10000-1-1-1-1-1-1-1-120000-1-1-1-10000000000
χ12222222-12222-12222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-10022-2-20000-2-2-2-2111100001111111120000-1-1-1-10000000000
χ13222222-12222-12222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-22-2000022-2-2-1-1110000-1-1-1-11111-2000011110000000000
χ14222222-12222-12222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-2-220000-2-22211-1-100001111-1-1-1-1-2000011110000000000
χ15222222-1-2-222-12222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100220000000000−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3-20000-1-1110000000000
χ16222222-1-2-222-12222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100220000000000i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3-20000-1-1110000000000
χ17222222-1-2-222-12222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100-2-20000000000−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i32000011-1-10000000000
χ18222222-1-2-222-12222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100-2-20000000000i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i32000011-1-10000000000
χ1922222-12222-1222-1-122-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-122000222-1-100-1-10022-1-1-1-10000-1-1-1-10002200000000-1-1-1-100
χ2022222-12222-1222-1-122-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-122000-222-1-1001100-2-2-1-1-1-100001111000-2-200000000111100
χ2122222-12222-1222-1-122-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-20002-2-21100-1-1002211110000-1-1-1-1000-2-200000000111100
χ2222222-12222-1222-1-122-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2000-2-2-211001100-2-21111000011110002200000000-1-1-1-100
χ232222-12222-122-1-12222-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1220020-1-122-1-1002200-1-1-1-1-1-1-1-10000022000000-1-1-1-1000000
χ242222-12222-122-1-12222-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-12200-20-1-1221100-2-200-1-1-1-1111100000-2-20000001111000000
χ252222-12222-122-1-12222-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-2002011-2-2-1-10022001111-1-1-1-100000-2-20000001111000000
χ262222-12222-122-1-12222-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2011-2-21100-2-200111111110000022000000-1-1-1-1000000
χ2722-2-22222-2222-2-2-2-2-2-2222-2-2-2222-2-2-2222-2-2-22-2-222-22-22-222-2-2000000000000000000000000000000000000000000000002-2
χ2822-2-22222-2222-2-2-2-2-2-2222-2-2-2222-2-2-2222-2-2-22-2-222-22-22-222-2-200000000000000000000000000000000000000000000000-22
χ2922-2-2222-22222-2-2-2-2-2-2222-2-2-2222-2-2-2-2-2-22222-2-22-22-22-22-2-2222i−2i00002i−2i2i−2i000000002i2i−2i−2i000000000000000000000000000
χ3022-2-2222-22222-2-2-2-2-2-2222-2-2-2222-2-2-2-2-2-22222-2-22-22-22-22-2-222−2i2i0000−2i2i−2i2i00000000−2i−2i2i2i000000000000000000000000000
χ3122-2-22-12-222-12-2-211-2-2-12-11-21-12-11-21-21-222-1-111-11-1-221-111-1-12i−2i00002i−2i−ii003−30000−i−iii00003−33−30000000000000−i3−i3i3i300
χ3222-2-22-12-222-12-2-211-2-2-12-11-21-12-11-21-21-222-1-111-11-1-221-111-1-12i−2i00002i−2i−ii00−330000−i−iii0000−33−330000000000000i3i3−i3−i300
χ3322-2-22-12-222-12-2-211-2-2-12-11-21-12-11-21-21-222-1-111-11-1-221-111-1-1−2i2i0000−2i2ii−i003−30000ii−i−i00003−33−30000000000000i3i3−i3−i300
χ3422-2-22-12-222-12-2-211-2-2-12-11-21-12-11-21-21-222-1-111-11-1-221-111-1-1−2i2i0000−2i2ii−i00−330000ii−i−i0000−33−330000000000000−i3−i3i3i300
χ3522-2-2-122-22-12211-2-2-2-2-1-1211-2-1-1211-21-2-22-12-111-11-11-1-2211-1-12i−2i0000−ii2i−2i3−3000000−i−iii3−33−30000000000000−i3−i3i3i3000000
χ3622-2-2-122-22-12211-2-2-2-2-1-1211-2-1-1211-21-2-22-12-111-11-11-1-2211-1-12i−2i0000−ii2i−2i−33000000−i−iii−33−330000000000000i3i3−i3−i3000000
χ3722-2-2-122-22-12211-2-2-2-2-1-1211-2-1-1211-21-2-22-12-111-11-11-1-2211-1-1−2i2i0000i−i−2i2i3−3000000ii−i−i3−33−30000000000000i3i3−i3−i3000000
χ3822-2-2-122-22-12211-2-2-2-2-1-1211-2-1-1211-21-2-22-12-111-11-11-1-2211-1-1−2i2i0000i−i−2i2i−33000000ii−i−i−33−330000000000000−i3−i3i3i3000000
χ392-22-222200-2-2-22-22-22-2222-222-2-2-22-2-200000022-2-20000000000002-2000000000000000000000000000−i2i2−i2i22-200−i2i2−i2i2−i2i2−i2i200
χ402-22-222200-2-2-22-22-22-2222-222-2-2-22-2-200000022-2-20000000000002-2000000000000000000000000000i2−i2i2−i22-200i2−i2i2−i2i2−i2i2−i200
χ412-22-222200-2-2-22-22-22-2222-222-2-2-22-2-200000022-2-2000000000000-22000000000000000000000000000−i2i2i2−i2-2200−i2i2−i2i2i2−i2i2−i200
χ422-22-222200-2-2-22-22-22-2222-222-2-2-22-2-200000022-2-2000000000000-22000000000000000000000000000i2−i2−i2i2-2200i2−i2i2−i2−i2i2−i2i200
χ4344444-24-4-44-2444-2-244-24-2-24-2-24-2-24-2-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000
χ4444444-2-2444-2-244-2-2-2-2-2-21-2-21-2-21-2-214-2-2-24-21111-2-2-2-2111111000004000000-2-200-2-20000000011110000000000000000000
χ4544444-2-2444-2-244-2-2-2-2-2-21-2-21-2-21-2-214-2-2-24-21111-2-2-2-211111100000-400000022002200000000-1-1-1-10000000000000000000
χ4644444-2-2-4-44-2-244-2-2-2-2-2-21-2-21-2-21-2-21-4222-4211112222-1-1-1-1-1-10000000000000000−2i32i300000000i3i3−i3−i30000000000000000000
χ4744444-2-2-4-44-2-244-2-2-2-2-2-21-2-21-2-21-2-21-4222-4211112222-1-1-1-1-1-100000000000000002i3−2i300000000−i3−i3i3i30000000000000000000
χ484444-244-4-4-244-2-24444-2-24-2-24-2-24-2-242-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000000
χ494444-24-244-24-2-2-244-2-2-21-2-21-2-21-2-21-2-24-2-2-241111-2-211-2-211110000400000-2-200-2-2000000111100000000000000000000000
χ504444-24-244-24-2-2-244-2-2-21-2-21-2-21-2-21-2-24-2-2-241111-2-211-2-211110000-400000220022000000-1-1-1-100000000000000000000000
χ514444-24-2-4-4-24-2-2-244-2-2-21-2-21-2-21-2-21-22-4222-4111122-1-122-1-1-1-100000000000000−2i32i3000000i3i3−i3−i300000000000000000000000
χ524444-24-2-4-4-24-2-2-244-2-2-21-2-21-2-21-2-21-22-4222-4111122-1-122-1-1-1-1000000000000002i3−2i3000000−i3−i3i3i300000000000000000000000
χ534444-2-2444-2-24-2-2-2-2441-2-21-2-21-2-21-2-2-2-244-2-2111111-2-2-2-21111440000-2-2-2-2000000001111000000000000000000000000000
χ544444-2-2444-2-24-2-2-2-2441-2-21-2-21-2-21-2-2-2-244-2-2111111-2-2-2-21111-4-40000222200000000-1-1-1-1000000000000000000000000000
χ554444-2-24-4-4-2-24-2-2-2-2441-2-21-2-21-2-21-2-222-4-4221111-1-12222-1-1-1-10000000000000000003-33-3000000000000000000000000000
χ564444-2-24-4-4-2-24-2-2-2-2441-2-21-2-21-2-21-2-222-4-4221111-1-12222-1-1-1-1000000000000000000-33-33000000000000000000000000000
χ5744-4-444-24-444-2-4-4-4-4224-2-2-4224-2-2-42244-22-4-4-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000000
χ5844-4-444-2-4444-2-4-4-4-4224-2-2-4224-2-2-422-4-42-244-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000
χ5944-4-44-244-44-24-4-422-4-4-24-22-42-24-22-424-24-4-42-222-2-224-4-22-2-2220000000000000000000000000000000000000000000000000
χ6044-4-44-2-24-44-2-2-4-42222-2-2122-1-2-2122-14-2-22-421-1-11-22-221-111-1-1000000000000000000000000003i−3i−3i3i0000000000000000000
χ6144-4-44-2-24-44-2-2-4-42222-2-2122-1-2-2122-14-2-22-421-1-11-22-221-111-1-100000000000000000000000000−3i3i3i−3i0000000000000000000
χ6244-4-44-2-2-444-2-2-4-42222-2-2122-1-2-2122-1-422-24-21-1-112-22-2-11-1-11100000000000023−23000000000000−33−330000000000000000000
χ6344-4-44-2-2-444-2-2-4-42222-2-2122-1-2-2122-1-422-24-21-1-112-22-2-11-1-111000000000000−23230000000000003−33−30000000000000000000
χ6444-4-4-2444-4-24422-4-4-4-4-2-2422-4-2-2422-4-244-42-4-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000
χ6544-4-4-24-24-4-24-222-4-422-21-22-12-21-22-12-24-222-41-1-11-221-1-2211-1-100000000000000000000003i−3i−3i3i00000000000000000000000
χ6644-4-4-24-24-4-24-222-4-422-21-22-12-21-22-12-24-222-41-1-11-221-1-2211-1-10000000000000000000000−3i3i3i−3i00000000000000000000000
χ6744-4-4-24-2-44-24-222-4-422-21-22-12-21-22-122-42-2-241-1-112-2-112-2-1-111000000000023−230000000000−33−3300000000000000000000000
χ6844-4-4-24-2-44-24-222-4-422-21-22-12-21-22-122-42-2-241-1-112-2-112-2-1-1110000000000−232300000000003−33−300000000000000000000000
χ6944-4-4-2-244-4-2-242222-4-41-2-2-1221-2-2-122-2-24-4221-1-111-1-22-2211-1-10000000000000000003i−3i−3i3i000000000000000000000000000
χ7044-4-4-2-244-4-2-242222-4-41-2-2-1221-2-2-122-2-24-4221-1-111-1-22-2211-1-1000000000000000000−3i3i3i−3i000000000000000000000000000
χ7144-4-4-2-24-44-2-242222-4-41-2-2-1221-2-2-12222-44-2-21-1-11-112-22-2-1-1114i−4i0000−2i2i−2i2i00000000ii−i−i000000000000000000000000000
χ7244-4-4-2-24-44-2-242222-4-41-2-2-1221-2-2-12222-44-2-21-1-11-112-22-2-1-111−4i4i00002i−2i2i−2i00000000−i−iii000000000000000000000000000
χ734-44-444-200-4-424-44-4-224-2-2-4-2-2-422422000000-2-2220000000000004-40000000000000000000000000000000-22000000000000
χ744-44-444-200-4-424-44-4-224-2-2-4-2-2-422422000000-2-222000000000000-4400000000000000000000000000000002-2000000000000
χ754-44-44-2400-42-44-4-224-4-24-224-22-42-2-42000000-2-2220000000000000000000000000000000000000000000−2i22i200000000i2−i2i2−i200
χ764-44-44-2400-42-44-4-224-4-24-224-22-42-2-42000000-2-22200000000000000000000000000000000000000000002i2−2i200000000−i2i2−i2i200
χ774-44-4-244002-4-4-224-44-4-2-242-2422-4-22-4000000-2-22200000000000000000000000000000000000000000−2i22i2000000i2−i2i2−i2000000
χ784-44-4-244002-4-4-224-44-4-2-242-2422-4-22-4000000-2-222000000000000000000000000000000000000000002i2−2i2000000−i2i2−i2i2000000
χ794-4-4444400-4-4-4-44-44-444444-4-4-4-4-4-4440000004-44-400000000000000000000000000000000000000000000000000000000000
χ804-4-4444-200-4-42-44-442-24-2-2422-422-4-2-2000000-22-2200000000000000000000000000000000000000000000000−2i32i30000000000
χ814-4-4444-200-4-42-44-442-24-2-2422-422-4-2-2000000-22-22000000000000000000000000000000000000000000000002i3−2i30000000000
χ824-4-444-2400-42-4-442-2-44-24-2-2-422-4224-2000000-22-22000000000000000000000000000000000000000000000000000006−6−6600
χ834-4-444-2400-42-4-442-2-44-24-2-2-422-4224-2000000-22-2200000000000000000000000000000000000000000000000000000−666−600
χ844-4-44-244002-4-42-2-44-44-2-24-22-422-42-24000000-22-2200000000000000000000000000000000000000000000000006−6−66000000
χ854-4-44-244002-4-42-2-44-44-2-24-22-422-42-24000000-22-220000000000000000000000000000000000000000000000000−666−6000000
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
χ8888-8-8-4-4-48-8-4-4-4444444222-2-2-2222-2-2-2-4-4-4444-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000
χ8988-8-8-4-4-4-88-4-4-4444444222-2-2-2222-2-2-2444-4-4-4-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000
χ908-88-88-4-400-8448-8-44-44-4-424-4244-2-44-200000022-2-200000000000000000000000000000000000000000000000000000000000
χ918-88-8-48-4004-84-448-8-44-42-442-44-24-4-2400000022-2-200000000000000000000000000000000000000000000000000000000000
χ928-88-8-4-480044-8-44-448-82-4-4-2-4-4-24424400000022-2-200000000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-400444-44-44-44222-222-2-2-22-2-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000
χ948-88-8-4-4-400444-44-44-44222-222-2-2-22-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000
χ958-8-888-4-400-844-884-44-4-4-42-44-244-24-420000002-22-200000000000000000000000000000000000000000000000000000000000
χ968-8-88-48-4004-844-4-884-4-42-4-4-244-2442-40000002-22-200000000000000000000000000000000000000000000000000000000000
χ978-8-88-4-480044-84-44-4-882-4-4244-244-2-4-40000002-22-200000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-4004444-44-44-42222-2-2-2-2-2-222000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000
χ998-8-88-4-4-4004444-44-44-42222-2-2-2-2-2-222000000-11-11000000−333333−330000000000000000000000000000000000000000000000000

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