Finite Group Databasebeta

← Group #13156671

Character table — Group #13156671

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212242424242424242424242424242424242424363636363636727272727272108108
order1222333446666666663336666666661212121212121212121236661212121212121212441212121212121212121212121212121244121212121212121212121212121212128824242424441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ51111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-111-1-111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-22-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ11222222-12222-1222-1-122-1-12-12-1-1-1-12-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1202200-1-100-1-1-1-1000000000020-1-10000
χ12222222-12222-1222-1-122-1-12-12-1-1-1-12-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-20-2-200110011110000000000-20110000
χ13222222-12222-1222-1-122-1-12-12-1-1-1-12-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-2-2-2-21111-2-211111111202200-1-100-1-1-1-10000000000-20110000
χ14222222-12222-1222-1-122-1-12-12-1-1-1-12-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-2-2-2-21111-2-211111111-20-2-20011001111000000000020-1-10000
χ15222222-1-2-222-1222-1-122-1-12-12-1-1-1-12-1-2-2-2111111-2-1-1-1-1-2-21111112-222-1-111-2-2-1-1-1-11111000000−i3i300−i3−i3i3i3000000000000−i3i30000
χ16222222-1-2-222-1222-1-122-1-12-12-1-1-1-12-1-2-2-2111111-2-1-1-1-1-2-21111112-222-1-111-2-2-1-1-1-11111000000i3−i300i3i3−i3−i3000000000000i3−i30000
χ17222222-1-2-222-1222-1-122-1-12-12-1-1-1-12-1-2-2-2111111-2-1-1-1-1-2-2111111-22-2-211-1-1221111-1-1-1-1000000−i3i300−i3−i3i3i3000000000000i3−i30000
χ18222222-1-2-222-1222-1-122-1-12-12-1-1-1-12-1-2-2-2111111-2-1-1-1-1-2-2111111-22-2-211-1-1221111-1-1-1-1000000i3−i300i3i3−i3−i3000000000000−i3i30000
χ1922222-12222-122-1-1222-12-1-1-1-12-122-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-100000000
χ2022222-12222-122-1-1222-12-1-1-1-12-122-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002-2-1-11122-2-2-1-1-1-11111-2-2111100000000
χ2122222-12222-122-1-1222-12-1-1-1-12-122-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2211-1-1-2-2221111-1-1-1-1-2-2111100000000
χ2222222-12222-122-1-1222-12-1-1-1-12-122-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-21111-2-2-2-21111111122-1-1-1-100000000
χ232222-12222-122-12222-1-1-12-12-1-12-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-102002200-1-10000-1-1-1-10000000200-1-100
χ242222-12222-122-12222-1-1-12-12-1-12-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-10-200-2-20011000011110000000-2001100
χ252222-12222-122-12222-1-1-12-12-1-12-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2-2-2111111111102002200-1-10000-1-1-1-10000000-2001100
χ262222-12222-122-12222-1-1-12-12-1-12-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2-2-211111111110-200-2-20011000011110000000200-1-100
χ272222-122-2-2-122-12222-1-1-12-12-1-12-1-1-1211-2-2-21111-2-1-1-1-111-2-211112-2-1-122-2-211-1-1-1-1111100000000−i3i30000−i3−i3i3i30000000000−i3i300
χ282222-122-2-2-122-12222-1-1-12-12-1-12-1-1-1211-2-2-21111-2-1-1-1-111-2-211112-2-1-122-2-211-1-1-1-1111100000000i3−i30000i3i3−i3−i30000000000i3−i300
χ292222-122-2-2-122-12222-1-1-12-12-1-12-1-1-1211-2-2-21111-2-1-1-1-111-2-21111-2211-2-222-1-11111-1-1-1-100000000−i3i30000−i3−i3i3i30000000000i3−i300
χ302222-122-2-2-122-12222-1-1-12-12-1-12-1-1-1211-2-2-21111-2-1-1-1-111-2-21111-2211-2-222-1-11111-1-1-1-100000000i3−i30000i3i3−i3−i30000000000−i3i300
χ3122-2-22222-2222-2-2-2-2-2-2222-2-2222-2-2-2-22-2-22-222-2-222-2-222-22-222-2-20000000000000000000000000000000000002-222-2-200000000
χ3222-2-22222-2222-2-2-2-2-2-2222-2-2222-2-2-2-22-2-22-222-2-222-2-222-22-222-2-2000000000000000000000000000000000000-22-2-22200000000
χ3322-2-2222-22222-2-2-2-2-2-2222-2-2222-2-2-2-2-222-22-2-222-22-2-22-22-22-2-2220000000000000000000000000000000000000000000000002-2
χ3422-2-2222-22222-2-2-2-2-2-2222-2-2222-2-2-2-2-222-22-2-222-22-2-22-22-22-2-222000000000000000000000000000000000000000000000000-22
χ3522-2-22-122-22-12-211-2-2-2-12-111-12-1-2-2112-212-222-2-2-1-111-1-11-11-1-111000000000000000000003−33−300003−33−33−33−32-2-1-11100000000
χ3622-2-22-122-22-12-211-2-2-2-12-111-12-1-2-2112-212-222-2-2-1-111-1-11-11-1-111000000000000000000003−3−3300003−33−3−33−33-2211-1-100000000
χ3722-2-22-122-22-12-211-2-2-2-12-111-12-1-2-2112-212-222-2-2-1-111-1-11-11-1-11100000000000000000000−333−30000−33−333−33−3-2211-1-100000000
χ3822-2-22-122-22-12-211-2-2-2-12-111-12-1-2-2112-212-222-2-2-1-111-1-11-11-1-11100000000000000000000−33−330000−33−33−33−332-2-1-11100000000
χ3944444-24-4-44-244-2-2444-24-2-2-2-24-244-2-2-4-42-4-4-4-4-4-42-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ4044444-2-2444-2-24-2-2-2-24-2-21-21-2-21-2-2-2144-2-2-2-2-2-2-2-21111-2-211111100000000000000000040-2-200-2-2001111000000000000000000
χ4144444-2-2444-2-24-2-2-2-24-2-21-21-2-21-2-2-2144-2-2-2-2-2-2-2-21111-2-2111111000000000000000000-4022002200-1-1-1-1000000000000000000
χ4244444-2-2-4-44-2-24-2-2-2-24-2-21-21-2-21-2-2-21-4-422222222111122-1-1-1-1-1-1000000000000000000000000−2i32i300i3i3−i3−i3000000000000000000
χ4344444-2-2-4-44-2-24-2-2-2-24-2-21-21-2-21-2-2-21-4-422222222111122-1-1-1-1-1-10000000000000000000000002i3−2i300−i3−i3i3i3000000000000000000
χ444444-24-244-24-2-244-2-2-2-21-2-2-2-21-211-2-2-2-24-2-2111141111-2-2-2-2111144-2-2-2-2-2-2-2-21111111100000000000000000000000000000000
χ454444-24-244-24-2-244-2-2-2-21-2-2-2-21-211-2-2-2-24-2-2111141111-2-2-2-21111-4-422222222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ464444-24-2-4-4-24-2-244-2-2-2-21-2-2-2-21-211-2-222-422-1-1-1-1-411112222-1-1-1-14-4-2-2-2-222221111-1-1-1-100000000000000000000000000000000
χ474444-24-2-4-4-24-2-244-2-2-2-21-2-2-2-21-211-2-222-422-1-1-1-1-411112222-1-1-1-1-442222-2-2-2-2-1-1-1-1111100000000000000000000000000000000
χ484444-2-2444-2-24-2-2-244-21-2-21-21-2-2-2-21-2-2-2-244-2-2-2-2-2111111-2-211110000000000000000000400-2-200-2-20000111100000000000000
χ494444-2-2444-2-24-2-2-244-21-2-21-21-2-2-2-21-2-2-2-244-2-2-2-2-2111111-2-211110000000000000000000-4002200220000-1-1-1-100000000000000
χ504444-2-24-4-4-2-24-2-2-244-21-2-21-21-2-2-2-21-2222-4-4222221111-1-122-1-1-1-100000000000000000000000000−2i32i30000i3i3−i3−i300000000000000
χ514444-2-24-4-4-2-24-2-2-244-21-2-21-21-2-2-2-21-2222-4-4222221111-1-122-1-1-1-1000000000000000000000000002i3−2i30000−i3−i3i3i300000000000000
χ5244-4-444-24-444-2-4-4-422-44-2-2-424-2-222-424-4-4-22-2-2224-222-24-4-22-2-22200000000000000000000000000000000000000000000000000
χ5344-4-444-2-4444-2-4-4-422-44-2-2-424-2-222-42-4442-222-2-2-4-222-2-442-222-2-200000000000000000000000000000000000000000000000000
χ5444-4-44-24-444-24-422-4-4-4-24-222-24-2-4-422-44-2-44-4-4442-222-22-22-222-2-200000000000000000000000000000000000000000000000000
χ5544-4-44-2-24-44-2-2-42222-4-2-212-1-2-21222-14-42-22-2-222-21-1-11-221-111-1-10000000000000000000023−23000000−33−33000000000000000000
χ5644-4-44-2-24-44-2-2-42222-4-2-212-1-2-21222-14-42-22-2-222-21-1-11-221-111-1-100000000000000000000−23230000003−33−3000000000000000000
χ5744-4-44-2-2-444-2-2-42222-4-2-212-1-2-21222-1-44-22-222-2-221-1-112-2-11-1-11100000000000000000000000000003i−3i−3i3i000000000000000000
χ5844-4-44-2-2-444-2-2-42222-4-2-212-1-2-21222-1-44-22-222-2-221-1-112-2-11-1-1110000000000000000000000000000−3i3i3i−3i000000000000000000
χ5944-4-4-2444-4-2442-4-4-4-42-2-242-4-2-24222-4-22-44-4-2-2224-222-2-224-4-2-22200000000000000000000000000000000000000000000000000
χ6044-4-4-244-44-2442-4-4-4-42-2-242-4-2-24222-42-24-4422-2-2-4-222-22-2-4422-2-200000000000000000000000000000000000000000000000000
χ6144-4-4-24-24-4-24-22-4-4222-21-222-21-2-1-122-22-4-2211-1-141-1-11-22-2211-1-100000000003i3i−3i−3i3i3i−3i−3i00000000000000000000000000000000
χ6244-4-4-24-24-4-24-22-4-4222-21-222-21-2-1-122-22-4-2211-1-141-1-11-22-2211-1-10000000000−3i−3i3i3i−3i−3i3i3i00000000000000000000000000000000
χ6344-4-4-24-2-44-24-22-4-4222-21-222-21-2-1-1222-242-2-1-111-41-1-112-22-2-1-11100000000003i3i−3i−3i−3i−3i3i3i00000000000000000000000000000000
χ6444-4-4-24-2-44-24-22-4-4222-21-222-21-2-1-1222-242-2-1-111-41-1-112-22-2-1-1110000000000−3i−3i3i3i3i3i−3i−3i00000000000000000000000000000000
χ6544-4-4-2-244-4-2-24222-4-421-2-2-121-2-222-12-2224-4-2-222-21-1-111-1-2211-1-1000000000000000000000023−2300000000−33−3300000000000000
χ6644-4-4-2-244-4-2-24222-4-421-2-2-121-2-222-12-2224-4-2-222-21-1-111-1-2211-1-10000000000000000000000−2323000000003−33−300000000000000
χ6744-4-4-2-24-44-2-24222-4-421-2-2-121-2-222-122-2-2-4422-2-221-1-11-112-2-1-111000000000000000000000000000000003i−3i−3i3i00000000000000
χ6844-4-4-2-24-44-2-24222-4-421-2-2-121-2-222-122-2-2-4422-2-221-1-11-112-2-1-11100000000000000000000000000000000−3i3i3i−3i00000000000000
χ694-44-444400-4-4-444-44-4-44444-4-4-4-44-4-44000000000044-4-40000000000000000000000000000000000000000000000000000000000
χ704-44-444-200-4-4244-4-22-44-2-242-422-22-4-20000000000-2-2220000000000000023−2300000023−2323−2300000000000000000000000000000000
χ714-44-444-200-4-4244-4-22-44-2-242-422-22-4-20000000000-2-22200000000000000−2323000000−2323−232300000000000000000000000000000000
χ724-44-44-2400-42-44-224-4-4-24-2-222-424-42-20000000000-2-22200000000000000000000000000000000000000000000006−66−600000000
χ734-44-44-2400-42-44-224-4-4-24-2-222-424-42-20000000000-2-2220000000000000000000000000000000000000000000000−66−6600000000
χ744-44-4-244002-4-4-24-44-42-2-24-2-422-4-22240000000000-2-2220000000000−2i32i3000000−2i32i3−2i32i3000000000000000000000000000000000000
χ754-44-4-244002-4-4-24-44-42-2-24-2-422-4-22240000000000-2-22200000000002i3−2i30000002i3−2i32i3−2i3000000000000000000000000000000000000
χ764-44-4-24-2002-42-24-4-222-21-2-222-121-12-2000003i−3i3i−3i011-1-100003i−3i3i−3i00−2i32i30023−2300i3−i3i3−i3−33−3300000000000000000000000000000000
χ774-44-4-24-2002-42-24-4-222-21-2-222-121-12-2000003i−3i3i−3i011-1-100003i−3i3i−3i002i3−2i300−232300−i3i3−i3i33−33−300000000000000000000000000000000
χ784-44-4-24-2002-42-24-4-222-21-2-222-121-12-200000−3i3i−3i3i011-1-10000−3i3i−3i3i00−2i32i300−232300i3−i3i3−i33−33−300000000000000000000000000000000
χ794-44-4-24-2002-42-24-4-222-21-2-222-121-12-200000−3i3i−3i3i011-1-10000−3i3i−3i3i002i3−2i30023−2300−i3i3−i3i3−33−3300000000000000000000000000000000
χ804-4-4444400-4-4-4-4-44-444444-44-4-4-4-444-400000000004-44-40000000000000000000000000000000000000000000000000000000000
χ814-4-4444-200-4-42-4-442-244-2-2-4-2-4222-2420000000000-22-2200000000000023−23000023−23−2323000000000000000000000000000000000000
χ824-4-4444-200-4-42-4-442-244-2-2-4-2-4222-2420000000000-22-22000000000000−23230000−232323−23000000000000000000000000000000000000
χ834-4-444-2400-42-4-42-2-444-24-22-22-42-44-220000000000-22-2200000000000000000000000000000000000000000000006−6−6600000000
χ844-4-444-2400-42-4-42-2-444-24-22-22-42-44-220000000000-22-220000000000000000000000000000000000000000000000−666−600000000
χ854-4-44-244002-4-42-44-44-2-2-242422-42-2-2-40000000000-22-220000000000000000−2i32i30000−2i32i32i3−2i300000000000000000000000000000000
χ864-4-44-244002-4-42-44-44-2-2-242422-42-2-2-40000000000-22-2200000000000000002i3−2i300002i3−2i3−2i32i300000000000000000000000000000000
χ874-4-44-24-2002-422-442-2-2-21-22-22-12-11-22000003i−3i−3i3i01-11-100003i−3i−3i3i000023−23002i3−2i3−333−3−i3i3i3−i300000000000000000000000000000000
χ884-4-44-24-2002-422-442-2-2-21-22-22-12-11-22000003i−3i−3i3i01-11-100003i−3i−3i3i0000−232300−2i32i33−3−33i3−i3−i3i300000000000000000000000000000000
χ894-4-44-24-2002-422-442-2-2-21-22-22-12-11-2200000−3i3i3i−3i01-11-10000−3i3i3i−3i000023−2300−2i32i3−333−3i3−i3−i3i300000000000000000000000000000000
χ904-4-44-24-2002-422-442-2-2-21-22-22-12-11-2200000−3i3i3i−3i01-11-10000−3i3i3i−3i0000−2323002i3−2i33−3−33−i3i3i3−i300000000000000000000000000000000
χ918888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-42222-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000
χ928888-4-4-4-8-8-4-4-4-4-4-4-4-4-422222222222244444-2-2-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-48-8-4-4-4444444222-2-2222-2-2-2-2-444-4422-2-2-4-111-12-22-2-1-11100000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-88-4-4-4444444222-2-2222-2-2-2-24-4-44-4-2-2224-111-1-22-2211-1-100000000000000000000000000000000000000000000000000
χ958-88-88-4-400-8448-44-44-8-4-42-4-244-2-4442000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-480044-8-4-448-842-4-424-244-44-2-4000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-400444-4-44-4442222-2-2-2-22-2-22000006i−6i6i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000
χ988-88-8-4-4-400444-4-44-4442222-2-2-2-22-2-2200000−6i6i−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000
χ998-8-888-4-400-844-84-44-48-4-424244-24-4-4-200000000002-22-20000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-480044-844-4-88-42-4-4-2-4-2444-42400000000002-22-20000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-40044444-44-4-4222-22-2-2-2-222-2000006i−6i−6i6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-40044444-44-4-4222-22-2-2-2-222-200000−6i6i6i−6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000

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