Finite Group Databasebeta

← Group #13170579

Character table — Group #13170579

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122222222222444444444444444444448888888888888899121212121212121212121212121218181818181818242424242424242424242424242424242424242436363636363672727272108108
order1223334466666333666666666121212121212121236666121212121212121212224444881212121212121212244666612121212121212121212121224242424242424242244121266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ511111111111111111111111111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111111-11-1-1-11-11-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11-1111
χ711111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-11-11-1-1-11-11-1-1
χ811111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-11-11-111
χ911-1111-11-1-1111111-1-1-1-1-1-1111-1-11-111111-1-1-11-111-1-111-1-1111-11-11-111-1-111-1-1-11-111-1-11-11-111-1-111-1-11111-1-1-1-111-1-11-111-1-11-1
χ1011-1111-11-1-1111111-1-1-1-1-1-1111-1-11-111111-1-1-11-111-1-111-1-1111-11-1-1111-1-111-1-1-11-111-1-11-11-111-1-111-1-1-1-1-1-11111-1-1111-1-1-111-11
χ1111-1111-11-1-1111111-1-1-1-1-1-1111-1-11-111111-1-1-11-111-1-111-1-111-11-111-1-1-111-1-111-11-111-1-1-11-11-1-111-1-1111111-1-1-1-1-1-1111-1-1-1111-1
χ1211-1111-11-1-1111111-1-1-1-1-1-1111-1-11-111111-1-1-11-111-1-111-1-111-11-11-11-1-111-1-111-11-111-1-1-11-11-1-111-1-111-1-1-1-1111111-1-11-111-1-1-11
χ1311-1111-11-1-1111111-1-1-1-1-1-1111-1-11-111111-1-1-11-111-1-111-1-1-1-11-1-111-111-1-1-1-1111-11-1-1111-1-1111-1-1-1-1111111-1-1-1-11-1-11-111-1-11-11
χ1411-1111-11-1-1111111-1-1-1-1-1-1111-1-11-111111-1-1-11-111-1-111-1-1-1-11-1-11-1111-1-1-1-1111-11-1-1111-1-1111-1-1-1-111-1-1-1-11111-111-1-11-111-11-1
χ1511-1111-11-1-1111111-1-1-1-1-1-1111-1-11-111111-1-1-11-111-1-111-1-1-1-1-111-11-1-1-11111-1-11-11-1-111-111-1-1-11111-1-11111-1-1-1-1-111-1-11-111-1-11
χ1611-1111-11-1-1111111-1-1-1-1-1-1111-1-11-111111-1-1-11-111-1-111-1-1-1-1-111-1-11-1-11111-1-11-11-1-111-111-1-1-11111-1-1-1-1-1-111111-1-11-111-1-111-1
χ17222222-2-222222222222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-222000000000000002-2-22222000000000000000000000000-2-2000000
χ18222222-2-222222222222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-200000000000000-222-2-2-2-200000000000000000000000022000000
χ1922222-122222-122-1-12-122-1-1-12-12-1222-1-1-1-1-1-1-1-1-12-12-1-1-1-1-10000222200002222000000000-1-10000-1-1-1-12-1-1-12-1-1-10202000-10-100
χ2022222-122222-122-1-12-122-1-1-12-12-1222-1-1-1-1-1-1-1-1-12-12-1-1-1-1-1000022-2-200002222000000000-1-10000-1-1-1-1-2111-21110-20-200010100
χ2122222-122222-122-1-12-122-1-1-12-12-1222-1-1-1-1-1-1-1-1-12-12-1-1-1-1-10000-2-2220000-2-2-2-200000000011000011112-1-1-12-1-1-10-20-200010100
χ2222222-122222-122-1-12-122-1-1-12-12-1222-1-1-1-1-1-1-1-1-12-12-1-1-1-1-10000-2-2-2-20000-2-2-2-20000000001100001111-2111-21110202000-10-100
χ232222-122222-122-12-1-12-1-122-1-12-1222-12-1-1-1-1-1-1-1-1-12-12-1-1-1-100220022222200000000000-1-100-1-1-1-10000-12-1-1-12-1-1202000-10-1000
χ242222-122222-122-12-1-12-1-122-1-12-1222-12-1-1-1-1-1-1-1-1-12-12-1-1-1-1002200-2-2222200000000000-1-100-1-1-1-100001-2111-211-20-2000101000
χ252222-122222-122-12-1-12-1-122-1-12-1222-12-1-1-1-1-1-1-1-1-12-12-1-1-1-100-2-20022-2-2-2-200000000000110011110000-12-1-1-12-1-1-20-2000101000
χ262222-122222-122-12-1-12-1-122-1-12-1222-12-1-1-1-1-1-1-1-1-12-12-1-1-1-100-2-200-2-2-2-2-2-2000000000001100111100001-2111-211202000-10-1000
χ27222-12222-1-122-1-1-1222-1-1-1-12-1-122-1-12222-12-1-1-12-1-1-1-1-1-1-1-122222200-1-1-1-1-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1000000000000-1-1000000
χ28222-12222-1-122-1-1-1222-1-1-1-12-1-122-1-12222-12-1-1-12-1-1-1-1-1-1-1-122-2-2-2-20011111111222-1-1-1-1-2-2-2-211111111000000000000-1-1000000
χ29222-12222-1-122-1-1-1222-1-1-1-12-1-122-1-12222-12-1-1-12-1-1-1-1-1-1-1-1-2-222-2-200-1-1-1-11111-2-2-2111122-2-2-1-1-1-1111100000000000011000000
χ30222-12222-1-122-1-1-1222-1-1-1-12-1-122-1-12222-12-1-1-12-1-1-1-1-1-1-1-1-2-2-2-222001111-1-1-1-1-2-2-21111-2-2221111-1-1-1-100000000000011000000
χ31222-122-2-2-1-122-1-1-1222-1-1-1-12-1-1-2-211-2-2-2-2-12-1-1-1-21111111122000000−i3i3−i3i3−i3i3−i3i32-2-2-1-1-1-10000−i3i3−i3i3−i3i3−i3i300000000000011000000
χ32222-122-2-2-1-122-1-1-1222-1-1-1-12-1-1-2-211-2-2-2-2-12-1-1-1-21111111122000000i3−i3i3−i3i3−i3i3−i32-2-2-1-1-1-10000i3−i3i3−i3i3−i3i3−i300000000000011000000
χ33222-122-2-2-1-122-1-1-1222-1-1-1-12-1-1-2-211-2-2-2-2-12-1-1-1-211111111-2-2000000−i3i3−i3i3i3−i3i3−i3-22211110000−i3i3−i3i3i3−i3i3−i3000000000000-1-1000000
χ34222-122-2-2-1-122-1-1-1222-1-1-1-12-1-1-2-211-2-2-2-2-12-1-1-1-211111111-2-2000000i3−i3i3−i3−i3i3−i3i3-22211110000i3−i3i3−i3−i3i3−i3i3000000000000-1-1000000
χ3522-22222-2-2-2222222-2-2-2-2-2-222222-22-2-2-2-22-2-2-222-2-222-2-2222200000000000000-2-2222-2-2000000000000000000000000-22000000
χ3622-22222-2-2-2222222-2-2-2-2-2-222222-22-2-2-2-22-2-2-222-2-222-2-222-2-20000000000000022-2-2-2220000000000000000000000002-2000000
χ3722-222-1-22-2-22-122-1-1-21-2-211-12-1-212-22-1-1-1-1111-112-1-21-1-11100002-22-2000022-2-2000000000-110000-1-1112-1-1-1-2111020-2000-10100
χ3822-222-1-22-2-22-122-1-1-21-2-211-12-1-212-22-1-1-1-1111-112-1-21-1-11100002-2-22000022-2-2000000000-110000-1-111-21112-1-1-10-20200010-100
χ3922-222-1-22-2-22-122-1-1-21-2-211-12-1-212-22-1-1-1-1111-112-1-21-1-1110000-222-20000-2-2220000000001-1000011-1-12-1-1-1-21110-20200010-100
χ4022-222-1-22-2-22-122-1-1-21-2-211-12-1-212-22-1-1-1-1111-112-1-21-1-1110000-22-220000-2-2220000000001-1000011-1-1-21112-1-1-1020-2000-10100
χ4122-22-12-22-2-2-122-12-11-211-2-2-1-121-22-2-12-1-1-1111-11-121-2-1-111002-2002-222-2-200000000000-1100-1-1110000-12-1-11-21120-2000-101000
χ4222-22-12-22-2-2-122-12-11-211-2-2-1-121-22-2-12-1-1-1111-11-121-2-1-111002-200-2222-2-200000000000-1100-1-11100001-211-12-1-1-20200010-1000
χ4322-22-12-22-2-2-122-12-11-211-2-2-1-121-22-2-12-1-1-1111-11-121-2-1-11100-22002-2-2-222000000000001-10011-1-10000-12-1-11-211-20200010-1000
χ4422-22-12-22-2-2-122-12-11-211-2-2-1-121-22-2-12-1-1-1111-11-121-2-1-11100-2200-22-2-222000000000001-10011-1-100001-211-12-1-120-2000-101000
χ4522-2-1222-21122-1-1-12-2-211112-1-1221-1-2-2-2-2-1-211-1211-1-111-1-122000000−i3i3i3−i3−i3i3i3−i3-2-22-1-1110000−i3i3i3−i3−i3i3i3−i30000000000001-1000000
χ4622-2-1222-21122-1-1-12-2-211112-1-1221-1-2-2-2-2-1-211-1211-1-111-1-122000000i3−i3−i3i3i3−i3−i3i3-2-22-1-1110000i3−i3−i3i3i3−i3−i3i30000000000001-1000000
χ4722-2-1222-21122-1-1-12-2-211112-1-1221-1-2-2-2-2-1-211-1211-1-111-1-1-2-2000000−i3i3i3−i3i3−i3−i3i322-211-1-10000−i3i3i3−i3i3−i3−i3i3000000000000-11000000
χ4822-2-1222-21122-1-1-12-2-211112-1-1221-1-2-2-2-2-1-211-1211-1-111-1-1-2-2000000i3−i3−i3i3−i3i3i3−i322-211-1-10000i3−i3−i3i3−i3i3i3−i3000000000000-11000000
χ4922-2-122-221122-1-1-12-2-211112-1-1-2-2-112222-1-211-1-2-1-111-1-111222-22-200-1-111-1-111-22-2-1-1112-22-2-1-111-1-111000000000000-11000000
χ5022-2-122-221122-1-1-12-2-211112-1-1-2-2-112222-1-211-1-2-1-111-1-11122-22-220011-1-111-1-1-22-2-1-111-22-2211-1-111-1-1000000000000-11000000
χ5122-2-122-221122-1-1-12-2-211112-1-1-2-2-112222-1-211-1-2-1-111-1-111-2-22-2-2200-1-11111-1-12-2211-1-12-2-22-1-11111-1-10000000000001-1000000
χ5222-2-122-221122-1-1-12-2-211112-1-1-2-2-112222-1-211-1-2-1-111-1-111-2-2-222-20011-1-1-1-1112-2211-1-1-222-211-1-1-1-1110000000000001-1000000
χ5344444-2-4-4444-244-2-24-244-2-2-24-2-42-4-4-4222-2-2-2-2-22-42-4222220000000000000000000000000000000000000000000000000000000
χ544444-24-4-444-244-24-2-24-2-244-2-242-4-4-42-422-2-2-2-2-222-42-422220000000000000000000000000000000000000000000000000000000
χ554444-2-24444-2-24-2-21-2-2-2-2-2-21-2-2-2-244-2-211111111-2-2-2-2111100000044000000000000000000000000000-2-211-2-211000000000000
χ564444-2-24444-2-24-2-21-2-2-2-2-2-21-2-2-2-244-2-211111111-2-2-2-21111000000-4-400000000000000000000000000022-1-122-1-1000000000000
χ574444-2-2-4-444-2-24-2-21-2-2-2-2-2-21-2-222-4-422-1-111111-12222-1-1-1-100000000000000000000000000000000000003i−3i003i−3i000000000000
χ584444-2-2-4-444-2-24-2-21-2-2-2-2-2-21-2-222-4-422-1-111111-12222-1-1-1-10000000000000000000000000000000000000−3i3i00−3i3i000000000000
χ59444-24-244-2-24-2-2-21-24-2-2-211-2-214-2-2-24-2-2-21-2111-2-21-211111000044000000-2-2-2-2000000000-2-20000111100000000000000000000
χ60444-24-244-2-24-2-2-21-24-2-2-211-2-214-2-2-24-2-2-21-2111-2-21-2111110000-4-40000002222000000000220000-1-1-1-100000000000000000000
χ61444-24-2-4-4-2-24-2-2-21-24-2-2-211-2-21-4222-42221-211122-12-1-1-1-1-1000000000000−2i32i3−2i32i3000000000000000i3−i3i3−i300000000000000000000
χ62444-24-2-4-4-2-24-2-2-21-24-2-2-211-2-21-4222-42221-211122-12-1-1-1-1-10000000000002i3−2i32i3−2i3000000000000000−i3i3−i3i300000000000000000000
χ63444-2-2444-2-2-24-21-2-2-2411-2-2-21-2-24-2-2-24-2-21-2111-21-21-2111100440000-2-2-2-200000000000-2-2001111000000000000000000000000
χ64444-2-2444-2-2-24-21-2-2-2411-2-2-21-2-24-2-2-24-2-21-2111-21-21-2111100-4-400002222000000000002200-1-1-1-1000000000000000000000000
χ65444-2-24-4-4-2-2-24-21-2-2-2411-2-2-21-22-4222-4221-21112-12-12-1-1-1-100000000−2i32i3−2i32i3000000000000000i3−i3i3−i3000000000000000000000000
χ66444-2-24-4-4-2-2-24-21-2-2-2411-2-2-21-22-4222-4221-21112-12-12-1-1-1-1000000002i3−2i32i3−2i3000000000000000−i3i3−i3i3000000000000000000000000
χ6744-444-24-4-4-44-244-2-2-42-4-422-24-24-2-44-4222-2222-2-2-424-222-2-20000000000000000000000000000000000000000000000000000000
χ6844-44-244-4-4-4-244-24-22-422-4-4-2-24-24-442-422-2222-2-22-4-2422-2-20000000000000000000000000000000000000000000000000000000
χ6944-44-2-24-4-4-4-2-24-2-212222221-2-2-2-2-4422-1-11-1-1-11122-2-2-1-11100000000000000000000000000000000000003i−3i00−3i3i000000000000
χ7044-44-2-24-4-4-4-2-24-2-212222221-2-2-2-2-4422-1-11-1-1-11122-2-2-1-1110000000000000000000000000000000000000−3i3i003i−3i000000000000
χ7144-44-2-2-44-4-4-2-24-2-212222221-2-2224-4-2-2111-1-1-11-1-2-22211-1-10000004-4000000000000000000000000000-2-21122-1-1000000000000
χ7244-44-2-2-44-4-4-2-24-2-212222221-2-2224-4-2-2111-1-1-11-1-2-22211-1-1000000-4400000000000000000000000000022-1-1-2-211000000000000
χ7344-4-24-24-4224-2-2-21-2-4222-1-1-2-214-22-2-422212-1-11-22-1-21-1-111000000000000−2i32i32i3−2i3000000000000000i3−i3−i3i300000000000000000000
χ7444-4-24-24-4224-2-2-21-2-4222-1-1-2-214-22-2-422212-1-11-22-1-21-1-1110000000000002i3−2i3−2i32i3000000000000000−i3i3i3−i300000000000000000000
χ7544-4-24-2-44224-2-2-21-2-4222-1-1-2-21-42-224-2-2-212-1-112-212-111-1-100004-4000000-2-222000000000-22000011-1-100000000000000000000
χ7644-4-24-2-44224-2-2-21-2-4222-1-1-2-21-42-224-2-2-212-1-112-212-111-1-10000-4400000022-2-20000000002-20000-1-11100000000000000000000
χ7744-4-2-244-422-24-21-2-22-4-1-122-21-2-242-22-42212-1-11-2-121-2-1-11100000000−2i32i32i3−2i3000000000000000i3−i3−i3i3000000000000000000000000
χ7844-4-2-244-422-24-21-2-22-4-1-122-21-2-242-22-42212-1-11-2-121-2-1-111000000002i3−2i3−2i32i3000000000000000−i3i3i3−i3000000000000000000000000
χ7944-4-2-24-4422-24-21-2-22-4-1-122-21-22-4-22-24-2-212-1-1121-2-1211-1-1004-40000-2-22200000000000-220011-1-1000000000000000000000000
χ8044-4-2-24-4422-24-21-2-22-4-1-122-21-22-4-22-24-2-212-1-1121-2-1211-1-100-44000022-2-2000000000002-200-1-111000000000000000000000000
χ814-404440000-4-4-4444000000-4-4-4000000004000-40000000004-4000000000000000004-40000000000000000000000000000000000
χ824-404440000-4-4-4444000000-4-4-4000000004000-4000000000-4400000000000000000-440000000000000000000000000000000000
χ834-40-24400−2i32i3-4-42-2-2400−2i32i3−2i32i3-42200000000-20−2i32i320000000004-400000000000000000-22−2i32i300000000000000000000000000000000
χ844-40-24400−2i32i3-4-42-2-2400−2i32i3−2i32i3-42200000000-20−2i32i32000000000-44000000000000000002-22i3−2i300000000000000000000000000000000
χ854-40-244002i3−2i3-4-42-2-24002i3−2i32i3−2i3-42200000000-202i3−2i320000000004-400000000000000000-222i3−2i300000000000000000000000000000000
χ864-40-244002i3−2i3-4-42-2-24002i3−2i32i3−2i3-42200000000-202i3−2i32000000000-44000000000000000002-2−2i32i300000000000000000000000000000000
χ87888-4-4-488-4-4-4-4-4222-4-42222222-4-4-4-4-4-422-12-1-1-122222-1-1-1-10000000000000000000000000000000000000000000000000000000
χ88888-4-4-4-8-8-4-4-4-4-4222-4-42222222444444-2-2-12-1-1-1-2-2-2-2-211110000000000000000000000000000000000000000000000000000000
χ8988-8-4-4-48-844-4-4-422244-2-2-2-2222-4-44-444-2-2-1-211-12-2-22211-1-10000000000000000000000000000000000000000000000000000000
χ9088-8-4-4-4-8844-4-4-422244-2-2-2-222244-44-4-422-1-211-1-222-2-2-1-1110000000000000000000000000000000000000000000000000000000
χ918-8088-40000-84-88-4-40000004-8400000000-400040000000000000000000000000000000000000000000000000000000000000000
χ928-808-4800004-8-8-48-400000044-800000000-400040000000000000000000000000000000000000000000000000000000000000000
χ938-808-4-4000044-8-4-42000000-2440000006i−6i2000-2000006i−6i000000000000000000000000000000000000000000000000000000000
χ948-808-4-4000044-8-4-42000000-244000000−6i6i2000-200000−6i6i000000000000000000000000000000000000000000000000000000000
χ958-80-48-400−4i34i3-844-42-400−4i34i32i3−2i344-200000000202i3−2i3-20000000000000000000000000000000000000000000000000000000000000000
χ968-80-48-4004i3−4i3-844-42-4004i3−4i3−2i32i344-20000000020−2i32i3-20000000000000000000000000000000000000000000000000000000000000000
χ978-80-4-4800−4i34i34-842-4-4002i3−2i3−4i34i34-2400000000202i3−2i3-20000000000000000000000000000000000000000000000000000000000000000
χ988-80-4-48004i3−4i34-842-4-400−2i32i34i3−4i34-240000000020−2i32i3-20000000000000000000000000000000000000000000000000000000000000000
χ998-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-20000006i−6i-10−i3i3100000−3i3i33−330000000000000000000000000000000000000000000000000000000
χ1008-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-2000000−6i6i-10−i3i31000003i−3i−33330000000000000000000000000000000000000000000000000000000
χ1018-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-20000006i−6i-10i3−i3100000−3i3i−33330000000000000000000000000000000000000000000000000000000
χ1028-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-2000000−6i6i-10i3−i31000003i−3i33−330000000000000000000000000000000000000000000000000000000

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