Finite Group Databasebeta

← Group #13137391

Character table — Group #13137391

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order122234444446661212121212121212336666661212121212121212366612121212121212121212121212121212121212122222444466666666888812121212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ511111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ711111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111
χ811111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1
χ911-1-11ii−i−i1-11-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i1-11-1i−ii−i11-1-111-1-11-1i−iii−i−iii−i−i11-1-1ii−i−i
χ1011-1-11ii−i−i1-11-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i1-1-11i−i−ii11-1-1-1-111-11−iiii−i−i−i−iii-1-111−i−iii
χ1111-1-11ii−i−i1-11-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i-111-1−iii−i-1-11111-1-1-11−ii−i−iiiii−i−i-1-111−i−iii
χ1211-1-11ii−i−i1-11-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i-11-11−ii−ii-1-111-1-1111-1i−i−i−iii−i−iii11-1-1ii−i−i
χ1311-1-11−i−iii1-11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii1-11-1−ii−ii11-1-111-1-11-1−ii−i−iii−i−iii11-1-1−i−iii
χ1411-1-11−i−iii1-11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii1-1-11−iii−i11-1-1-1-111-11i−i−i−iiiii−i−i-1-111ii−i−i
χ1511-1-11−i−iii1-11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii-111-1i−i−ii-1-11111-1-1-11i−iii−i−i−i−iii-1-111ii−i−i
χ1611-1-11−i−iii1-11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii-11-11i−ii−i-1-111-1-1111-1−iiii−i−iii−i−i11-1-1−i−iii
χ1722222222222222222222222-12-12-12-122-1-122-1-1-1-1-1-12-12-12-12-1-1-1-1-1-1-1-1-1-1-1-1-1002200220000-1-1-1-100000000-1-1-1-100000000
χ1822222222222222222222222-12-12-12-122-1-122-1-1-1-1-1-12-12-12-12-1-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-20000111100000000111100000000
χ192222222222222222222222-12-12-12-12-1-122-1-122-1-1-1-1-12-12-12-12-1-1-1-1-1-1-1-1-1-1-1-122002200-1-1-1-100000000-1-1-1-1000000000000
χ202222222222222222222222-12-12-12-12-1-122-1-122-1-1-1-1-12-12-12-12-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2001111000000001111000000000000
χ21222222-22-2-2-2222-2-2-2-22-22-22222222222-2-222-2-22222-2-2-2-2-22-22-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ22222222-22-2-2-2222-2-2-2-22-22-22-12-12-12-122112211-1-1-1-1-21-21-2-1-2-11111-1-111-1-111000000000000−i3i3−i3i300000000−i3i3−i3i300000000
χ23222222-22-2-2-2222-2-2-2-22-22-22-12-12-12-122112211-1-1-1-1-21-21-2-1-2-11111-1-111-1-111000000000000i3−i3i3−i300000000i3−i3i3−i300000000
χ24222222-22-2-2-2222-2-2-2-22-22-2-12-12-12-12-1-1-2-2-1-1-2-2-1-1-1-11-21-212121111-1-111-1-11100000000−i3i3−i3i300000000−i3i3−i3i3000000000000
χ25222222-22-2-2-2222-2-2-2-22-22-2-12-12-12-12-1-1-2-2-1-1-2-2-1-1-1-11-21-212121111-1-111-1-11100000000i3−i3i3−i300000000i3−i3i3−i3000000000000
χ2622222-22-22-2-2222-2-2-2-2-22-2222222222-2-222-2-2222222-2-2-2-22-22-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ2722222-22-22-2-2222-2-2-2-2-22-222-12-12-12-1-2-2-1-1-2-2-1-1-1-1-1-1-21-212121111111-1-111-1-1000000000000−i3i3−i3i300000000i3−i3i3−i300000000
χ2822222-22-22-2-2222-2-2-2-2-22-222-12-12-12-1-2-2-1-1-2-2-1-1-1-1-1-1-21-212121111111-1-111-1-1000000000000i3−i3i3−i300000000−i3i3−i3i300000000
χ2922222-22-22-2-2222-2-2-2-2-22-22-12-12-12-1211221122-1-1-1-11-21-2-1-2-1-2111111-1-111-1-100000000−i3i3−i3i300000000i3−i3i3−i3000000000000
χ3022222-22-22-2-2222-2-2-2-2-22-22-12-12-12-1211221122-1-1-1-11-21-2-1-2-1-2111111-1-111-1-100000000i3−i3i3−i300000000−i3i3−i3i3000000000000
χ3122222-2-2-2-2222222222-2-2-2-22-12-12-12-1-2-211-2-211-1-1-1-12-12-1-21-21-1-1-1-111111111002200-2-20000-1-1-1-100000000111100000000
χ3222222-2-2-2-2222222222-2-2-2-22-12-12-12-1-2-211-2-211-1-1-1-12-12-1-21-21-1-1-1-11111111100-2-200220000111100000000-1-1-1-100000000
χ3322222-2-2-2-2222222222-2-2-2-2-12-12-12-1211-2-211-2-2-1-1-1-1-12-121-21-2-1-1-1-1111111112200-2-200-1-1-1-1000000001111000000000000
χ3422222-2-2-2-2222222222-2-2-2-2-12-12-12-1211-2-211-2-2-1-1-1-1-12-121-21-2-1-1-1-111111111-2-2002200111100000000-1-1-1-1000000000000
χ3522-2-222i2i−2i−2i2-22-2-222-2-22i2i−2i−2i2-12-1-21-212i2i−i−i−2i−2iii-1-1112-1-212i−i−2ii-1-111−i−i−i−iiiii002-2002i−2i0000-1-11100000000−i−iii00000000
χ3622-2-222i2i−2i−2i2-22-2-222-2-22i2i−2i−2i2-12-1-21-212i2i−i−i−2i−2iii-1-1112-1-212i−i−2ii-1-111−i−i−i−iiiii00-2200−2i2i000011-1-100000000ii−i−i00000000
χ3722-2-222i2i−2i−2i2-22-2-222-2-22i2i−2i−2i-12-121-21-2−i−i2i2iii−2i−2i-1-111-121-2−i2ii−2i-1-111−i−i−i−iiiii2-2002i−2i00-1-11100000000−i−iii000000000000
χ3822-2-222i2i−2i−2i2-22-2-222-2-22i2i−2i−2i-12-121-21-2−i−i2i2iii−2i−2i-1-111-121-2−i2ii−2i-1-111−i−i−i−iiiii-2200−2i2i0011-1-100000000ii−i−i000000000000
χ3922-2-222i−2i−2i2i-222-2-2-2-2222i−2i−2i2i2222-2-2-2-22i2i−2i−2i−2i−2i2i2i22-2-2-2-222−2i2i2i−2i-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ4022-2-222i−2i−2i2i-222-2-2-2-2222i−2i−2i2i2-12-1-21-212i2iii−2i−2i−i−i-1-111-212-1−2i−i2ii11-1-1−i−iiiii−i−i000000000000−i3i3i3−i3000000003−3−3300000000
χ4122-2-222i−2i−2i2i-222-2-2-2-2222i−2i−2i2i2-12-1-21-212i2iii−2i−2i−i−i-1-111-212-1−2i−i2ii11-1-1−i−iiiii−i−i000000000000i3−i3−i3i300000000−333−300000000
χ4222-2-222i−2i−2i2i-222-2-2-2-2222i−2i−2i2i-12-121-21-2−i−i−2i−2iii2i2i-1-1111-2-12i2i−i−2i11-1-1−i−iiiii−i−i00000000−i3i3i3−i3000000003−3−33000000000000
χ4322-2-222i−2i−2i2i-222-2-2-2-2222i−2i−2i2i-12-121-21-2−i−i−2i−2iii2i2i-1-1111-2-12i2i−i−2i11-1-1−i−iiiii−i−i00000000i3−i3−i3i300000000−333−3000000000000
χ4422-2-22−2i2i2i−2i-222-2-2-2-222−2i2i2i−2i2222-2-2-2-2−2i−2i2i2i2i2i−2i−2i22-2-2-2-2222i−2i−2i2i-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4522-2-22−2i2i2i−2i-222-2-2-2-222−2i2i2i−2i2-12-1-21-21−2i−2i−i−i2i2iii-1-111-212-12ii−2i−i11-1-1ii−i−i−i−iii000000000000−i3i3i3−i300000000−333−300000000
χ4622-2-22−2i2i2i−2i-222-2-2-2-222−2i2i2i−2i2-12-1-21-21−2i−2i−i−i2i2iii-1-111-212-12ii−2i−i11-1-1ii−i−i−i−iii000000000000i3−i3−i3i3000000003−3−3300000000
χ4722-2-22−2i2i2i−2i-222-2-2-2-222−2i2i2i−2i-12-121-21-2ii2i2i−i−i−2i−2i-1-1111-2-12−i−2ii2i11-1-1ii−i−i−i−iii00000000−i3i3i3−i300000000−333−3000000000000
χ4822-2-22−2i2i2i−2i-222-2-2-2-222−2i2i2i−2i-12-121-21-2ii2i2i−i−i−2i−2i-1-1111-2-12−i−2ii2i11-1-1ii−i−i−i−iii00000000i3−i3−i3i3000000003−3−33000000000000
χ4922-2-22−2i−2i2i2i2-22-2-222-2-2−2i−2i2i2i2-12-1-21-21−2i−2iii2i2i−i−i-1-1112-1-21−2ii2i−i-1-111iiii−i−i−i−i002-200−2i2i0000-1-11100000000ii−i−i00000000
χ5022-2-22−2i−2i2i2i2-22-2-222-2-2−2i−2i2i2i2-12-1-21-21−2i−2iii2i2i−i−i-1-1112-1-21−2ii2i−i-1-111iiii−i−i−i−i00-22002i−2i000011-1-100000000−i−iii00000000
χ5122-2-22−2i−2i2i2i2-22-2-222-2-2−2i−2i2i2i-12-121-21-2ii−2i−2i−i−i2i2i-1-111-121-2i−2i−i2i-1-111iiii−i−i−i−i2-200−2i2i00-1-11100000000ii−i−i000000000000
χ5222-2-22−2i−2i2i2i2-22-2-222-2-2−2i−2i2i2i-12-121-21-2ii−2i−2i−i−i2i2i-1-111-121-2i−2i−i2i-1-111iiii−i−i−i−i-22002i−2i0011-1-100000000−i−iii000000000000
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ54444444-44-4-4-4444-4-4-4-44-44-4-2-2-2-2-2-2-2-2-2-222-2-222111122222-22-2-1-1-1-111-1-111-1-1000000000000000000000000000000000000
χ5544444-44-44-4-4444-4-4-4-4-44-44-2-2-2-2-2-2-2-222-2-222-2-211112222-22-22-1-1-1-1-1-111-1-111000000000000000000000000000000000000
χ5644444-4-4-4-4444444444-4-4-4-4-2-2-2-2-2-2-2-2222222221111-2-2-2-222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5744-4-444i4i−4i−4i4-44-4-444-4-44i4i−4i−4i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i11-1-1-2-222−2i−2i2i2i11-1-1iiii−i−i−i−i000000000000000000000000000000000000
χ5844-4-444i−4i−4i4i-444-4-4-4-4444i−4i−4i4i-2-2-2-22222−2i−2i2i2i2i2i−2i−2i11-1-122-2-22i−2i−2i2i-1-111ii−i−i−i−iii000000000000000000000000000000000000
χ5944-4-44−4i4i4i−4i-444-4-4-4-444−4i4i4i−4i-2-2-2-222222i2i−2i−2i−2i−2i2i2i11-1-122-2-2−2i2i2i−2i-1-111−i−iiiii−i−i000000000000000000000000000000000000
χ6044-4-44−4i−4i4i4i4-44-4-444-4-4−4i−4i4i4i-2-2-2-222222i2i2i2i−2i−2i−2i−2i11-1-1-2-2222i2i−2i−2i11-1-1−i−i−i−iiiii000000000000000000000000000000000000
χ614-44-44000000-44-40000000044-4-4-444-4000000004-44-400000000000000000000000000000000000000000000000000000000
χ624-44-44000000-44-4000000004-2-42-4-2420023−230023−23-22-220000000000000023−230023−23000000000000000000000000000000000000
χ634-44-44000000-44-4000000004-2-42-4-24200−232300−2323-22-2200000000000000−232300−2323000000000000000000000000000000000000
χ644-44-44000000-44-400000000-242-424-2-4−2i32i300−2i32i300-22-22000000000000−2i32i300−2i32i300000000000000000000000000000000000000
χ654-44-44000000-44-400000000-242-424-2-42i3−2i3002i3−2i300-22-220000000000002i3−2i3002i3−2i300000000000000000000000000000000000000
χ664-44-44000000-44-400000000-2-2222-2-22−2i32i323−23−2i32i323−231-11-1000000003i−3i3i−3ii3−i3−33i3−i3−33000000000000000000000000000000000000
χ674-44-44000000-44-400000000-2-2222-2-22−2i32i3−2323−2i32i3−23231-11-100000000−3i3i−3i3ii3−i33−3i3−i33−3000000000000000000000000000000000000
χ684-44-44000000-44-400000000-2-2222-2-222i3−2i323−232i3−2i323−231-11-100000000−3i3i−3i3i−i3i3−33−i3i3−33000000000000000000000000000000000000
χ694-44-44000000-44-400000000-2-2222-2-222i3−2i3−23232i3−2i3−23231-11-1000000003i−3i3i−3i−i3i33−3−i3i33−3000000000000000000000000000000000000
χ704-4-444000000-4-440000000044-4-44-4-44000000004-4-4400000000000000000000000000000000000000000000000000000000
χ714-4-444000000-4-44000000004-2-4242-4-200−2i32i3002i3−2i3-222-200000000000000−2i32i3002i3−2i3000000000000000000000000000000000000
χ724-4-444000000-4-44000000004-2-4242-4-2002i3−2i300−2i32i3-222-2000000000000002i3−2i300−2i32i3000000000000000000000000000000000000
χ734-4-444000000-4-4400000000-242-4-2-42423−2300−232300-222-200000000000023−2300−232300000000000000000000000000000000000000
χ744-4-444000000-4-4400000000-242-4-2-424−23230023−2300-222-2000000000000−23230023−2300000000000000000000000000000000000000
χ754-4-444000000-4-4400000000-2-222-222-223−23−2i32i3−23232i3−2i31-1-1100000000−3i3i3i−3i−33i3−i33−3−i3i3000000000000000000000000000000000000
χ764-4-444000000-4-4400000000-2-222-222-223−232i3−2i3−2323−2i32i31-1-11000000003i−3i−3i3i−33−i3i33−3i3−i3000000000000000000000000000000000000
χ774-4-444000000-4-4400000000-2-222-222-2−2323−2i32i323−232i3−2i31-1-11000000003i−3i−3i3i3−3i3−i3−33−i3i3000000000000000000000000000000000000
χ784-4-444000000-4-4400000000-2-222-222-2−23232i3−2i323−23−2i32i31-1-1100000000−3i3i3i−3i3−3−i3i3−33i3−i3000000000000000000000000000000000000
χ796666-3666666-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
χ806666-3666666-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000000000000000-2-2-2-20000000011111111
χ816666-36-66-6-6-6-3-3-33333-33-33000000000000000000000000000000000000000000000000000000000000000000003−33−33−33−3
χ826666-36-66-6-6-6-3-3-33333-33-3300000000000000000000000000000000000000000000000000000000000000000000−33−33−33−33
χ836666-3-66-66-6-6-3-3-333333-33-3000000000000000000000000000000000000000000000000000000000000000000003−33−3−33−33
χ846666-3-66-66-6-6-3-3-333333-33-300000000000000000000000000000000000000000000000000000000000000000000−33−333−33−3
χ856666-3-6-6-6-666-3-3-3-3-3-3-333330000000000000000000000000000000000000000000000000000000022-2-200000000-1-1-1-11111
χ866666-3-6-6-6-666-3-3-3-3-3-3-3333300000000000000000000000000000000000000000000000000000000-2-222000000001111-1-1-1-1
χ8766-6-6-36i6i−6i−6i6-6-333-3-333−3i−3i3i3i000000000000000000000000000000000000000000000000000000002-22i−2i00000000-1-111−i−iii
χ8866-6-6-36i6i−6i−6i6-6-333-3-333−3i−3i3i3i00000000000000000000000000000000000000000000000000000000-22−2i2i0000000011-1-1ii−i−i
χ8966-6-6-36i−6i−6i6i-66-33333-3-3−3i3i3i−3i000000000000000000000000000000000000000000000000000000000000000000003−3−33i3−i3−i3i3
χ9066-6-6-36i−6i−6i6i-66-33333-3-3−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000000000000−333−3−i3i3i3−i3
χ9166-6-6-3−6i6i6i−6i-66-33333-3-33i−3i−3i3i000000000000000000000000000000000000000000000000000000000000000000003−3−33−i3i3i3−i3
χ9266-6-6-3−6i6i6i−6i-66-33333-3-33i−3i−3i3i00000000000000000000000000000000000000000000000000000000000000000000−333−3i3−i3−i3i3
χ9366-6-6-3−6i−6i6i6i6-6-333-3-3333i3i−3i−3i000000000000000000000000000000000000000000000000000000002-2−2i2i00000000-1-111ii−i−i
χ9466-6-6-3−6i−6i6i6i6-6-333-3-3333i3i−3i−3i00000000000000000000000000000000000000000000000000000000-222i−2i0000000011-1-1−i−iii
χ9512-1212-12-60000006-6663−6363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212-12-60000006-66−6363−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-1212-600000066-663−63−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-1212-600000066-6−636363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000

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