Finite Group Databasebeta

← Group #13147844

Character table — Group #13147844

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222344444466612121212121212123366666612121212121212123666121212121212121212121212121212121212121222222444444466666666661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ51111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ61111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ81111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111111111
χ911111-1-111-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-11-11-11-11-11-11111-1-111-1-111-1-1-1-111-1-111-1-1
χ1011111-1-111-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-11-111-1-11-11-1-111-1-1-1-111-1-1111111-1-1-1-111
χ1111111-1-111-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-11-111-1-11-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1211111-1-111-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-111-1-11-111-111-1-111-1-11111-1-1-1-1-1-111-1-111
χ1311111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-11-1-11-11-111-1-1-111-1-111-1-111-1-111-1-111-1-111
χ1411111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-111-1-111-1-111111-1-1-1-111-1-111-1-1-1-11111-1-1
χ1511111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-111-11-11-1-11-1111-1-11111-1-1-1-111-1-111-1-1-1-111
χ1611111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-11-11-111-11-11-1-1-1-1-111-1-11111-1-11111-1-111-1-1
χ1722222222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1002200002200000000-1-1-1-10000000000-1-1-1-1
χ1822222222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-200000000111100000000001111
χ192222222222222222222222-12-1-122-12-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122000022000000-1-1-1-10000000000-1-1-1-10000
χ202222222222222222222222-12-1-122-12-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000-2-20000001111000000000011110000
χ212222222-2-2-2-22222222-2-2-2-22-122-1-12-1-2-2-2-21111-1-1-1-122-1-111-2-2-1-1-1-11111111100220000-2-200000000-1-1-1-100000000001111
χ222222222-2-2-2-22222222-2-2-2-22-122-1-12-1-2-2-2-21111-1-1-1-122-1-111-2-2-1-1-1-11111111100-2-20000220000000011110000000000-1-1-1-1
χ232222222-2-2-2-22222222-2-2-2-2-12-1-122-121111-2-2-2-2-1-1-1-1-1-122-2-211-1-1-1-111111111220000-2-2000000-1-1-1-1000000000011110000
χ242222222-2-2-2-22222222-2-2-2-2-12-1-122-121111-2-2-2-2-1-1-1-1-1-122-2-211-1-1-1-111111111-2-200002200000011110000000000-1-1-1-10000
χ2522222-2-222-2-2222-2-2-2-222-2-22-122-1-12-122221111-1-1-1-1-2-211-1-1-2-21111-1-1-1-11111002-200002-200000000-1-1110000000000-1-111
χ2622222-2-222-2-2222-2-2-2-222-2-22-122-1-12-122221111-1-1-1-1-2-211-1-1-2-21111-1-1-1-1111100-220000-220000000011-1-1000000000011-1-1
χ2722222-2-222-2-2222-2-2-2-222-2-2-12-1-122-12-1-1-1-1-2-2-2-2-1-1-1-111-2-222111111-1-1-1-111112-200002-2000000-1-1110000000000-1-1110000
χ2822222-2-222-2-2222-2-2-2-222-2-2-12-1-122-12-1-1-1-1-2-2-2-2-1-1-1-111-2-222111111-1-1-1-11111-220000-2200000011-1-1000000000011-1-10000
χ2922222-2-2-2-222222-2-2-2-2-2-2222-122-1-12-1-2-2-2-2-1-1-1-1-1-1-1-1-2-211112211111111-1-1-1-1002-20000-2200000000-1-111000000000011-1-1
χ3022222-2-2-2-222222-2-2-2-2-2-2222-122-1-12-1-2-2-2-2-1-1-1-1-1-1-1-1-2-211112211111111-1-1-1-100-2200002-20000000011-1-10000000000-1-111
χ3122222-2-2-2-222222-2-2-2-2-2-222-12-1-122-1211112222-1-1-1-111-2-2-2-2-1-111111111-1-1-1-12-20000-22000000-1-111000000000011-1-10000
χ3222222-2-2-2-222222-2-2-2-2-2-222-12-1-122-1211112222-1-1-1-111-2-2-2-2-1-111111111-1-1-1-1-2200002-200000011-1-10000000000-1-1110000
χ3322-2-222-22i−2i2i−2i2-2-222-2-22i−2i2i−2i222-22-2-2-22i2i−2i−2i2i2i−2i−2i22-2-22-22-22i−2i2i−2i22-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ3422-2-222-22i−2i2i−2i2-2-222-2-22i−2i2i−2i2-12-2-11-212i2i−2i−2i−i−iii-1-1112-2-11−ii2i−2i-1-111−i−iii−i−iii000000000000000000−i3i3−i3i300000000003−33−3
χ3522-2-222-22i−2i2i−2i2-2-222-2-22i−2i2i−2i2-12-2-11-212i2i−2i−2i−i−iii-1-1112-2-11−ii2i−2i-1-111−i−iii−i−iii000000000000000000i3−i3i3−i30000000000−33−33
χ3622-2-222-22i−2i2i−2i2-2-222-2-22i−2i2i−2i-12-112-21-2−i−iii2i2i−2i−2i-1-111-112-22i−2i−ii-1-111−i−iii−i−iii00000000000000−i3i3−i3i300000000003−33−30000
χ3722-2-222-22i−2i2i−2i2-2-222-2-22i−2i2i−2i-12-112-21-2−i−iii2i2i−2i−2i-1-111-112-22i−2i−ii-1-111−i−iii−i−iii00000000000000i3−i3i3−i30000000000−33−330000
χ3822-2-222-2−2i2i−2i2i2-2-222-2-2−2i2i−2i2i222-22-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-22-22-2−2i2i−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ3922-2-222-2−2i2i−2i2i2-2-222-2-2−2i2i−2i2i2-12-2-11-21−2i−2i2i2iii−i−i-1-1112-2-11i−i−2i2i-1-111ii−i−iii−i−i000000000000000000−i3i3−i3i30000000000−33−33
χ4022-2-222-2−2i2i−2i2i2-2-222-2-2−2i2i−2i2i2-12-2-11-21−2i−2i2i2iii−i−i-1-1112-2-11i−i−2i2i-1-111ii−i−iii−i−i000000000000000000i3−i3i3−i300000000003−33−3
χ4122-2-222-2−2i2i−2i2i2-2-222-2-2−2i2i−2i2i-12-112-21-2ii−i−i−2i−2i2i2i-1-111-112-2−2i2ii−i-1-111ii−i−iii−i−i00000000000000−i3i3−i3i30000000000−33−330000
χ4222-2-222-2−2i2i−2i2i2-2-222-2-2−2i2i−2i2i-12-112-21-2ii−i−i−2i−2i2i2i-1-111-112-2−2i2ii−i-1-111ii−i−iii−i−i00000000000000i3−i3i3−i300000000003−33−30000
χ4322-2-22-222i−2i−2i2i2-2-2-2-2222i−2i−2i2i222-22-2-2-22i2i−2i−2i−2i−2i2i2i22-2-2-22-222i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ4422-2-22-222i−2i−2i2i2-2-2-2-2222i−2i−2i2i2-12-2-11-212i2i−2i−2iii−i−i-1-111-221-1−ii−2i2i11-1-1−i−iiiii−i−i000000000000000000−i3i3i3−i300000000003−3−33
χ4522-2-22-222i−2i−2i2i2-2-2-2-2222i−2i−2i2i2-12-2-11-212i2i−2i−2iii−i−i-1-111-221-1−ii−2i2i11-1-1−i−iiiii−i−i000000000000000000i3−i3−i3i30000000000−333−3
χ4622-2-22-222i−2i−2i2i2-2-2-2-2222i−2i−2i2i-12-112-21-2−i−iii−2i−2i2i2i-1-1111-1-222i−2ii−i11-1-1−i−iiiii−i−i00000000000000−i3i3i3−i300000000003−3−330000
χ4722-2-22-222i−2i−2i2i2-2-2-2-2222i−2i−2i2i-12-112-21-2−i−iii−2i−2i2i2i-1-1111-1-222i−2ii−i11-1-1−i−iiiii−i−i00000000000000i3−i3−i3i30000000000−333−30000
χ4822-2-22-22−2i2i2i−2i2-2-2-2-222−2i2i2i−2i222-22-2-2-2−2i−2i2i2i2i2i−2i−2i22-2-2-22-22−2i2i2i−2i-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4922-2-22-22−2i2i2i−2i2-2-2-2-222−2i2i2i−2i2-12-2-11-21−2i−2i2i2i−i−iii-1-111-221-1i−i2i−2i11-1-1ii−i−i−i−iii000000000000000000−i3i3i3−i30000000000−333−3
χ5022-2-22-22−2i2i2i−2i2-2-2-2-222−2i2i2i−2i2-12-2-11-21−2i−2i2i2i−i−iii-1-111-221-1i−i2i−2i11-1-1ii−i−i−i−iii000000000000000000i3−i3−i3i300000000003−3−33
χ5122-2-22-22−2i2i2i−2i2-2-2-2-222−2i2i2i−2i-12-112-21-2ii−i−i2i2i−2i−2i-1-1111-1-22−2i2i−ii11-1-1ii−i−i−i−iii00000000000000−i3i3i3−i30000000000−333−30000
χ5222-2-22-22−2i2i2i−2i2-2-2-2-222−2i2i2i−2i-12-112-21-2ii−i−i2i2i−2i−2i-1-1111-1-22−2i2i−ii11-1-1ii−i−i−i−iii00000000000000i3−i3−i3i300000000003−3−330000
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
χ544444444-4-4-4-44444444-4-4-4-4-2-2-2-2-2-2-2-2222222221111-2-2-2-222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5544444-4-444-4-4444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-2222211112222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ5644444-4-4-4-444444-4-4-4-4-4-444-2-2-2-2-2-2-2-22222-2-2-2-21111222222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ5744-4-444-44i−4i4i−4i4-4-444-4-44i−4i4i−4i-2-2-22-2222−2i−2i2i2i−2i−2i2i2i11-1-1-22-22−2i2i−2i2i11-1-1ii−i−iii−i−i000000000000000000000000000000000000
χ5844-4-444-4−4i4i−4i4i4-4-444-4-4−4i4i−4i4i-2-2-22-22222i2i−2i−2i2i2i−2i−2i11-1-1-22-222i−2i2i−2i11-1-1−i−iii−i−iii000000000000000000000000000000000000
χ5944-4-44-444i−4i−4i4i4-4-4-4-4444i−4i−4i4i-2-2-22-2222−2i−2i2i2i2i2i−2i−2i11-1-12-22-2−2i2i2i−2i-1-111ii−i−i−i−iii000000000000000000000000000000000000
χ6044-4-44-44−4i4i4i−4i4-4-4-4-444−4i4i4i−4i-2-2-22-22222i2i−2i−2i−2i−2i2i2i11-1-12-22-22i−2i−2i2i-1-111−i−iiiii−i−i000000000000000000000000000000000000
χ614-44-44000000-44-40000000044-4-4-444-4000000004-44-400000000000000000000000000000000000000000000000000000000
χ624-44-44000000-44-4000000004-2-4-42-242000023−2323−23-22-22000000000000000023−2323−23000000000000000000000000000000000000
χ634-44-44000000-44-4000000004-2-4-42-2420000−2323−2323-22-220000000000000000−2323−2323000000000000000000000000000000000000
χ644-44-44000000-44-400000000-2422-44-2-4−2i32i3−2i32i30000-22-22000000000000−2i32i3−2i32i30000000000000000000000000000000000000000
χ654-44-44000000-44-400000000-2422-44-2-42i3−2i32i3−2i30000-22-220000000000002i3−2i32i3−2i30000000000000000000000000000000000000000
χ664-44-44000000-44-400000000-2-2222-2-22−2i32i3−2i32i323−2323−231-11-1000000003i−3i3i−3ii3−i3i3−i3−33−33000000000000000000000000000000000000
χ674-44-44000000-44-400000000-2-2222-2-22−2i32i3−2i32i3−2323−23231-11-100000000−3i3i−3i3ii3−i3i3−i33−33−3000000000000000000000000000000000000
χ684-44-44000000-44-400000000-2-2222-2-222i3−2i32i3−2i323−2323−231-11-100000000−3i3i−3i3i−i3i3−i3i3−33−33000000000000000000000000000000000000
χ694-44-44000000-44-400000000-2-2222-2-222i3−2i32i3−2i3−2323−23231-11-1000000003i−3i3i−3i−i3i3−i3i33−33−3000000000000000000000000000000000000
χ704-4-444000000-4-440000000044-44-4-4-44000000004-4-4400000000000000000000000000000000000000000000000000000000
χ714-4-444000000-4-44000000004-2-4422-4-20000−2i32i32i3−2i3-222-20000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ724-4-444000000-4-44000000004-2-4422-4-200002i3−2i3−2i32i3-222-200000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ734-4-444000000-4-4400000000-242-2-4-42423−23−23230000-222-200000000000023−23−23230000000000000000000000000000000000000000
χ744-4-444000000-4-4400000000-242-2-4-424−232323−230000-222-2000000000000−232323−230000000000000000000000000000000000000000
χ754-4-444000000-4-4400000000-2-22-2222-223−23−2323−2i32i32i3−2i31-1-1100000000−3i3i3i−3i−333−3i3−i3−i3i3000000000000000000000000000000000000
χ764-4-444000000-4-4400000000-2-22-2222-223−23−23232i3−2i3−2i32i31-1-11000000003i−3i−3i3i−333−3−i3i3i3−i3000000000000000000000000000000000000
χ774-4-444000000-4-4400000000-2-22-2222-2−232323−23−2i32i32i3−2i31-1-11000000003i−3i−3i3i3−3−33i3−i3−i3i3000000000000000000000000000000000000
χ784-4-444000000-4-4400000000-2-22-2222-2−232323−232i3−2i3−2i32i31-1-1100000000−3i3i3i−3i3−3−33−i3i3i3−i3000000000000000000000000000000000000
χ796666-3666666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000000022000022-1-100000000-1-1-1-1-1-100000000
χ806666-3666666-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000-2-20000-2-2110000000011111100000000
χ816666-366-6-6-6-6-3-3-3-3-3-3-3333300000000000000000000000000000000000000000000220000-2-2-1-1000000001111-1-100000000
χ826666-366-6-6-6-6-3-3-3-3-3-3-3333300000000000000000000000000000000000000000000-2-20000221100000000-1-1-1-11100000000
χ836666-3-6-666-6-6-3-3-33333-3-333000000000000000000000000000000000000000000002-200002-2-1-100000000-1-1111100000000
χ846666-3-6-666-6-6-3-3-33333-3-33300000000000000000000000000000000000000000000-220000-22110000000011-1-1-1-100000000
χ856666-3-6-6-6-666-3-3-3333333-3-3000000000000000000000000000000000000000000002-20000-22-1-10000000011-1-11100000000
χ866666-3-6-6-6-666-3-3-3333333-3-300000000000000000000000000000000000000000000-2200002-21100000000-1-111-1-100000000
χ8766-6-6-36-66i−6i6i−6i-333-3-333−3i3i−3i3i0000000000000000000000000000000000000000000000000000−i3i3000000003−33−3−i3i300000000
χ8866-6-6-36-66i−6i6i−6i-333-3-333−3i3i−3i3i0000000000000000000000000000000000000000000000000000i3−i300000000−33−33i3−i300000000
χ8966-6-6-36-6−6i6i−6i6i-333-3-3333i−3i3i−3i0000000000000000000000000000000000000000000000000000−i3i300000000−33−33−i3i300000000
χ9066-6-6-36-6−6i6i−6i6i-333-3-3333i−3i3i−3i0000000000000000000000000000000000000000000000000000i3−i3000000003−33−3i3−i300000000
χ9166-6-6-3-666i−6i−6i6i-33333-3-3−3i3i3i−3i0000000000000000000000000000000000000000000000000000−i3i3000000003−3−33i3−i300000000
χ9266-6-6-3-666i−6i−6i6i-33333-3-3−3i3i3i−3i0000000000000000000000000000000000000000000000000000i3−i300000000−333−3−i3i300000000
χ9366-6-6-3-66−6i6i6i−6i-33333-3-33i−3i−3i3i0000000000000000000000000000000000000000000000000000−i3i300000000−333−3i3−i300000000
χ9466-6-6-3-66−6i6i6i−6i-33333-3-33i−3i−3i3i0000000000000000000000000000000000000000000000000000i3−i3000000003−3−33−i3i300000000
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).