Finite Group Databasebeta

← Group #13147888

Character table — Group #13147888

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222344444466612121212121212123366666612121212121212123666121212121212121212121212121212121212121222222444444466666666661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ51111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ61111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ81111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ911111-1-111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11-11-11-11-11-11-111-1-11111-1-111-1-111-1-1-1-111-1-1
χ1011111-1-111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11-1-11-111-1-11-1111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111-1-111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-111-1-11-111-1-11-1-111-1-111-1-1-1-111-1-1111111-1-1
χ1211111-1-111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-11-111-1-11-111-1-1-11111-1-111-1-11111-1-1-1-1-1-111
χ1311111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-11-1-11-11-111-111-1-1-1-111-1-1-1-11111-1-111-1-111
χ1411111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-111-1-111-1-1111-1-111-1-111-1-111-1-111-1-111-1-1
χ1511111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-111-11-11-1-11-11-1-1111111-1-111-1-1-1-111-1-1-1-111
χ1611111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-11-11-111-11-11-1-1-111-1-1-1-11111-1-111-1-11111-1-1
χ1722222222222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1002200002200000000-1-1-1-10000000000-1-1-1-1
χ1822222222222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-200000000111100000000001111
χ192222222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000220000220000-1-100000000-1-1-1-1-1-10000
χ202222222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-20000-2-2000011000000001111110000
χ212222222-2-2-2-2222-2-2-2-222-2-22-1-1-1222-122221111-1-1-1-1-1-111-2-2-2-2-1-1-1-11111111100220000-2-200000000-1-1-1-100000000001111
χ222222222-2-2-2-2222-2-2-2-222-2-22-1-1-1222-122221111-1-1-1-1-1-111-2-2-2-2-1-1-1-11111111100-2-20000220000000011110000000000-1-1-1-1
χ232222222-2-2-2-2222-2-2-2-222-2-2-1222-1-1-12-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-1111111110000220000-2-20000-1-1000000001111-1-10000
χ242222222-2-2-2-2222-2-2-2-222-2-2-1222-1-1-12-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-1111111110000-2-200002200001100000000-1-1-1-1110000
χ2522222-2-222-2-22222222-2-2-2-22-1-1-1222-1-2-2-2-21111-1-1-1-111-1-122-2-21111-1-1-1-11111002-200002-200000000-1-1110000000000-1-111
χ2622222-2-222-2-22222222-2-2-2-22-1-1-1222-1-2-2-2-21111-1-1-1-111-1-122-2-21111-1-1-1-1111100-220000-220000000011-1-1000000000011-1-1
χ2722222-2-222-2-22222222-2-2-2-2-1222-1-1-121111-2-2-2-2-1-1-1-1-2-222-1-1111111-1-1-1-1111100002-200002-20000-1-100000000-1-111110000
χ2822222-2-222-2-22222222-2-2-2-2-1222-1-1-121111-2-2-2-2-1-1-1-1-2-222-1-1111111-1-1-1-111110000-220000-220000110000000011-1-1-1-10000
χ2922222-2-2-2-222222-2-2-2-2-2-2222-1-1-1222-1-2-2-2-2-1-1-1-1-1-1-1-11111-2-22211111111-1-1-1-1002-20000-2200000000-1-111000000000011-1-1
χ3022222-2-2-2-222222-2-2-2-2-2-2222-1-1-1222-1-2-2-2-2-1-1-1-1-1-1-1-11111-2-22211111111-1-1-1-100-2200002-20000000011-1-10000000000-1-111
χ3122222-2-2-2-222222-2-2-2-2-2-222-1222-1-1-1211112222-1-1-1-1-2-2-2-211-1-111111111-1-1-1-100002-20000-220000-1-10000000011-1-1110000
χ3222222-2-2-2-222222-2-2-2-2-2-222-1222-1-1-1211112222-1-1-1-1-2-2-2-211-1-111111111-1-1-1-10000-2200002-200001100000000-1-111-1-10000
χ3322-2-222-22i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i222-22-2-2-222-2-22i2i−2i−2i22-2-22-22i−2i2i−2i2i−2i22-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ3422-2-222-22i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i2-1-112-2-2122-2-2−i−iii-1-111-11−ii2i−2i2i−2i-1-111−i−iii−i−iii000000000000000000−i3i3−i3i300000000003−33−3
χ3522-2-222-22i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i2-1-112-2-2122-2-2−i−iii-1-111-11−ii2i−2i2i−2i-1-111−i−iii−i−iii000000000000000000i3−i3i3−i30000000000−33−33
χ3622-2-222-22i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i-122-2-111-2-1-1112i2i−2i−2i-1-1112-22i−2i−ii−ii-1-111−i−iii−i−iii0000000000000000−i3i3000000003−33−3−i3i30000
χ3722-2-222-22i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i-122-2-111-2-1-1112i2i−2i−2i-1-1112-22i−2i−ii−ii-1-111−i−iii−i−iii0000000000000000i3−i300000000−33−33i3−i30000
χ3822-2-222-2−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i222-22-2-2-222-2-2−2i−2i2i2i22-2-22-2−2i2i−2i2i−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ3922-2-222-2−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i2-1-112-2-2122-2-2ii−i−i-1-111-11i−i−2i2i−2i2i-1-111ii−i−iii−i−i000000000000000000−i3i3−i3i30000000000−33−33
χ4022-2-222-2−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i2-1-112-2-2122-2-2ii−i−i-1-111-11i−i−2i2i−2i2i-1-111ii−i−iii−i−i000000000000000000i3−i3i3−i300000000003−33−3
χ4122-2-222-2−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i-122-2-111-2-1-111−2i−2i2i2i-1-1112-2−2i2ii−ii−i-1-111ii−i−iii−i−i0000000000000000−i3i300000000−33−33−i3i30000
χ4222-2-222-2−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i-122-2-111-2-1-111−2i−2i2i2i-1-1112-2−2i2ii−ii−i-1-111ii−i−iii−i−i0000000000000000i3−i3000000003−33−3i3−i30000
χ4322-2-22-222i−2i−2i2i2-2-22i2i−2i−2i-22−2i2i222-22-2-2-2-2-222−2i−2i2i2i22-2-2-222i−2i2i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ4422-2-22-222i−2i−2i2i2-2-22i2i−2i−2i-22−2i2i2-1-112-2-21-2-222ii−i−i-1-1111-1−ii2i−2i−2i2i11-1-1−i−iiiii−i−i000000000000000000−i3i3i3−i300000000003−3−33
χ4522-2-22-222i−2i−2i2i2-2-22i2i−2i−2i-22−2i2i2-1-112-2-21-2-222ii−i−i-1-1111-1−ii2i−2i−2i2i11-1-1−i−iiiii−i−i000000000000000000i3−i3−i3i30000000000−333−3
χ4622-2-22-222i−2i−2i2i2-2-22i2i−2i−2i-22−2i2i-122-2-111-211-1-1−2i−2i2i2i-1-111-222i−2i−iii−i11-1-1−i−iiiii−i−i0000000000000000−i3i3000000003−3−33i3−i30000
χ4722-2-22-222i−2i−2i2i2-2-22i2i−2i−2i-22−2i2i-122-2-111-211-1-1−2i−2i2i2i-1-111-222i−2i−iii−i11-1-1−i−iiiii−i−i0000000000000000i3−i300000000−333−3−i3i30000
χ4822-2-22-22−2i2i2i−2i2-2-2−2i−2i2i2i-222i−2i222-22-2-2-2-2-2222i2i−2i−2i22-2-2-22−2i2i−2i2i2i−2i-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4922-2-22-22−2i2i2i−2i2-2-2−2i−2i2i2i-222i−2i2-1-112-2-21-2-222−i−iii-1-1111-1i−i−2i2i2i−2i11-1-1ii−i−i−i−iii000000000000000000−i3i3i3−i30000000000−333−3
χ5022-2-22-22−2i2i2i−2i2-2-2−2i−2i2i2i-222i−2i2-1-112-2-21-2-222−i−iii-1-1111-1i−i−2i2i2i−2i11-1-1ii−i−i−i−iii000000000000000000i3−i3−i3i300000000003−3−33
χ5122-2-22-22−2i2i2i−2i2-2-2−2i−2i2i2i-222i−2i-122-2-111-211-1-12i2i−2i−2i-1-111-22−2i2ii−i−ii11-1-1ii−i−i−i−iii0000000000000000−i3i300000000−333−3i3−i30000
χ5222-2-22-22−2i2i2i−2i2-2-2−2i−2i2i2i-222i−2i-122-2-111-211-1-12i2i−2i−2i-1-111-22−2i2ii−i−ii11-1-1ii−i−i−i−iii0000000000000000i3−i3000000003−3−33−i3i30000
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
χ544444444-4-4-4-4444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-222221111-2-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5544444-4-444-4-44444444-4-4-4-4-2-2-2-2-2-2-2-222222222111122-2-2-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
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−4i4-4-44i4i−4i−4i4-44i−4i-2-2-22-2222-2-222−2i−2i2i2i11-1-1-22−2i2i−2i2i−2i2i11-1-1ii−i−iii−i−i000000000000000000000000000000000000
χ5844-4-444-4−4i4i−4i4i4-4-4−4i−4i4i4i4-4−4i4i-2-2-22-2222-2-2222i2i−2i−2i11-1-1-222i−2i2i−2i2i−2i11-1-1−i−iii−i−iii000000000000000000000000000000000000
χ5944-4-44-444i−4i−4i4i4-4-44i4i−4i−4i-44−4i4i-2-2-22-222222-2-22i2i−2i−2i11-1-12-2−2i2i−2i2i2i−2i-1-111ii−i−i−i−iii000000000000000000000000000000000000
χ6044-4-44-44−4i4i4i−4i4-4-4−4i−4i4i4i-444i−4i-2-2-22-222222-2-2−2i−2i2i2i11-1-12-22i−2i2i−2i−2i2i-1-111−i−iiiii−i−i000000000000000000000000000000000000
χ614-44-44000000-4-440000000044-44-44-4-4000000004-44-400000000000000000000000000000000000000000000000000000000
χ624-44-44000000-4-44000000004-22-2-44-42000023−2323−23-22-22000000000000000023−2323−23000000000000000000000000000000000000
χ634-44-44000000-4-44000000004-22-2-44-420000−2323−2323-22-220000000000000000−2323−2323000000000000000000000000000000000000
χ644-44-44000000-4-4400000000-24-442-22-423−2323−230000-22-220000000023−2323−2300000000000000000000000000000000000000000000
χ654-44-44000000-4-4400000000-24-442-22-4−2323−23230000-22-2200000000−2323−232300000000000000000000000000000000000000000000
χ664-44-44000000-4-4400000000-2-22-22-22223−2323−2323−2323−231-11-100000000−33−333-33-3−33−33000000000000000000000000000000000000
χ674-44-44000000-4-4400000000-2-22-22-22223−2323−23−2323−23231-11-100000000−33−33-33-333−33−3000000000000000000000000000000000000
χ684-44-44000000-4-4400000000-2-22-22-222−2323−232323−2323−231-11-1000000003−33−3-33-33−33−33000000000000000000000000000000000000
χ694-44-44000000-4-4400000000-2-22-22-222−2323−2323−2323−23231-11-1000000003−33−33-33-33−33−3000000000000000000000000000000000000
χ704-4-444000000-44-40000000044-4-4-4-444000000004-4-4400000000000000000000000000000000000000000000000000000000
χ714-4-444000000-44-4000000004-222-4-44-20000−2i32i32i3−2i3-222-20000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ724-4-444000000-44-4000000004-222-4-44-200002i3−2i3−2i32i3-222-200000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ734-4-444000000-44-400000000-24-4-422-2423−23−23230000-222-20000000023−23−232300000000000000000000000000000000000000000000
χ744-4-444000000-44-400000000-24-4-422-24−232323−230000-222-200000000−232323−2300000000000000000000000000000000000000000000
χ754-4-444000000-44-400000000-2-22222-2-223−23−2323−2i32i32i3−2i31-1-1100000000−333−3−3i3i3i−3ii3−i3−i3i3000000000000000000000000000000000000
χ764-4-444000000-44-400000000-2-22222-2-223−23−23232i3−2i3−2i32i31-1-1100000000−333−33i−3i−3i3i−i3i3i3−i3000000000000000000000000000000000000
χ774-4-444000000-44-400000000-2-22222-2-2−232323−23−2i32i32i3−2i31-1-11000000003−3−333i−3i−3i3ii3−i3−i3i3000000000000000000000000000000000000
χ784-4-444000000-44-400000000-2-22222-2-2−232323−232i3−2i3−2i32i31-1-11000000003−3−33−3i3i3i−3i−i3i3i3−i3000000000000000000000000000000000000
χ796666-3666666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000220000220000-1-1-1-1000000-1-1-1-10000000000
χ806666-3666666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000-2-20000-2-20000111100000011110000000000
χ816666-366-6-6-6-6-3-3-33333-3-3330000000000000000000000000000000000000000220000-2-20000-1-1-1-100000011110000000000
χ826666-366-6-6-6-6-3-3-33333-3-3330000000000000000000000000000000000000000-2-200002200001111000000-1-1-1-10000000000
χ836666-3-6-666-6-6-3-3-3-3-3-3-3333300000000000000000000000000000000000000002-200002-20000-1-111000000-1-1110000000000
χ846666-3-6-666-6-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000-220000-22000011-1-100000011-1-10000000000
χ856666-3-6-6-6-666-3-3-3333333-3-300000000000000000000000000000000000000002-20000-220000-1-11100000011-1-10000000000
χ866666-3-6-6-6-666-3-3-3333333-3-30000000000000000000000000000000000000000-2200002-2000011-1-1000000-1-1110000000000
χ8766-6-6-36-66i−6i6i−6i-333−3i−3i3i3i-33−3i3i0000000000000000000000000000000000000000000000000000−i3i3−i3i30000003−33−30000000000
χ8866-6-6-36-66i−6i6i−6i-333−3i−3i3i3i-33−3i3i0000000000000000000000000000000000000000000000000000i3−i3i3−i3000000−33−330000000000
χ8966-6-6-36-6−6i6i−6i6i-3333i3i−3i−3i-333i−3i0000000000000000000000000000000000000000000000000000−i3i3−i3i3000000−33−330000000000
χ9066-6-6-36-6−6i6i−6i6i-3333i3i−3i−3i-333i−3i0000000000000000000000000000000000000000000000000000i3−i3i3−i30000003−33−30000000000
χ9166-6-6-3-666i−6i−6i6i-333−3i−3i3i3i3-33i−3i0000000000000000000000000000000000000000000000000000−i3i3i3−i30000003−3−330000000000
χ9266-6-6-3-666i−6i−6i6i-333−3i−3i3i3i3-33i−3i0000000000000000000000000000000000000000000000000000i3−i3−i3i3000000−333−30000000000
χ9366-6-6-3-66−6i6i6i−6i-3333i3i−3i−3i3-3−3i3i0000000000000000000000000000000000000000000000000000−i3i3i3−i3000000−333−30000000000
χ9466-6-6-3-66−6i6i6i−6i-3333i3i−3i−3i3-3−3i3i0000000000000000000000000000000000000000000000000000i3−i3−i3i30000003−3−330000000000
χ9512-1212-12-600000066-6−6i36i3−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212-12-600000066-66i3−6i36i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-1212-60000006-6663−63−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-1212-60000006-66−636363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000

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