Finite Group Databasebeta

← Group #13147889

Character table — Group #13147889

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order12223444444666121212121212121233666666121212121212121236661212121212121212121212121212121212121212222444444444666666121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1111-1-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-11-11-111-11111-1-111-1-1-1-111-1-11111-1-1-1-1
χ61111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-111-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-11111
χ71111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11-111-1111-1-11111-1-1-1-1-1-111-1-1-1-11111
χ81111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-11-11-1-1-1-1-111-1-11111-1-1111111-1-1-1-1
χ911111-1-111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111-11-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-111-1-1
χ1011111-1-111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-11-111-1-11-1-1-1-1111111-1-111-1-1-1-1-1-111-1-111
χ1111111-1-111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11-111111-1-1-111-1-1-1-1-1-111-1-11111-1-111-1-111
χ1211111-1-111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-1-111111-1-1-1-1-1-111-1-111111111-1-111-1-1
χ1311111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-111-1-11-11-11-11111-1-1-1-1-1-111-1-11111-1-1-1-111
χ1411111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-111-1-111-11-1-111-1-11111-1-1-1-111-1-11111-1-1
χ1511111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1111-11-11-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1
χ1611111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-11-1-11-111-111-1-1-1-1-1111111-1-111-1-111-1-1-1-111
χ1722222222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122000002200000-1-1-1-1000000-1-1-1-100000000
χ1822222222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200000-2-2000001111000000111100000000
χ192222222222222222222222-12-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000022000220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000-2-2000-2-2000000000000000011111111
χ212222222-2-2-2-2222-2-2-2-222-2-22-12-1-122-122221111-1-1-1-1-1-111-2-2-2-2-1-1-1-1111111112-2000002-200000-1-111000000-1-11100000000
χ222222222-2-2-2-2222-2-2-2-222-2-22-12-1-122-122221111-1-1-1-1-1-111-2-2-2-2-1-1-1-111111111-2200000-220000011-1-100000011-1-100000000
χ232222222-2-2-2-2222-2-2-2-222-2-2-12-122-1-12-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111111111000002-20002-20000000000000000-1-1-1-11111
χ242222222-2-2-2-2222-2-2-2-222-2-2-12-122-1-12-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-11111111100000-22000-2200000000000000001111-1-1-1-1
χ2522222-2-222-2-22222222-2-2-2-22-12-1-122-1-2-2-2-21111-1-1-1-111-1-122-2-21111-1-1-1-111112200000-2-200000-1-1-1-1000000111100000000
χ2622222-2-222-2-22222222-2-2-2-22-12-1-122-1-2-2-2-21111-1-1-1-111-1-122-2-21111-1-1-1-11111-2-20000022000001111000000-1-1-1-100000000
χ2722222-2-222-2-22222222-2-2-2-2-12-122-1-121111-2-2-2-2-1-1-1-1-2-222-1-1111111-1-1-1-111110000022000-2-2000000000000000011-1-111-1-1
χ2822222-2-222-2-22222222-2-2-2-2-12-122-1-121111-2-2-2-2-1-1-1-1-2-222-1-1111111-1-1-1-1111100000-2-2000220000000000000000-1-111-1-111
χ2922222-2-2-2-222222-2-2-2-2-2-2222-12-1-122-1-2-2-2-2-1-1-1-1-1-1-1-11111-2-22211111111-1-1-1-12-200000-2200000-1-11100000011-1-100000000
χ3022222-2-2-2-222222-2-2-2-2-2-2222-12-1-122-1-2-2-2-2-1-1-1-1-1-1-1-11111-2-22211111111-1-1-1-1-22000002-20000011-1-1000000-1-11100000000
χ3122222-2-2-2-222222-2-2-2-2-2-222-12-122-1-1211112222-1-1-1-1-2-2-2-211-1-111111111-1-1-1-1000002-2000-22000000000000000011-1-1-1-111
χ3222222-2-2-2-222222-2-2-2-2-2-222-12-122-1-1211112222-1-1-1-1-2-2-2-211-1-111111111-1-1-1-100000-220002-20000000000000000-1-11111-1-1
χ332-22-222i−2i2-22i−2i2-2-222-2-22i−2i2i−2i22-22-22-2-22i2i−2i−2i2i2i−2i−2i22-2-22i−2i2-22-22i−2i2i2i−2i−2i22-2-22i2i−2i−2i000000000000000000000000000000000000
χ342-22-222i−2i2-22i−2i2-2-222-2-22i−2i2i−2i2-1-2-112-212i2i−2i−2i−i−iii-1-111−ii-112-22i−2i−i−iii-1-111−i−iii00000000000000−i3i3−i3i30000003−33−300000000
χ352-22-222i−2i2-22i−2i2-2-222-2-22i−2i2i−2i2-1-2-112-212i2i−2i−2i−i−iii-1-111−ii-112-22i−2i−i−iii-1-111−i−iii00000000000000i3−i3i3−i3000000−33−3300000000
χ362-22-222i−2i2-22i−2i2-2-222-2-22i−2i2i−2i-1212-2-11-2−i−iii2i2i−2i−2i-1-1112i−2i2-2-11−ii−i−iii-1-111−i−iii00000000000000000000000000003−3−i3i33−3−i3i3
χ372-22-222i−2i2-22i−2i2-2-222-2-22i−2i2i−2i-1212-2-11-2−i−iii2i2i−2i−2i-1-1112i−2i2-2-11−ii−i−iii-1-111−i−iii0000000000000000000000000000−33i3−i3−33i3−i3
χ382-22-222i−2i-22−2i2i2-2-2-2-2222i−2i−2i2i22-22-22-2-22i2i−2i−2i−2i−2i2i2i22-2-22i−2i-22-22−2i2i2i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000000000000000
χ392-22-222i−2i-22−2i2i2-2-2-2-2222i−2i−2i2i2-1-2-112-212i2i−2i−2iii−i−i-1-111−ii1-1-22−2i2i−i−iii11-1-1ii−i−i00000000000000−i3i3i3−i30000003−3−3300000000
χ402-22-222i−2i-22−2i2i2-2-2-2-2222i−2i−2i2i2-1-2-112-212i2i−2i−2iii−i−i-1-111−ii1-1-22−2i2i−i−iii11-1-1ii−i−i00000000000000i3−i3−i3i3000000−333−300000000
χ412-22-222i−2i-22−2i2i2-2-2-2-2222i−2i−2i2i-1212-2-11-2−i−iii−2i−2i2i2i-1-1112i−2i-221-1i−i−i−iii11-1-1ii−i−i00000000000000000000000000003−3−i3i3−33i3−i3
χ422-22-222i−2i-22−2i2i2-2-2-2-2222i−2i−2i2i-1212-2-11-2−i−iii−2i−2i2i2i-1-1112i−2i-221-1i−i−i−iii11-1-1ii−i−i0000000000000000000000000000−33i3−i33−3−i3i3
χ432-22-22−2i2i2-2−2i2i2-2-222-2-2−2i2i−2i2i22-22-22-2-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i2-22-2−2i2i−2i−2i2i2i22-2-2−2i−2i2i2i000000000000000000000000000000000000
χ442-22-22−2i2i2-2−2i2i2-2-222-2-2−2i2i−2i2i2-1-2-112-21−2i−2i2i2iii−i−i-1-111i−i-112-2−2i2iii−i−i-1-111ii−i−i00000000000000−i3i3−i3i3000000−33−3300000000
χ452-22-22−2i2i2-2−2i2i2-2-222-2-2−2i2i−2i2i2-1-2-112-21−2i−2i2i2iii−i−i-1-111i−i-112-2−2i2iii−i−i-1-111ii−i−i00000000000000i3−i3i3−i30000003−33−300000000
χ462-22-22−2i2i2-2−2i2i2-2-222-2-2−2i2i−2i2i-1212-2-11-2ii−i−i−2i−2i2i2i-1-111−2i2i2-2-11i−iii−i−i-1-111ii−i−i00000000000000000000000000003−3i3−i33−3i3−i3
χ472-22-22−2i2i2-2−2i2i2-2-222-2-2−2i2i−2i2i-1212-2-11-2ii−i−i−2i−2i2i2i-1-111−2i2i2-2-11i−iii−i−i-1-111ii−i−i0000000000000000000000000000−33−i3i3−33−i3i3
χ482-22-22−2i2i-222i−2i2-2-2-2-222−2i2i2i−2i22-22-22-2-2−2i−2i2i2i2i2i−2i−2i22-2-2−2i2i-22-222i−2i−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000000000000000
χ492-22-22−2i2i-222i−2i2-2-2-2-222−2i2i2i−2i2-1-2-112-21−2i−2i2i2i−i−iii-1-111i−i1-1-222i−2iii−i−i11-1-1−i−iii00000000000000−i3i3i3−i3000000−333−300000000
χ502-22-22−2i2i-222i−2i2-2-2-2-222−2i2i2i−2i2-1-2-112-21−2i−2i2i2i−i−iii-1-111i−i1-1-222i−2iii−i−i11-1-1−i−iii00000000000000i3−i3−i3i30000003−3−3300000000
χ512-22-22−2i2i-222i−2i2-2-2-2-222−2i2i2i−2i-1212-2-11-2ii−i−i2i2i−2i−2i-1-111−2i2i-221-1−iiii−i−i11-1-1−i−iii00000000000000000000000000003−3i3−i3−33−i3i3
χ522-22-22−2i2i-222i−2i2-2-2-2-222−2i2i2i−2i-1212-2-11-2ii−i−i2i2i−2i−2i-1-111−2i2i-221-1−iiii−i−i11-1-1−i−iii0000000000000000000000000000−33−i3i33−3i3−i3
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
χ5744-4-44000000-44-400000000444-44-4-4-4000000004-44-400000000000000000000000000000000000000000000000000000000
χ5844-4-44000000-44-4000000004-242-2-4-42000023−2323−23-22-22000000000000000023−2323−23000000000000000000000000000000000000
χ5944-4-44000000-44-4000000004-242-2-4-420000−2323−2323-22-220000000000000000−2323−2323000000000000000000000000000000000000
χ6044-4-44000000-44-400000000-24-2-4422-4−2i32i3−2i32i30000-22-2200000000−2i32i3−2i32i300000000000000000000000000000000000000000000
χ6144-4-44000000-44-400000000-24-2-4422-42i3−2i32i3−2i30000-22-22000000002i3−2i32i3−2i300000000000000000000000000000000000000000000
χ6244-4-44000000-44-400000000-2-2-22-2222−2i32i3−2i32i323−2323−231-11-100000000i3−i3i3−i33i−3i3i−3i−33−33000000000000000000000000000000000000
χ6344-4-44000000-44-400000000-2-2-22-2222−2i32i3−2i32i3−2323−23231-11-100000000i3−i3i3−i3−3i3i−3i3i3−33−3000000000000000000000000000000000000
χ6444-4-44000000-44-400000000-2-2-22-22222i3−2i32i3−2i323−2323−231-11-100000000−i3i3−i3i3−3i3i−3i3i−33−33000000000000000000000000000000000000
χ6544-4-44000000-44-400000000-2-2-22-22222i3−2i32i3−2i3−2323−23231-11-100000000−i3i3−i3i33i−3i3i−3i3−33−3000000000000000000000000000000000000
χ664-44-444i−4i4-44i−4i4-4-444-4-44i−4i4i−4i-2-22-22-222−2i−2i2i2i−2i−2i2i2i11-1-1−2i2i-22-22−2i2iii−i−i11-1-1ii−i−i000000000000000000000000000000000000
χ674-44-444i−4i-44−4i4i4-4-4-4-4444i−4i−4i4i-2-22-22-222−2i−2i2i2i2i2i−2i−2i11-1-1−2i2i2-22-22i−2iii−i−i-1-111−i−iii000000000000000000000000000000000000
χ684-44-44−4i4i4-4−4i4i4-4-444-4-4−4i4i−4i4i-2-22-22-2222i2i−2i−2i2i2i−2i−2i11-1-12i−2i-22-222i−2i−i−iii11-1-1−i−iii000000000000000000000000000000000000
χ694-44-44−4i4i-444i−4i4-4-4-4-444−4i4i4i−4i-2-22-22-2222i2i−2i−2i−2i−2i2i2i11-1-12i−2i2-22-2−2i2i−i−iii-1-111ii−i−i000000000000000000000000000000000000
χ704-4-444000000-4-440000000044-4-4-4-444000000004-4-4400000000000000000000000000000000000000000000000000000000
χ714-4-444000000-4-44000000004-2-422-44-20000−2i32i32i3−2i3-222-20000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ724-4-444000000-4-44000000004-2-422-44-200002i3−2i3−2i32i3-222-200000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ734-4-444000000-4-4400000000-242-4-42-2423−23−23230000-222-20000000023−23−232300000000000000000000000000000000000000000000
χ744-4-444000000-4-4400000000-242-4-42-24−232323−230000-222-200000000−232323−2300000000000000000000000000000000000000000000
χ754-4-444000000-4-4400000000-2-22222-2-223−23−2323−2i32i32i3−2i31-1-1100000000−333−3−3i3i3i−3ii3−i3−i3i3000000000000000000000000000000000000
χ764-4-444000000-4-4400000000-2-22222-2-223−23−23232i3−2i3−2i32i31-1-1100000000−333−33i−3i−3i3i−i3i3i3−i3000000000000000000000000000000000000
χ774-4-444000000-4-4400000000-2-22222-2-2−232323−23−2i32i32i3−2i31-1-11000000003−3−333i−3i−3i3ii3−i3−i3i3000000000000000000000000000000000000
χ784-4-444000000-4-4400000000-2-22222-2-2−232323−232i3−2i3−2i32i31-1-11000000003−3−33−3i3i3i−3i−i3i3i3−i3000000000000000000000000000000000000
χ796666-3666666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000002220000200-1-10000-1-1-1-1-1-1000000000000
χ806666-3666666-3-3-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000000000-2-2-20000-200110000111111000000000000
χ816666-366-6-6-6-6-3-3-33333-3-3330000000000000000000000000000000000000000002-2-20000200-1-10000-1-11111000000000000
χ826666-366-6-6-6-6-3-3-33333-3-333000000000000000000000000000000000000000000-2220000-20011000011-1-1-1-1000000000000
χ836666-3-6-666-6-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000002-220000-200-1-1000011-1-111000000000000
χ846666-3-6-666-6-6-3-3-3-3-3-3-33333000000000000000000000000000000000000000000-22-20000200110000-1-111-1-1000000000000
χ856666-3-6-6-6-666-3-3-3333333-3-300000000000000000000000000000000000000000022-20000-200-1-100001111-1-1000000000000
χ866666-3-6-6-6-666-3-3-3333333-3-3000000000000000000000000000000000000000000-2-220000200110000-1-1-1-111000000000000
χ876-66-6-36i−6i6-66i−6i-333-3-333−3i3i−3i3i0000000000000000000000000000000000000000000000000000−i3i300003−3−i3i33−3000000000000
χ886-66-6-36i−6i6-66i−6i-333-3-333−3i3i−3i3i0000000000000000000000000000000000000000000000000000i3−i30000−33i3−i3−33000000000000
χ896-66-6-36i−6i-66−6i6i-33333-3-3−3i3i3i−3i0000000000000000000000000000000000000000000000000000−i3i300003−3i3−i3−33000000000000
χ906-66-6-36i−6i-66−6i6i-33333-3-3−3i3i3i−3i0000000000000000000000000000000000000000000000000000i3−i30000−33−i3i33−3000000000000
χ916-66-6-3−6i6i6-6−6i6i-333-3-3333i−3i3i−3i0000000000000000000000000000000000000000000000000000−i3i30000−33−i3i3−33000000000000
χ926-66-6-3−6i6i6-6−6i6i-333-3-3333i−3i3i−3i0000000000000000000000000000000000000000000000000000i3−i300003−3i3−i33−3000000000000
χ936-66-6-3−6i6i-666i−6i-33333-3-33i−3i−3i3i0000000000000000000000000000000000000000000000000000−i3i30000−33i3−i33−3000000000000
χ946-66-6-3−6i6i-666i−6i-33333-3-33i−3i−3i3i0000000000000000000000000000000000000000000000000000i3−i300003−3−i3i3−33000000000000
χ951212-12-12-60000006-6663−6363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-12-60000006-66−6363−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-1212-600000066-663−63−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-1212-600000066-6−636363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000

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