Finite Group Databasebeta

← Group #13147759

Character table — Group #13147759

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order122234444446661212121212121212336666661212121212121212366612121212121212121212121212121212121212122444444444446612121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ51111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-11-11-1-11-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-11-1-11-111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-11-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111-1-111-1-1111-1-1-1-1-1-11111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-11-1-111-111-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111-1-111-1-1111-1-1-1-1-1-11111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-11-1-1111-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111-1-111-1-1111-1-1-1-1-1-11111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-11-11-11-11-1-111-1-11111-1-111-1-1-1-111-1-111
χ1211111-1-111-1-1111-1-1-1-1-1-11111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11-1111-11-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ1311111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1411111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1
χ1611111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222222-12-122-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000022000220000000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-12-122-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000-2-2000-2-2000000000000000011111111
χ192222222222222222222222-12-12-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100022000220000000000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222-12-12-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000-2-2000-2-200000000001111111100000000
χ212222222-2-2-2-2222-2-2-2-222-2-22-12-122-1-122221111-1-1-1-1-1-1-2-2-2-211-1-1-1-111111111000002-20002-20000000000000000-1-1-1-11111
χ222222222-2-2-2-2222-2-2-2-222-2-22-12-122-1-122221111-1-1-1-1-1-1-2-2-2-211-1-1-1-11111111100000-22000-2200000000000000001111-1-1-1-1
χ232222222-2-2-2-2222-2-2-2-222-2-2-12-12-1-122-1-1-1-1-2-2-2-2-1-1-1-1221111-2-2-1-1-1-1111111110002-20002-20000000000-1-1-1-1111100000000
χ242222222-2-2-2-2222-2-2-2-222-2-2-12-12-1-122-1-1-1-1-2-2-2-2-1-1-1-1221111-2-2-1-1-1-111111111000-22000-2200000000001111-1-1-1-100000000
χ2522222-2-222-2-2222-2-2-2-2-2-2222-12-122-1-1-2-2-2-2-1-1-1-1-1-1-1-11122-2-2111111-1-1-1-11111000002-2000-22000000000000000011-1-111-1-1
χ2622222-2-222-2-2222-2-2-2-2-2-2222-12-122-1-1-2-2-2-2-1-1-1-1-1-1-1-11122-2-2111111-1-1-1-1111100000-220002-20000000000000000-1-111-1-111
χ2722222-2-222-2-2222-2-2-2-2-2-222-12-12-1-12211112222-1-1-1-1-2-2-1-111-2-21111-1-1-1-111110002-2000-220000000000-1-111-1-11100000000
χ2822222-2-222-2-2222-2-2-2-2-2-222-12-12-1-12211112222-1-1-1-1-2-2-1-111-2-21111-1-1-1-11111000-220002-2000000000011-1-111-1-100000000
χ2922222-2-2-2-2222222222-2-2-2-22-12-122-1-1-2-2-2-21111-1-1-1-111-2-222-1-111111111-1-1-1-10000022000-2-2000000000000000011-1-1-1-111
χ3022222-2-2-2-2222222222-2-2-2-22-12-122-1-1-2-2-2-21111-1-1-1-111-2-222-1-111111111-1-1-1-100000-2-2000220000000000000000-1-11111-1-1
χ3122222-2-2-2-2222222222-2-2-2-2-12-12-1-1221111-2-2-2-2-1-1-1-1-2-211-1-12211111111-1-1-1-100022000-2-20000000000-1-11111-1-100000000
χ3222222-2-2-2-2222222222-2-2-2-2-12-12-1-1221111-2-2-2-2-1-1-1-1-2-211-1-12211111111-1-1-1-1000-2-200022000000000011-1-1-1-11100000000
χ332-2-2222i−2i2i−2i2-22-2-222-2-22i−2i2i−2i22-2-22-22-22i2i−2i−2i2i2i−2i−2i22-2-22i−2i2i−2i2-22-22i2i−2i−2i2i2i−2i−2i22-2-2000000000000000000000000000000000000
χ342-2-2222i−2i2i−2i2-22-2-222-2-22i−2i2i−2i2-1-212-2-112i2i−2i−2i−i−iii-1-111−ii2i−2i2-2-11−i−iii−i−iii-1-1110000000000000000000000000000−i3i33−33−3−i3i3
χ352-2-2222i−2i2i−2i2-22-2-222-2-22i−2i2i−2i2-1-212-2-112i2i−2i−2i−i−iii-1-111−ii2i−2i2-2-11−i−iii−i−iii-1-1110000000000000000000000000000i3−i3−33−33i3−i3
χ362-2-2222i−2i2i−2i2-22-2-222-2-22i−2i2i−2i-121-2-112-2−i−iii2i2i−2i−2i-1-1112i−2i−ii-112-2−i−iii−i−iii-1-111000000000000000000003−3−i3i3−i3i33−300000000
χ372-2-2222i−2i2i−2i2-22-2-222-2-22i−2i2i−2i-121-2-112-2−i−iii2i2i−2i−2i-1-1112i−2i−ii-112-2−i−iii−i−iii-1-11100000000000000000000−33i3−i3i3−i3−3300000000
χ382-2-2222i−2i−2i2i-222-2-2-2-2222i−2i−2i2i22-2-22-22-22i2i−2i−2i−2i−2i2i2i22-2-22i−2i−2i2i-22-222i2i−2i−2i−2i−2i2i2i-2-222000000000000000000000000000000000000
χ392-2-2222i−2i−2i2i-222-2-2-2-2222i−2i−2i2i2-1-212-2-112i2i−2i−2iii−i−i-1-111−ii−2i2i-221-1−i−iiiii−i−i11-1-10000000000000000000000000000−i3i33−3−33i3−i3
χ402-2-2222i−2i−2i2i-222-2-2-2-2222i−2i−2i2i2-1-212-2-112i2i−2i−2iii−i−i-1-111−ii−2i2i-221-1−i−iiiii−i−i11-1-10000000000000000000000000000i3−i3−333−3−i3i3
χ412-2-2222i−2i−2i2i-222-2-2-2-2222i−2i−2i2i-121-2-112-2−i−iii−2i−2i2i2i-1-1112i−2ii−i1-1-22−i−iiiii−i−i11-1-1000000000000000000003−3−i3i3i3−i3−3300000000
χ422-2-2222i−2i−2i2i-222-2-2-2-2222i−2i−2i2i-121-2-112-2−i−iii−2i−2i2i2i-1-1112i−2ii−i1-1-22−i−iiiii−i−i11-1-100000000000000000000−33i3−i3−i3i33−300000000
χ432-2-222−2i2i2i−2i-222-2-2-2-222−2i2i2i−2i22-2-22-22-2−2i−2i2i2i2i2i−2i−2i22-2-2−2i2i2i−2i-22-22−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000000000000000
χ442-2-222−2i2i2i−2i-222-2-2-2-222−2i2i2i−2i2-1-212-2-11−2i−2i2i2i−i−iii-1-111i−i2i−2i-221-1ii−i−i−i−iii11-1-10000000000000000000000000000−i3i3−333−3i3−i3
χ452-2-222−2i2i2i−2i-222-2-2-2-222−2i2i2i−2i2-1-212-2-11−2i−2i2i2i−i−iii-1-111i−i2i−2i-221-1ii−i−i−i−iii11-1-10000000000000000000000000000i3−i33−3−33−i3i3
χ462-2-222−2i2i2i−2i-222-2-2-2-222−2i2i2i−2i-121-2-112-2ii−i−i2i2i−2i−2i-1-111−2i2i−ii1-1-22ii−i−i−i−iii11-1-1000000000000000000003−3i3−i3−i3i3−3300000000
χ472-2-222−2i2i2i−2i-222-2-2-2-222−2i2i2i−2i-121-2-112-2ii−i−i2i2i−2i−2i-1-111−2i2i−ii1-1-22ii−i−i−i−iii11-1-100000000000000000000−33−i3i3i3−i33−300000000
χ482-2-222−2i2i−2i2i2-22-2-222-2-2−2i2i−2i2i22-2-22-22-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i−2i2i2-22-2−2i−2i2i2i−2i−2i2i2i22-2-2000000000000000000000000000000000000
χ492-2-222−2i2i−2i2i2-22-2-222-2-2−2i2i−2i2i2-1-212-2-11−2i−2i2i2iii−i−i-1-111i−i−2i2i2-2-11ii−i−iii−i−i-1-1110000000000000000000000000000−i3i3−33−33−i3i3
χ502-2-222−2i2i−2i2i2-22-2-222-2-2−2i2i−2i2i2-1-212-2-11−2i−2i2i2iii−i−i-1-111i−i−2i2i2-2-11ii−i−iii−i−i-1-1110000000000000000000000000000i3−i33−33−3i3−i3
χ512-2-222−2i2i−2i2i2-22-2-222-2-2−2i2i−2i2i-121-2-112-2ii−i−i−2i−2i2i2i-1-111−2i2ii−i-112-2ii−i−iii−i−i-1-111000000000000000000003−3i3−i3i3−i33−300000000
χ522-2-222−2i2i−2i2i2-22-2-222-2-2−2i2i−2i2i-121-2-112-2ii−i−i−2i−2i2i2i-1-111−2i2ii−i-112-2ii−i−iii−i−i-1-11100000000000000000000−33−i3i3−i3i3−3300000000
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
χ5544444-4-444-4-4444-4-4-4-4-4-444-2-2-2-2-2-2-2-22222-2-2-2-2111122-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ5644444-4-4-4-4444444444-4-4-4-4-2-2-2-2-2-2-2-22222222211112222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ5744-4-44000000-44-400000000444-4-4-4-44000000004-44-400000000000000000000000000000000000000000000000000000000
χ5844-4-44000000-44-4000000004-242-4-42-2000023−2323−23-22-2200000000000023−2323−230000000000000000000000000000000000000000
χ5944-4-44000000-44-4000000004-242-4-42-20000−2323−2323-22-22000000000000−2323−23230000000000000000000000000000000000000000
χ6044-4-44000000-44-400000000-24-2-422-44−2i32i3−2i32i30000-22-2200000000−2i32i3−2i32i300000000000000000000000000000000000000000000
χ6144-4-44000000-44-400000000-24-2-422-442i3−2i32i3−2i30000-22-22000000002i3−2i32i3−2i300000000000000000000000000000000000000000000
χ6244-4-44000000-44-400000000-2-2-22222-2−2i32i3−2i32i323−2323−231-11-100000000i3−i3i3−i3−33−333i−3i3i−3i000000000000000000000000000000000000
χ6344-4-44000000-44-400000000-2-2-22222-2−2i32i3−2i32i3−2323−23231-11-100000000i3−i3i3−i33−33−3−3i3i−3i3i000000000000000000000000000000000000
χ6444-4-44000000-44-400000000-2-2-22222-22i3−2i32i3−2i323−2323−231-11-100000000−i3i3−i3i3−33−33−3i3i−3i3i000000000000000000000000000000000000
χ6544-4-44000000-44-400000000-2-2-22222-22i3−2i32i3−2i3−2323−23231-11-100000000−i3i3−i3i33−33−33i−3i3i−3i000000000000000000000000000000000000
χ664-44-44000000-4-440000000044-44-44-4-4000000004-4-4400000000000000000000000000000000000000000000000000000000
χ674-44-44000000-4-44000000004-2-4-2-44220000−2i32i32i3−2i3-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ684-44-44000000-4-44000000004-2-4-2-442200002i3−2i3−2i32i3-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ694-44-44000000-4-4400000000-24242-2-4-423−23−23230000-222-20000000023−23−232300000000000000000000000000000000000000000000
χ704-44-44000000-4-4400000000-24242-2-4-4−232323−230000-222-200000000−232323−2300000000000000000000000000000000000000000000
χ714-44-44000000-4-4400000000-2-22-22-22223−23−2323−2i32i32i3−2i31-1-1100000000−333−3i3−i3−i3i3−3i3i3i−3i000000000000000000000000000000000000
χ724-44-44000000-4-4400000000-2-22-22-22223−23−23232i3−2i3−2i32i31-1-1100000000−333−3−i3i3i3−i33i−3i−3i3i000000000000000000000000000000000000
χ734-44-44000000-4-4400000000-2-22-22-222−232323−23−2i32i32i3−2i31-1-11000000003−3−33i3−i3−i3i33i−3i−3i3i000000000000000000000000000000000000
χ744-44-44000000-4-4400000000-2-22-22-222−232323−232i3−2i3−2i32i31-1-11000000003−3−33−i3i3i3−i3−3i3i3i−3i000000000000000000000000000000000000
χ754-4-4444i−4i4i−4i4-44-4-444-4-44i−4i4i−4i-2-222-22-22−2i−2i2i2i−2i−2i2i2i11-1-1−2i2i−2i2i-22-22ii−i−iii−i−i11-1-1000000000000000000000000000000000000
χ764-4-4444i−4i−4i4i-444-4-4-4-4444i−4i−4i4i-2-222-22-22−2i−2i2i2i2i2i−2i−2i11-1-1−2i2i2i−2i2-22-2ii−i−i−i−iii-1-111000000000000000000000000000000000000
χ774-4-444−4i4i4i−4i-444-4-4-4-444−4i4i4i−4i-2-222-22-222i2i−2i−2i−2i−2i2i2i11-1-12i−2i−2i2i2-22-2−i−iiiii−i−i-1-111000000000000000000000000000000000000
χ784-4-444−4i4i−4i4i4-44-4-444-4-4−4i4i−4i4i-2-222-22-222i2i−2i−2i2i2i−2i−2i11-1-12i−2i2i−2i-22-22−i−iii−i−iii11-1-1000000000000000000000000000000000000
χ796666-3666666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000222000020000-1-1-1-1-1-1-1-10000000000000000
χ806666-3666666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000-2-2-20000-20000111111110000000000000000
χ816666-366-6-6-6-6-3-3-33333-3-333000000000000000000000000000000000000000022-20000-20000-1-1-1-111110000000000000000
χ826666-366-6-6-6-6-3-3-33333-3-3330000000000000000000000000000000000000000-2-220000200001111-1-1-1-10000000000000000
χ836666-3-6-666-6-6-3-3-3333333-3-300000000000000000000000000000000000000002-220000-20000-1-111-1-1110000000000000000
χ846666-3-6-666-6-6-3-3-3333333-3-30000000000000000000000000000000000000000-22-200002000011-1-111-1-10000000000000000
χ856666-3-6-6-6-666-3-3-3-3-3-3-3333300000000000000000000000000000000000000002-2-2000020000-1-11111-1-10000000000000000
χ866666-3-6-6-6-666-3-3-3-3-3-3-333330000000000000000000000000000000000000000-2220000-2000011-1-1-1-1110000000000000000
χ876-6-66-36i−6i6i−6i6-6-333-3-333−3i3i−3i3i0000000000000000000000000000000000000000000000000000−i3i33−33−3−i3i30000000000000000
χ886-6-66-36i−6i6i−6i6-6-333-3-333−3i3i−3i3i0000000000000000000000000000000000000000000000000000i3−i3−33−33i3−i30000000000000000
χ896-6-66-36i−6i−6i6i-66-33333-3-3−3i3i3i−3i0000000000000000000000000000000000000000000000000000−i3i33−3−33i3−i30000000000000000
χ906-6-66-36i−6i−6i6i-66-33333-3-3−3i3i3i−3i0000000000000000000000000000000000000000000000000000i3−i3−333−3−i3i30000000000000000
χ916-6-66-3−6i6i6i−6i-66-33333-3-33i−3i−3i3i0000000000000000000000000000000000000000000000000000−i3i3−333−3i3−i30000000000000000
χ926-6-66-3−6i6i6i−6i-66-33333-3-33i−3i−3i3i0000000000000000000000000000000000000000000000000000i3−i33−3−33−i3i30000000000000000
χ936-6-66-3−6i6i−6i6i6-6-333-3-3333i−3i3i−3i0000000000000000000000000000000000000000000000000000−i3i3−33−33−i3i30000000000000000
χ946-6-66-3−6i6i−6i6i6-6-333-3-3333i−3i3i−3i0000000000000000000000000000000000000000000000000000i3−i33−33−3i3−i30000000000000000
χ951212-12-12-60000006-6663−6363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-12-60000006-66−6363−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-1212-12-600000066-663−63−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-1212-12-600000066-6−636363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000

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