Finite Group Databasebeta

← Group #13147849

Character table — Group #13147849

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order12223444444666121212121212121233666666121212121212121236661212121212121212121212121212121212121212222444444444666666121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111111111111111111111-1-1111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ51111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11-11-1-11-11-111-11111-1-11111-1-1-1-111-1-1-1-111-1-1
χ61111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-111-1-1-11-1-111-1-1-1-1-1-11111-1-1111111-1-1
χ71111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1-11-111-1111-1-111-1-1-1-1111111-1-1-1-1-1-111
χ81111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1111-1-11-11-1-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ911111-1-111-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-11-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1
χ1011111-1-111-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-11-111-1-11-1-1-1-11111-1-111-1-11111-1-111-1-1-1-1
χ1111111-1-111-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-111111-1-1-111-1-1-1-1-1-111-1-111-1-111-1-11111
χ1211111-1-111-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-1-111111-1-1-1-1-1-111-1-111-1-111-1-1111111
χ1311111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-111-1-11-11-11-11111-1-111-1-1-1-111-1-1-1-111-1-111
χ1411111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-111-1-111-11-1-111-1-1-1-11111-1-11111-1-1-1-111
χ1511111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1111-11-11-1-1-1111-1-111-1-11111-1-1-1-1-1-11111-1-1
χ1611111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-11-1-11-111-111-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1722222222222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122000002200000-1-1-1-100000000000000-1-1-1-1
χ1822222222222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200000-2-2000001111000000000000001111
χ192222222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002220000200-1-1000000000000-1-1-1-1-1-10000
χ202222222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-20000-200110000000000001111110000
χ212222222-2-2-2-22222222-2-2-2-22-1-1-1222-1-2-2-2-21111-1-1-1-1-1-11122-2-2-1-1-1-1111111112-2000002-200000-1-11100000000000000-1-111
χ222222222-2-2-2-22222222-2-2-2-22-1-1-1222-1-2-2-2-21111-1-1-1-1-1-11122-2-2-1-1-1-111111111-2200000-220000011-1-10000000000000011-1-1
χ232222222-2-2-2-22222222-2-2-2-2-1222-1-1-121111-2-2-2-2-1-1-1-122-2-2-1-111-1-1-1-111111111002-2-20000200-1-1000000000000-1-111110000
χ242222222-2-2-2-22222222-2-2-2-2-1222-1-1-121111-2-2-2-2-1-1-1-122-2-2-1-111-1-1-1-11111111100-2220000-2001100000000000011-1-1-1-10000
χ2522222-2-222-2-2222-2-2-2-222-2-22-1-1-1222-122221111-1-1-1-111-1-1-2-2-2-21111-1-1-1-111112200000-2-200000-1-1-1-1000000000000001111
χ2622222-2-222-2-2222-2-2-2-222-2-22-1-1-1222-122221111-1-1-1-111-1-1-2-2-2-21111-1-1-1-11111-2-2000002200000111100000000000000-1-1-1-1
χ2722222-2-222-2-2222-2-2-2-222-2-2-1222-1-1-12-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-11111002-220000-200-1-100000000000011-1-1110000
χ2822222-2-222-2-2222-2-2-2-222-2-2-1222-1-1-12-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-1111100-22-2000020011000000000000-1-111-1-10000
χ2922222-2-2-2-222222-2-2-2-2-2-2222-1-1-1222-1-2-2-2-2-1-1-1-1-1-1-1-11111-2-22211111111-1-1-1-12-200000-2200000-1-1110000000000000011-1-1
χ3022222-2-2-2-222222-2-2-2-2-2-2222-1-1-1222-1-2-2-2-2-1-1-1-1-1-1-1-11111-2-22211111111-1-1-1-1-22000002-20000011-1-100000000000000-1-111
χ3122222-2-2-2-222222-2-2-2-2-2-222-1222-1-1-1211112222-1-1-1-1-2-2-2-211-1-111111111-1-1-1-10022-20000-200-1-10000000000001111-1-10000
χ3222222-2-2-2-222222-2-2-2-2-2-222-1222-1-1-1211112222-1-1-1-1-2-2-2-211-1-111111111-1-1-1-100-2-22000020011000000000000-1-1-1-1110000
χ332-22-222i−2i2-22i−2i-22-22i2i−2i−2i2-22i−2i222-22-2-2-222-2-22i2i−2i−2i22-2-22i−2i2-22i−2i2i−2i2i2i−2i−2i22-2-22i2i−2i−2i000000000000000000000000000000000000
χ342-22-222i−2i2-22i−2i-22-22i2i−2i−2i2-22i−2i2-1-112-2-2122-2-2−i−iii-1-111−ii-112i−2i2i−2i−i−iii-1-111−i−iii00000000000000−i3i3−i3i3000000000000003−33−3
χ352-22-222i−2i2-22i−2i-22-22i2i−2i−2i2-22i−2i2-1-112-2-2122-2-2−i−iii-1-111−ii-112i−2i2i−2i−i−iii-1-111−i−iii00000000000000i3−i3i3−i300000000000000−33−33
χ362-22-222i−2i2-22i−2i-22-22i2i−2i−2i2-22i−2i-122-2-111-2-1-1112i2i−2i−2i-1-1112i−2i2-2−ii−ii−i−iii-1-111−i−iii000000000000−i3i30000000000003−3−i3i33−30000
χ372-22-222i−2i2-22i−2i-22-22i2i−2i−2i2-22i−2i-122-2-111-2-1-1112i2i−2i−2i-1-1112i−2i2-2−ii−ii−i−iii-1-111−i−iii000000000000i3−i3000000000000−33i3−i3−330000
χ382-22-222i−2i-22−2i2i-22-22i2i−2i−2i-22−2i2i222-22-2-2-2-2-222−2i−2i2i2i22-2-22i−2i-222i−2i−2i2i2i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000000000000000
χ392-22-222i−2i-22−2i2i-22-22i2i−2i−2i-22−2i2i2-1-112-2-21-2-222ii−i−i-1-111−ii1-12i−2i−2i2i−i−iii11-1-1ii−i−i00000000000000−i3i3i3−i3000000000000003−3−33
χ402-22-222i−2i-22−2i2i-22-22i2i−2i−2i-22−2i2i2-1-112-2-21-2-222ii−i−i-1-111−ii1-12i−2i−2i2i−i−iii11-1-1ii−i−i00000000000000i3−i3−i3i300000000000000−333−3
χ412-22-222i−2i-22−2i2i-22-22i2i−2i−2i-22−2i2i-122-2-111-211-1-1−2i−2i2i2i-1-1112i−2i-22−iii−i−i−iii11-1-1ii−i−i000000000000−i3i30000000000003−3i3−i3−330000
χ422-22-222i−2i-22−2i2i-22-22i2i−2i−2i-22−2i2i-122-2-111-211-1-1−2i−2i2i2i-1-1112i−2i-22−iii−i−i−iii11-1-1ii−i−i000000000000i3−i3000000000000−33−i3i33−30000
χ432-22-22−2i2i2-2−2i2i-22-2−2i−2i2i2i2-2−2i2i222-22-2-2-222-2-2−2i−2i2i2i22-2-2−2i2i2-2−2i2i−2i2i−2i−2i2i2i22-2-2−2i−2i2i2i000000000000000000000000000000000000
χ442-22-22−2i2i2-2−2i2i-22-2−2i−2i2i2i2-2−2i2i2-1-112-2-2122-2-2ii−i−i-1-111i−i-11−2i2i−2i2iii−i−i-1-111ii−i−i00000000000000−i3i3−i3i300000000000000−33−33
χ452-22-22−2i2i2-2−2i2i-22-2−2i−2i2i2i2-2−2i2i2-1-112-2-2122-2-2ii−i−i-1-111i−i-11−2i2i−2i2iii−i−i-1-111ii−i−i00000000000000i3−i3i3−i3000000000000003−33−3
χ462-22-22−2i2i2-2−2i2i-22-2−2i−2i2i2i2-2−2i2i-122-2-111-2-1-111−2i−2i2i2i-1-111−2i2i2-2i−ii−iii−i−i-1-111ii−i−i000000000000−i3i3000000000000−33−i3i3−330000
χ472-22-22−2i2i2-2−2i2i-22-2−2i−2i2i2i2-2−2i2i-122-2-111-2-1-111−2i−2i2i2i-1-111−2i2i2-2i−ii−iii−i−i-1-111ii−i−i000000000000i3−i30000000000003−3i3−i33−30000
χ482-22-22−2i2i-222i−2i-22-2−2i−2i2i2i-222i−2i222-22-2-2-2-2-2222i2i−2i−2i22-2-2−2i2i-22−2i2i2i−2i−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000000000000000
χ492-22-22−2i2i-222i−2i-22-2−2i−2i2i2i-222i−2i2-1-112-2-21-2-222−i−iii-1-111i−i1-1−2i2i2i−2iii−i−i11-1-1−i−iii00000000000000−i3i3i3−i300000000000000−333−3
χ502-22-22−2i2i-222i−2i-22-2−2i−2i2i2i-222i−2i2-1-112-2-21-2-222−i−iii-1-111i−i1-1−2i2i2i−2iii−i−i11-1-1−i−iii00000000000000i3−i3−i3i3000000000000003−3−33
χ512-22-22−2i2i-222i−2i-22-2−2i−2i2i2i-222i−2i-122-2-111-211-1-12i2i−2i−2i-1-111−2i2i-22i−i−iiii−i−i11-1-1−i−iii000000000000−i3i3000000000000−33i3−i33−30000
χ522-22-22−2i2i-222i−2i-22-2−2i−2i2i2i-222i−2i-122-2-111-211-1-12i2i−2i−2i-1-111−2i2i-22i−i−iiii−i−i11-1-1−i−iii000000000000i3−i30000000000003−3−i3i3−330000
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
χ544444444-4-4-4-44444444-4-4-4-4-2-2-2-2-2-2-2-2222222221111-2-222-2-2221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5544444-4-444-4-4444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-22222111122-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
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
χ5744-4-440000004-4-40000000044-44-44-4-4000000004-44-400000000000000000000000000000000000000000000000000000000
χ5844-4-440000004-4-4000000004-22-2-44-42000023−2323−23-22-22000000000000000023−2323−23000000000000000000000000000000000000
χ5944-4-440000004-4-4000000004-22-2-44-420000−2323−2323-22-220000000000000000−2323−2323000000000000000000000000000000000000
χ6044-4-440000004-4-400000000-24-442-22-423−2323−230000-22-2200000000000023−2323−230000000000000000000000000000000000000000
χ6144-4-440000004-4-400000000-24-442-22-4−2323−23230000-22-22000000000000−2323−23230000000000000000000000000000000000000000
χ6244-4-440000004-4-400000000-2-22-22-22223−2323−2323−2323−231-11-1000000003-33-3−33−33−33−33000000000000000000000000000000000000
χ6344-4-440000004-4-400000000-2-22-22-22223−2323−23−2323−23231-11-100000000-33-33−33−333−33−3000000000000000000000000000000000000
χ6444-4-440000004-4-400000000-2-22-22-222−2323−232323−2323−231-11-100000000-33-333−33−3−33−33000000000000000000000000000000000000
χ6544-4-440000004-4-400000000-2-22-22-222−2323−2323−2323−23231-11-1000000003-33-33−33−33−33−3000000000000000000000000000000000000
χ664-44-444i−4i4-44i−4i-44-44i4i−4i−4i4-44i−4i-2-2-22-2222-2-222−2i−2i2i2i11-1-1−2i2i-22−2i2i−2i2iii−i−i11-1-1ii−i−i000000000000000000000000000000000000
χ674-44-444i−4i-44−4i4i-44-44i4i−4i−4i-44−4i4i-2-2-22-222222-2-22i2i−2i−2i11-1-1−2i2i2-2−2i2i2i−2iii−i−i-1-111−i−iii000000000000000000000000000000000000
χ684-44-44−4i4i4-4−4i4i-44-4−4i−4i4i4i4-4−4i4i-2-2-22-2222-2-2222i2i−2i−2i11-1-12i−2i-222i−2i2i−2i−i−iii11-1-1−i−iii000000000000000000000000000000000000
χ694-44-44−4i4i-444i−4i-44-4−4i−4i4i4i-444i−4i-2-2-22-222222-2-2−2i−2i2i2i11-1-12i−2i2-22i−2i−2i2i−i−iii-1-111ii−i−i000000000000000000000000000000000000
χ704-4-444000000-4-440000000044-4-4-4-444000000004-4-4400000000000000000000000000000000000000000000000000000000
χ714-4-444000000-4-44000000004-222-4-44-20000−2i32i32i3−2i3-222-20000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ724-4-444000000-4-44000000004-222-4-44-200002i3−2i3−2i32i3-222-200000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ734-4-444000000-4-4400000000-24-4-422-2423−23−23230000-222-200000000000023−23−23230000000000000000000000000000000000000000
χ744-4-444000000-4-4400000000-24-4-422-24−232323−230000-222-2000000000000−232323−230000000000000000000000000000000000000000
χ754-4-444000000-4-4400000000-2-22222-2-223−23−2323−2i32i32i3−2i31-1-1100000000−3i3i3i−3i−333−3i3−i3−i3i3000000000000000000000000000000000000
χ764-4-444000000-4-4400000000-2-22222-2-223−23−23232i3−2i3−2i32i31-1-11000000003i−3i−3i3i−333−3−i3i3i3−i3000000000000000000000000000000000000
χ774-4-444000000-4-4400000000-2-22222-2-2−232323−23−2i32i32i3−2i31-1-11000000003i−3i−3i3i3−3−33i3−i3−i3i3000000000000000000000000000000000000
χ784-4-444000000-4-4400000000-2-22222-2-2−232323−232i3−2i3−2i32i31-1-1100000000−3i3i3i−3i3−3−33−i3i3i3−i3000000000000000000000000000000000000
χ796666-3666666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000000002200022000000-1-1-1-1-1-1-1-10000000000
χ806666-3666666-3-3-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000000000000-2-2000-2-2000000111111110000000000
χ816666-366-6-6-6-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000000002-20002-2000000-1-1-1-111110000000000
χ826666-366-6-6-6-6-3-3-3-3-3-3-33333000000000000000000000000000000000000000000000-22000-220000001111-1-1-1-10000000000
χ836666-3-6-666-6-6-3-3-33333-3-33300000000000000000000000000000000000000000000022000-2-200000011-1-111-1-10000000000
χ846666-3-6-666-6-6-3-3-33333-3-333000000000000000000000000000000000000000000000-2-200022000000-1-111-1-1110000000000
χ856666-3-6-6-6-666-3-3-3333333-3-30000000000000000000000000000000000000000000002-2000-2200000011-1-1-1-1110000000000
χ866666-3-6-6-6-666-3-3-3333333-3-3000000000000000000000000000000000000000000000-220002-2000000-1-11111-1-10000000000
χ876-66-6-36i−6i6-66i−6i3-33−3i−3i3i3i-33−3i3i00000000000000000000000000000000000000000000000000000000003−3−i3i33−3−i3i30000000000
χ886-66-6-36i−6i6-66i−6i3-33−3i−3i3i3i-33−3i3i0000000000000000000000000000000000000000000000000000000000−33i3−i3−33i3−i30000000000
χ896-66-6-36i−6i-66−6i6i3-33−3i−3i3i3i3-33i−3i00000000000000000000000000000000000000000000000000000000003−3−i3i3−33i3−i30000000000
χ906-66-6-36i−6i-66−6i6i3-33−3i−3i3i3i3-33i−3i0000000000000000000000000000000000000000000000000000000000−33i3−i33−3−i3i30000000000
χ916-66-6-3−6i6i6-6−6i6i3-333i3i−3i−3i-333i−3i00000000000000000000000000000000000000000000000000000000003−3i3−i33−3i3−i30000000000
χ926-66-6-3−6i6i6-6−6i6i3-333i3i−3i−3i-333i−3i0000000000000000000000000000000000000000000000000000000000−33−i3i3−33−i3i30000000000
χ936-66-6-3−6i6i-666i−6i3-333i3i−3i−3i3-3−3i3i00000000000000000000000000000000000000000000000000000000003−3i3−i3−33−i3i30000000000
χ946-66-6-3−6i6i-666i−6i3-333i3i−3i−3i3-3−3i3i0000000000000000000000000000000000000000000000000000000000−33−i3i33−3i3−i30000000000
χ951212-12-12-6000000-666−6i36i3−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-12-6000000-6666i3−6i36i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-1212-600000066-663−63−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-1212-600000066-6−636363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000

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