Finite Group Databasebeta

← Group #13150859

Character table — Group #13150859

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222223444466612121212661212336666666666121212123666666666121212121212121212121212121222444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-11-11-1-1-11-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-11-11-11-1-1-11-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ61111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-11-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1
χ71111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1
χ81111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111
χ91111-1-1111-1-11111111-1-1-1-1111-1-1-1-111111-1-1-1-11-1-111-1-1-1-111111-1-11111-1-1-1-111-11-1-11-11-11-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111-1-1111-1-11111111-1-1-1-1111-1-1-1-111111-1-1-1-11-1-111-1-1-1-111111-1-11111-1-1-1-11-1-1-1-11-1111-1111-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111-1-1111-1-11111111-1-1-1-1111-1-1-1-111111-1-1-1-11-1-111-1-1-1-111111-1-11111-1-1-1-1-11111-1-11-1-1-11-1-1111111-1-1-1-111-1-1-1-111-1-111
χ121111-1-1111-1-11111111-1-1-1-1111-1-1-1-111111-1-1-1-11-1-111-1-1-1-111111-1-11111-1-1-1-1-1-11-1111-1-111-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ131111-1-11-1-111111-1-1-1-1-1-111111-1-1-1-11111111111-1-111-1-1-1-11-1-1-1-111-1-1-1-11111111-1-1-1-11-111-11111-1-111-1-1-1-1-1-111-1-11111-1-1
χ141111-1-11-1-111111-1-1-1-1-1-111111-1-1-1-11111111111-1-111-1-1-1-11-1-1-1-111-1-1-1-111111-111-111-1-1-1-1111-1-1-1-111-1-11111-1-111-1-1-1-111
χ151111-1-11-1-111111-1-1-1-1-1-111111-1-1-1-11111111111-1-111-1-1-1-11-1-1-1-111-1-1-1-11111-11-1-11-11-111-11-1-11111-1-111-1-1-1-11111-1-1-1-111
χ161111-1-11-1-111111-1-1-1-1-1-111111-1-1-1-11111111111-1-111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1111-111-11-1-1-1-1-111-1-1111111-1-1-1-11111-1-1
χ1722222222222222222222222-122222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-102020200020000-1-1000000-1-1-1-1-1-100000000
χ1822222222222222222222222-122222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10-20-20-2000-200001100000011111100000000
χ192222222222222222222222-12-1-1-1-1-1222-1-12222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000002200220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-1-1-1-1222-1-12222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000-2-200-2-2000000000000000011111111
χ212222222-2-2-2-2222-2-2-2-222-2-22-122222-1-1-1221111-1-1-1-1-1-1-1-1-1-111-2-2-2-211111111020-202000-20000-1-1000000-1-1111100000000
χ222222222-2-2-2-2222-2-2-2-222-2-22-122222-1-1-1221111-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111110-2020-2000200001100000011-1-1-1-100000000
χ232222222-2-2-2-2222-2-2-2-222-2-2-12-1-1-1-1-1222-1-1-2-2-2-2-122-1-1-1-1-1-1-1-2-21111111111110000002200-2-20000000000000000-1-1-1-11111
χ242222222-2-2-2-2222-2-2-2-222-2-2-12-1-1-1-1-1222-1-1-2-2-2-2-122-1-1-1-1-1-1-1-2-2111111111111000000-2-2002200000000000000001111-1-1-1-1
χ252222-2-2222-2-22222222-2-2-2-22-12-2-2-2-2-1-1-1221111-111-1-11111-1-1-122-2-2-1-1-1-1111102020-2000-20000-1-100000011-1-11100000000
χ262222-2-2222-2-22222222-2-2-2-22-12-2-2-2-2-1-1-1221111-111-1-11111-1-1-122-2-2-1-1-1-111110-20-2020002000011000000-1-111-1-100000000
χ272222-2-2222-2-22222222-2-2-2-2-12-11111222-1-1-2-2-2-2-1-2-2-1-11111-122-1-111-1-1-1-111110000002-2002-20000000000000000-1-111-1-111
χ282222-2-2222-2-22222222-2-2-2-2-12-11111222-1-1-2-2-2-2-1-2-2-1-11111-122-1-111-1-1-1-11111000000-2200-22000000000000000011-1-111-1-1
χ292222-2-22-2-222222-2-2-2-2-2-2222-12-2-2-2-2-1-1-122-1-1-1-1-111-1-11111-111-2-2221111-1-1-1-1020-20-200020000-1-10000001111-1-100000000
χ302222-2-22-2-222222-2-2-2-2-2-2222-12-2-2-2-2-1-1-122-1-1-1-1-111-1-11111-111-2-2221111-1-1-1-10-20202000-2000011000000-1-1-1-11100000000
χ312222-2-22-2-222222-2-2-2-2-2-222-12-11111222-1-12222-1-2-2-1-11111-1-2-211-1-11111-1-1-1-10000002-200-220000000000000000-1-11111-1-1
χ322222-2-22-2-222222-2-2-2-2-2-222-12-11111222-1-12222-1-2-2-1-11111-1-2-211-1-11111-1-1-1-1000000-22002-2000000000000000011-1-1-1-111
χ332-22-22-222i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i22-222-2-22-2-22-22i2i−2i−2i22-22-222-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ342-22-22-222i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i2-1-222-2-2-1112-2−i−iii-1-11-11-1-1111−ii2i−2i2i−2i−i−iii−i−iii00000000000000−i3i3000000−i3i33−33−300000000
χ352-22-22-222i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i2-1-222-2-2-1112-2−i−iii-1-11-11-1-1111−ii2i−2i2i−2i−i−iii−i−iii00000000000000i3−i3000000i3−i3−33−3300000000
χ362-22-22-222i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i-121-1-1112-2-2-112i2i−2i−2i-12-2-11-1-11112i−2i−ii−ii−i−iii−i−iii0000000000000000000000000000−i3i3−i3i33−33−3
χ372-22-22-222i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i-121-1-1112-2-2-112i2i−2i−2i-12-2-11-1-11112i−2i−ii−ii−i−iii−i−iii0000000000000000000000000000i3−i3i3−i3−33−33
χ382-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i22-222-2-22-2-22-2−2i−2i2i2i22-22-222-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ392-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i2-1-222-2-2-1112-2ii−i−i-1-11-11-1-1111i−i−2i2i−2i2iii−i−iii−i−i00000000000000−i3i3000000−i3i3−33−3300000000
χ402-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i2-1-222-2-2-1112-2ii−i−i-1-11-11-1-1111i−i−2i2i−2i2iii−i−iii−i−i00000000000000i3−i3000000i3−i33−33−300000000
χ412-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i-121-1-1112-2-2-11−2i−2i2i2i-12-2-11-1-1111−2i2ii−ii−iii−i−iii−i−i0000000000000000000000000000−i3i3−i3i3−33−33
χ422-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i-121-1-1112-2-2-11−2i−2i2i2i-12-2-11-1-1111−2i2ii−ii−iii−i−iii−i−i0000000000000000000000000000i3−i3i3−i33−33−3
χ432-22-2-2222i−2i−2i2i2-2-22i2i−2i−2i-22−2i2i22-2-2-2222-2-22-2−2i−2i2i2i2-222-2-2-222-22i−2i2i−2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ442-22-2-2222i−2i−2i2i2-2-22i2i−2i−2i-22−2i2i2-1-2-2-222-1112-2ii−i−i-11-1-1111-1-11−ii2i−2i−2i2i−i−iiiii−i−i00000000000000−i3i3000000i3−i33−3−3300000000
χ452-22-2-2222i−2i−2i2i2-2-22i2i−2i−2i-22−2i2i2-1-2-2-222-1112-2ii−i−i-11-1-1111-1-11−ii2i−2i−2i2i−i−iiiii−i−i00000000000000i3−i3000000−i3i3−333−300000000
χ462-22-2-2222i−2i−2i2i2-2-22i2i−2i−2i-22−2i2i-12111-1-12-2-2-11−2i−2i2i2i-1-22-1111-1-112i−2i−iii−i−i−iiiii−i−i0000000000000000000000000000−i3i3i3−i33−3−33
χ472-22-2-2222i−2i−2i2i2-2-22i2i−2i−2i-22−2i2i-12111-1-12-2-2-11−2i−2i2i2i-1-22-1111-1-112i−2i−iii−i−i−iiiii−i−i0000000000000000000000000000i3−i3−i3i3−333−3
χ482-22-2-222−2i2i2i−2i2-2-2−2i−2i2i2i-222i−2i22-2-2-2222-2-22-22i2i−2i−2i2-222-2-2-222-2−2i2i−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ492-22-2-222−2i2i2i−2i2-2-2−2i−2i2i2i-222i−2i2-1-2-2-222-1112-2−i−iii-11-1-1111-1-11i−i−2i2i2i−2iii−i−i−i−iii00000000000000−i3i3000000i3−i3−333−300000000
χ502-22-2-222−2i2i2i−2i2-2-2−2i−2i2i2i-222i−2i2-1-2-2-222-1112-2−i−iii-11-1-1111-1-11i−i−2i2i2i−2iii−i−i−i−iii00000000000000i3−i3000000−i3i33−3−3300000000
χ512-22-2-222−2i2i2i−2i2-2-2−2i−2i2i2i-222i−2i-12111-1-12-2-2-112i2i−2i−2i-1-22-1111-1-11−2i2ii−i−iiii−i−i−i−iii0000000000000000000000000000−i3i3i3−i3−333−3
χ522-22-2-222−2i2i2i−2i2-2-2−2i−2i2i2i-222i−2i-12111-1-12-2-2-112i2i−2i−2i-1-22-1111-1-11−2i2ii−i−iiii−i−i−i−iii0000000000000000000000000000i3−i3−i3i33−3−33
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ544444444-4-4-4-4444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-222221-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ554444-4-4444-4-44444444-4-4-4-4-2-2-22222-2-2-2-2-2222212211-1-1-1-11-2-2-2-2221111-1-1-1-1000000000000000000000000000000000000
χ564444-4-44-4-444444-4-4-4-4-4-444-2-2-22222-2-2-2-2-2-2-2-2-212211-1-1-1-112222-2-2-1-1-1-11111000000000000000000000000000000000000
χ5744-4-40040000-44-4000000004440000-44-4-4-40000400-440000-400000000000000000000000000000000000000000000000000
χ5844-4-40040000-44-4000000004-2400002-22-4-423−2323−23-2002-200002000000000023−2323−23000000000000000000000000000000000000
χ5944-4-40040000-44-4000000004-2400002-22-4-4−2323−2323-2002-2000020000000000−2323−2323000000000000000000000000000000000000
χ6044-4-40040000-44-400000000-24-2−2i32i3−2i32i3-44-4220000-2002-2−2i32i3−2i32i3200000000000000000000000000000000000000000000000000
χ6144-4-40040000-44-400000000-24-22i3−2i32i3−2i3-44-4220000-2002-22i3−2i32i3−2i3200000000000000000000000000000000000000000000000000
χ6244-4-40040000-44-400000000-2-2-2−2i32i3−2i32i32-222223−2323−23100-11i3−i3i3−i3-10000003i−3i3i−3i−33−33000000000000000000000000000000000000
χ6344-4-40040000-44-400000000-2-2-2−2i32i3−2i32i32-2222−2323−2323100-11i3−i3i3−i3-1000000−3i3i−3i3i3−33−3000000000000000000000000000000000000
χ6444-4-40040000-44-400000000-2-2-22i3−2i32i3−2i32-222223−2323−23100-11−i3i3−i3i3-1000000−3i3i−3i3i−33−33000000000000000000000000000000000000
χ6544-4-40040000-44-400000000-2-2-22i3−2i32i3−2i32-2222−2323−2323100-11−i3i3−i3i3-10000003i−3i3i−3i3−33−3000000000000000000000000000000000000
χ664-44-44-444i−4i4i−4i4-4-44i4i−4i−4i4-44i−4i-2-22-2-222-222-22−2i−2i2i2i1-221-111-1-1-1−2i2i−2i2i−2i2iii−i−iii−i−i000000000000000000000000000000000000
χ674-44-44-44−4i4i−4i4i4-4-4−4i−4i4i4i4-4−4i4i-2-22-2-222-222-222i2i−2i−2i1-221-111-1-1-12i−2i2i−2i2i−2i−i−iii−i−iii000000000000000000000000000000000000
χ684-44-4-4444i−4i−4i4i4-4-44i4i−4i−4i-44−4i4i-2-2222-2-2-222-222i2i−2i−2i12-21-1-1-111-1−2i2i−2i2i2i−2iii−i−i−i−iii000000000000000000000000000000000000
χ694-44-4-444−4i4i4i−4i4-4-4−4i−4i4i4i-444i−4i-2-2222-2-2-222-22−2i−2i2i2i12-21-1-1-111-12i−2i2i−2i−2i2i−i−iiiii−i−i000000000000000000000000000000000000
χ704-4-440040000-4-440000000044-40000-4-44-440000400-4-40000400000000000000000000000000000000000000000000000000
χ714-4-440040000-4-44000000004-2-4000022-2-44−2i32i32i3−2i3-200220000-20000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ724-4-440040000-4-44000000004-2-4000022-2-442i3−2i3−2i32i3-200220000-200000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ734-4-440040000-4-4400000000-242−2i32i32i3−2i3-4-442-20000-20022−2i32i32i3−2i3-200000000000000000000000000000000000000000000000000
χ744-4-440040000-4-4400000000-2422i3−2i3−2i32i3-4-442-20000-200222i3−2i3−2i32i3-200000000000000000000000000000000000000000000000000
χ754-4-440040000-4-4400000000-2-22−2i32i32i3−2i322-22-2−2i32i32i3−2i3100-1-1i3−i3−i3i310000003-3-33i3−i3−i3i3000000000000000000000000000000000000
χ764-4-440040000-4-4400000000-2-22−2i32i32i3−2i322-22-22i3−2i3−2i32i3100-1-1i3−i3−i3i31000000-333-3−i3i3i3−i3000000000000000000000000000000000000
χ774-4-440040000-4-4400000000-2-222i3−2i3−2i32i322-22-2−2i32i32i3−2i3100-1-1−i3i3i3−i31000000-333-3i3−i3−i3i3000000000000000000000000000000000000
χ784-4-440040000-4-4400000000-2-222i3−2i3−2i32i322-22-22i3−2i3−2i32i3100-1-1−i3i3i3−i310000003-3-33−i3i3i3−i3000000000000000000000000000000000000
χ79666666-36666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000202020002000-1-100-1-1-1-1-1-100000000000000
χ80666666-36666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000-20-20-2000-2000110011111100000000000000
χ81666666-3-6-6-6-6-3-3-33333-3-333000000000000000000000000000000000000000020-202000-2000-1-100-1-1111100000000000000
χ82666666-3-6-6-6-6-3-3-33333-3-3330000000000000000000000000000000000000000-2020-20002000110011-1-1-1-100000000000000
χ836666-6-6-366-6-6-3-3-3-3-3-3-33333000000000000000000000000000000000000000020-20-20002000-1-1001111-1-100000000000000
χ846666-6-6-366-6-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000-20202000-20001100-1-1-1-11100000000000000
χ856666-6-6-3-6-666-3-3-3333333-3-300000000000000000000000000000000000000002020-2000-2000-1-10011-1-11100000000000000
χ866666-6-6-3-6-666-3-3-3333333-3-30000000000000000000000000000000000000000-20-20200020001100-1-111-1-100000000000000
χ876-66-66-6-36i−6i6i−6i-333−3i−3i3i3i-33−3i3i0000000000000000000000000000000000000000000000000000−i3i300−i3i33−33−300000000000000
χ886-66-66-6-36i−6i6i−6i-333−3i−3i3i3i-33−3i3i0000000000000000000000000000000000000000000000000000i3−i300i3−i3−33−3300000000000000
χ896-66-66-6-3−6i6i−6i6i-3333i3i−3i−3i-333i−3i0000000000000000000000000000000000000000000000000000−i3i300−i3i3−33−3300000000000000
χ906-66-66-6-3−6i6i−6i6i-3333i3i−3i−3i-333i−3i0000000000000000000000000000000000000000000000000000i3−i300i3−i33−33−300000000000000
χ916-66-6-66-36i−6i−6i6i-333−3i−3i3i3i3-33i−3i0000000000000000000000000000000000000000000000000000−i3i300i3−i3−333−300000000000000
χ926-66-6-66-36i−6i−6i6i-333−3i−3i3i3i3-33i−3i0000000000000000000000000000000000000000000000000000i3−i300−i3i33−3−3300000000000000
χ936-66-6-66-3−6i6i6i−6i-3333i3i−3i−3i3-3−3i3i0000000000000000000000000000000000000000000000000000−i3i300i3−i33−3−3300000000000000
χ946-66-6-66-3−6i6i6i−6i-3333i3i−3i−3i3-3−3i3i0000000000000000000000000000000000000000000000000000i3−i300−i3i3−333−300000000000000
χ951212-12-1200-600006-6663−6363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-1200-600006-66−6363−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-121200-6000066-6−6i36i36i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-121200-6000066-66i3−6i3−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000000000

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