Finite Group Databasebeta

← Group #13147899

Character table — Group #13147899

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222444436661212121244121212123366666612121212121212123666121212121212121212121212121212121212121222222244444422444466666666661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-11-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-11-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ51111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-111-1-111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111-1111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1111-1-1-111-1-111-1-1-1-111-1-1111111-1-1
χ81111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-111-1-11111-1-1-1-1-1-111
χ91111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ101111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-11-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1
χ111111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1111-1-1-1-1-1-111-1-1111111-1-111-1-111
χ121111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-11-1-1-1-1-111-1-1111111-1-111-1-111-1-1
χ131111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-111-111-1-1111111-1-111-1-1-1-111-1-1-1-1
χ141111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ151111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111111-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1
χ161111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-11-11-1-11111-1-1-1-111-1-1-1-1-1-1111111
χ1722222222222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1002200002200020002000000-1-1-1-10000000000-1-1-1-1
χ1822222222222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2000-2000-2000000111100000000001111
χ192222222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000220000220022000000-1-100000000-1-1-1-1-1-10000
χ202222222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-20000-2-200-2-200000011000000001111110000
χ212222222222222222-2-2-2-2-2-22-1-1-1222-12222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-1111111110022000022000-2000-2000000-1-1110000000000-1-111
χ222222222222222222-2-2-2-2-2-22-1-1-1222-12222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-11111111100-2-20000-2-20002000200000011-1-1000000000011-1-1
χ232222222222222222-2-2-2-2-2-2-1222-1-1-12-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-11111111100002200002200-2-2000000-1-100000000-1-111110000
χ242222222222222222-2-2-2-2-2-2-1222-1-1-12-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1111111110000-2-20000-2-20022000000110000000011-1-1-1-10000
χ252222-2-2-2-22222-2-2-2-22-222-2-22-1-1-1222-1-2-2-2-21111-1-1-1-1-1-11122-2-21111-1-1-1-1111100220000-2-2000-20002000000-1-111000000000011-1-1
χ262222-2-2-2-22222-2-2-2-22-222-2-22-1-1-1222-1-2-2-2-21111-1-1-1-1-1-11122-2-21111-1-1-1-1111100-2-20000220002000-200000011-1-10000000000-1-111
χ272222-2-2-2-22222-2-2-2-22-222-2-2-1222-1-1-121111-2-2-2-2-1-1-1-122-2-2-1-1111111-1-1-1-111110000220000-2-2002-2000000-1-10000000011-1-1110000
χ282222-2-2-2-22222-2-2-2-22-222-2-2-1222-1-1-121111-2-2-2-2-1-1-1-122-2-2-1-1111111-1-1-1-111110000-2-200002200-220000001100000000-1-111-1-10000
χ292222-2-2-2-22222-2-2-2-2-22-2-2222-1-1-1222-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-100220000-2-20002000-2000000-1-1-1-100000000001111
χ302222-2-2-2-22222-2-2-2-2-22-2-2222-1-1-1222-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-100-2-2000022000-2000200000011110000000000-1-1-1-1
χ312222-2-2-2-22222-2-2-2-2-22-2-222-1222-1-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-10000220000-2-200-22000000-1-1000000001111-1-10000
χ322222-2-2-2-22222-2-2-2-2-22-2-222-1222-1-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-10000-2-2000022002-20000001100000000-1-1-1-1110000
χ3322-2-22i2i−2i−2i22-2-22i2i−2i−2i000000222-22-2-2-22i2i−2i−2i2i2i−2i−2i22-2-2000000002i2i−2i−2i000000002-200002i−2i00000000002-2000000002i−2i000000000000
χ3422-2-22i2i−2i−2i22-2-22i2i−2i−2i000000222-22-2-2-22i2i−2i−2i2i2i−2i−2i22-2-2000000002i2i−2i−2i00000000-220000−2i2i0000000000-2200000000−2i2i000000000000
χ3522-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000222-22-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-200000000−2i−2i2i2i000000002-20000−2i2i00000000002-200000000−2i2i000000000000
χ3622-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000222-22-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-200000000−2i−2i2i2i00000000-2200002i−2i0000000000-22000000002i−2i000000000000
χ372-22-22i−2i2i−2i2-22-22i−2i2i−2i00000022-22-22-2-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i00000000002-200002i−2i000000000000002-20000000000002i−2i00
χ382-22-22i−2i2i−2i2-22-22i−2i2i−2i00000022-22-22-2-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i0000000000-220000−2i2i00000000000000-22000000000000−2i2i00
χ392-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-11-1-22-212i−2i2i−2i−ii−ii-11-113−3−i3i30000−ii−ii33−3−3−i3−i3i3i3002-200002i−2i00000000000000-11−i3i30000000000−ii3−3
χ402-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-11-1-22-212i−2i2i−2i−ii−ii-11-113−3−i3i30000−ii−ii33−3−3−i3−i3i3i300-220000−2i2i000000000000001-1i3−i30000000000i−i−33
χ412-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-11-1-22-212i−2i2i−2i−ii−ii-11-11−33i3−i30000−ii−ii−3−333i3i3−i3−i3002-200002i−2i00000000000000-11i3−i30000000000−ii−33
χ422-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-11-1-22-212i−2i2i−2i−ii−ii-11-11−33i3−i30000−ii−ii−3−333i3i3−i3−i300-220000−2i2i000000000000001-1−i3i30000000000i−i3−3
χ432-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i00000000002-20000−2i2i000000000000002-2000000000000−2i2i00
χ442-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i0000000000-2200002i−2i00000000000000-220000000000002i−2i00
χ452-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-11-1-22-21−2i2i−2i2ii−ii−i-11-113−3i3−i30000i−ii−i33−3−3i3i3−i3−i3002-20000−2i2i00000000000000-11i3−i30000000000i−i3−3
χ462-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-11-1-22-21−2i2i−2i2ii−ii−i-11-113−3i3−i30000i−ii−i33−3−3i3i3−i3−i300-2200002i−2i000000000000001-1−i3i30000000000−ii−33
χ472-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-11-1-22-21−2i2i−2i2ii−ii−i-11-11−33−i3i30000i−ii−i−3−333−i3−i3i3i3002-20000−2i2i00000000000000-11−i3i30000000000i−i−33
χ482-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-11-1-22-21−2i2i−2i2ii−ii−i-11-11−33−i3i30000i−ii−i−3−333−i3−i3i3i300-2200002i−2i000000000000001-1i3−i30000000000−ii3−3
χ492-2-222-2-222-2-222-2-2200000022-2-2-2-2222-2-222-2-222-2-22000000002-2-220000000000002-200002-200000000002-2000000002-200000000
χ502-2-222-2-222-2-222-2-2200000022-2-2-2-2222-2-222-2-222-2-22000000002-2-22000000000000-220000-220000000000-2200000000-2200000000
χ512-2-222-2-222-2-222-2-22000000-12-2-211-12-111-12-2-22-111-100003−33−3-111-13−33−33−33−300002-200002-20000000000-1100000000-113−33−30000
χ522-2-222-2-222-2-222-2-22000000-12-2-211-12-111-12-2-22-111-100003−33−3-111-13−33−33−33−30000-220000-2200000000001-1000000001-1−33−330000
χ532-2-222-2-222-2-222-2-22000000-12-2-211-12-111-12-2-22-111-10000−33−33-111-1−33−33−33−3300002-200002-20000000000-1100000000-11−33−330000
χ542-2-222-2-222-2-222-2-22000000-12-2-211-12-111-12-2-22-111-10000−33−33-111-1−33−33−33−330000-220000-2200000000001-1000000001-13−33−30000
χ552-2-22-222-22-2-22-222-200000022-2-2-2-222-222-2-222-22-2-2200000000-222-20000000000002-20000-2200000000002-200000000-2200000000
χ562-2-22-222-22-2-22-222-200000022-2-2-2-222-222-2-222-22-2-2200000000-222-2000000000000-2200002-20000000000-22000000002-200000000
χ572-2-22-222-22-2-22-222-2000000-12-2-211-121-1-11-222-2-111-100003−3−331-1-113−33−3−33−3300002-20000-220000000000-11000000001-13−3−330000
χ582-2-22-222-22-2-22-222-2000000-12-2-211-121-1-11-222-2-111-100003−3−331-1-113−33−3−33−330000-2200002-200000000001-100000000-11−333−30000
χ592-2-22-222-22-2-22-222-2000000-12-2-211-121-1-11-222-2-111-10000−333−31-1-11−33−333−33−300002-20000-220000000000-11000000001-1−333−30000
χ602-2-22-222-22-2-22-222-2000000-12-2-211-121-1-11-222-2-111-10000−333−31-1-11−33−333−33−30000-2200002-200000000001-100000000-113−3−330000
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111222222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ634444-4-4-4-44444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-2222222221111-2-222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000000000
χ644444-4-4-4-44444-4-4-4-4-44-4-444-2-2-2-2-2-2-2-222222222111122-2-222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000000000
χ6544-4-44i4i−4i−4i44-4-44i4i−4i−4i0000004-2-224-4-424i4i−4i−4i−2i−2i2i2i-2-22200000000−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ6644-4-44i4i−4i−4i44-4-44i4i−4i−4i000000-244-4-222-4−2i−2i2i2i4i4i−4i−4i-2-22200000000−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ6744-4-44i4i−4i−4i44-4-44i4i−4i−4i000000-2-2-22-2222−2i−2i2i2i−2i−2i2i2i11-1-100000000ii−i−i3-3-33−3i3i3i−3i000000000000000000000000000000000000000000
χ6844-4-44i4i−4i−4i44-4-44i4i−4i−4i000000-2-2-22-2222−2i−2i2i2i−2i−2i2i2i11-1-100000000ii−i−i-333-33i−3i−3i3i000000000000000000000000000000000000000000
χ6944-4-4−4i−4i4i4i44-4-4−4i−4i4i4i0000004-2-224-4-42−4i−4i4i4i2i2i−2i−2i-2-222000000002i2i−2i−2i00000000000000000000000000000000000000000000000000
χ7044-4-4−4i−4i4i4i44-4-4−4i−4i4i4i000000-244-4-222-42i2i−2i−2i−4i−4i4i4i-2-222000000002i2i−2i−2i00000000000000000000000000000000000000000000000000
χ7144-4-4−4i−4i4i4i44-4-4−4i−4i4i4i000000-2-2-22-22222i2i−2i−2i2i2i−2i−2i11-1-100000000−i−iii3-3-333i−3i−3i3i000000000000000000000000000000000000000000
χ7244-4-4−4i−4i4i4i44-4-4−4i−4i4i4i000000-2-2-22-22222i2i−2i−2i2i2i−2i−2i11-1-100000000−i−iii-333-3−3i3i3i−3i000000000000000000000000000000000000000000
χ734-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-24-442-22-4−2i2i−2i2i4i−4i4i−4i-22-2200000000−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ744-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-2-22-22-222−2i2i−2i2i−2i2i−2i2i1-11-123−23−2i32i30000i−ii−i−3−333i3i3−i3−i3000000000000000000000000000000000000000000
χ754-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-2-22-22-222−2i2i−2i2i−2i2i−2i2i1-11-1−23232i3−2i30000i−ii−i33−3−3−i3−i3i3i3000000000000000000000000000000000000000000
χ764-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-24-442-22-42i−2i2i−2i−4i4i−4i4i-22-22000000002i−2i2i−2i00000000000000000000000000000000000000000000000000
χ774-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-2-22-22-2222i−2i2i−2i2i−2i2i−2i1-11-123−232i3−2i30000−ii−ii−3−333−i3−i3i3i3000000000000000000000000000000000000000000
χ784-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-2-22-22-2222i−2i2i−2i2i−2i2i−2i1-11-1−2323−2i32i30000−ii−ii33−3−3i3i3−i3−i3000000000000000000000000000000000000000000
χ794-4-444-4-444-4-444-4-440000004-222-4-44-24-4-44-222-2-222-200000000-222-200000000000000000000000000000000000000000000000000
χ804-4-444-4-444-4-444-4-44000000-2-22222-2-2-222-2-222-21-1-11000023−2323−231-1-11−33−33−33−33000000000000000000000000000000000000000000
χ814-4-444-4-444-4-444-4-44000000-2-22222-2-2-222-2-222-21-1-110000−2323−23231-1-113−33−33−33−3000000000000000000000000000000000000000000
χ824-4-44-444-44-4-44-444-40000004-222-4-44-2-444-42-2-22-222-2000000002-2-2200000000000000000000000000000000000000000000000000
χ834-4-44-444-44-4-44-444-4000000-2-22222-2-22-2-222-2-221-1-11000023−23−2323-111-1−33−333−33−3000000000000000000000000000000000000000000
χ844-4-44-444-44-4-44-444-4000000-2-22222-2-22-2-222-2-221-1-110000−232323−23-111-13−33−3−33−33000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000220000220000200020-1-1-1-1000000-1-1-1-10000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-20000-2-20000-2000-20111100000011110000000000
χ8766666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000220000220000-2000-20-1-111000000-1-1110000000000
χ8866666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-20000-2-2000020002011-1-100000011-1-10000000000
χ896666-6-6-6-6-3-3-3-333336-6-3-3330000000000000000000000000000000000000000220000-2-200002000-20-1-1-1-100000011110000000000
χ906666-6-6-6-6-3-3-3-333336-6-3-3330000000000000000000000000000000000000000-2-20000220000-2000201111000000-1-1-1-10000000000
χ916666-6-6-6-6-3-3-3-33333-6633-3-30000000000000000000000000000000000000000220000-2-20000-200020-1-11100000011-1-10000000000
χ926666-6-6-6-6-3-3-3-33333-6633-3-30000000000000000000000000000000000000000-2-200002200002000-2011-1-1000000-1-1110000000000
χ9366-6-66i6i−6i−6i-3-333−3i−3i3i3i00−3i33i333−3300000000000000000000000000000000000000002-200002i−2i0000000000-11−i3i3000000−ii3−30000000000
χ9466-6-66i6i−6i−6i-3-333−3i−3i3i3i00−3i33i333−330000000000000000000000000000000000000000-220000−2i2i00000000001-1i3−i3000000i−i−330000000000
χ9566-6-66i6i−6i−6i-3-333−3i−3i3i3i003i3−3i3−333300000000000000000000000000000000000000002-200002i−2i0000000000-11i3−i3000000−ii−330000000000
χ9666-6-66i6i−6i−6i-3-333−3i−3i3i3i003i3−3i3−33330000000000000000000000000000000000000000-220000−2i2i00000000001-1−i3i3000000i−i3−30000000000
χ9766-6-6−6i−6i6i6i-3-3333i3i−3i−3i00−3i33i3−333300000000000000000000000000000000000000002-20000−2i2i0000000000-11−i3i3000000i−i−330000000000
χ9866-6-6−6i−6i6i6i-3-3333i3i−3i−3i00−3i33i3−33330000000000000000000000000000000000000000-2200002i−2i00000000001-1i3−i3000000−ii3−30000000000
χ9966-6-6−6i−6i6i6i-3-3333i3i−3i−3i003i3−3i333−3300000000000000000000000000000000000000002-20000−2i2i0000000000-11i3−i3000000i−i3−30000000000
χ10066-6-6−6i−6i6i6i-3-3333i3i−3i−3i003i3−3i333−330000000000000000000000000000000000000000-2200002i−2i00000000001-1−i3i3000000−ii−330000000000
χ10112-1212-1212i−12i12i−12i-66-66−6i6i−6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12−12i12i−12i12i-66-666i−6i6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-121212-12-1212-666-6-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-1212-121212-12-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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