Finite Group Databasebeta

← Group #13147908

Character table — Group #13147908

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222444436661212121244121212123366666612121212121212123666121212121212121212121212121212121212121222222244444422444466666666661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
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
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ51111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-111-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111-11-1-111-1-1-1-111-1-1111111-1-1-1-111
χ71111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1111-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ81111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-11111-1-1-1-1-1-111-1-111
χ91111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ101111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-11-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1
χ111111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1111-1-1-1-1-1-111-1-111-1-1111111-1-111
χ121111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-11-111-1-1-1-1-1-111-1-111-1-1111111-1-1
χ131111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-111-11111-1-11111-1-1-1-111-1-111-1-1-1-1
χ141111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11-111-1-111-1-1-1-1-1-11111-1-1-1-1111111
χ151111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111111-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1
χ161111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-11-1111-1-111-1-1-1-1-1-1-1-11111-1-11111
χ1722222222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1002200002200020002000000-1-1-1-10000000000-1-1-1-1
χ1822222222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2000-2000-2000000111100000000001111
χ192222222222222222222222-12-1-122-12-1-1-1-12222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-122000022000020002000-1-1-1-10000000000-1-1-1-10000
χ202222222222222222222222-12-1-122-12-1-1-1-12222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-20000-2-20000-2000-20001111000000000011110000
χ212222222222222222-2-2-2-2-2-22-122-1-12-12222-1-1-1-1-1-1-1-1-2-211-2-211-1-1-1-1111111110022000022000-2000-2000000-1-1110000000000-1-111
χ222222222222222222-2-2-2-2-2-22-122-1-12-12222-1-1-1-1-1-1-1-1-2-211-2-211-1-1-1-11111111100-2-20000-2-20002000200000011-1-1000000000011-1-1
χ232222222222222222-2-2-2-2-2-2-12-1-122-12-1-1-1-12222-1-1-1-111-2-211-2-2-1-1-1-111111111220000220000-2000-2000-1-1110000000000-1-1110000
χ242222222222222222-2-2-2-2-2-2-12-1-122-12-1-1-1-12222-1-1-1-111-2-211-2-2-1-1-1-111111111-2-20000-2-200002000200011-1-1000000000011-1-10000
χ252222-2-2-2-22222-2-2-2-22-222-2-22-122-1-12-1-2-2-2-21111-1-1-1-122-1-1-2-2111111-1-1-1-1111100220000-2-2000-20002000000-1-111000000000011-1-1
χ262222-2-2-2-22222-2-2-2-22-222-2-22-122-1-12-1-2-2-2-21111-1-1-1-122-1-1-2-2111111-1-1-1-1111100-2-20000220002000-200000011-1-10000000000-1-111
χ272222-2-2-2-22222-2-2-2-22-222-2-2-12-1-122-121111-2-2-2-2-1-1-1-1-1-12211-2-21111-1-1-1-11111220000-2-200002000-2000-1-1-1-1000000000011110000
χ282222-2-2-2-22222-2-2-2-22-222-2-2-12-1-122-121111-2-2-2-2-1-1-1-1-1-12211-2-21111-1-1-1-11111-2-20000220000-2000200011110000000000-1-1-1-10000
χ292222-2-2-2-22222-2-2-2-2-22-2-2222-122-1-12-1-2-2-2-21111-1-1-1-1-2-21122-1-111111111-1-1-1-100220000-2-20002000-2000000-1-1-1-100000000001111
χ302222-2-2-2-22222-2-2-2-2-22-2-2222-122-1-12-1-2-2-2-21111-1-1-1-1-2-21122-1-111111111-1-1-1-100-2-2000022000-2000200000011110000000000-1-1-1-1
χ312222-2-2-2-22222-2-2-2-2-22-2-222-12-1-122-121111-2-2-2-2-1-1-1-111-2-2-1-12211111111-1-1-1-1220000-2-20000-20002000-1-111000000000011-1-10000
χ322222-2-2-2-22222-2-2-2-2-22-2-222-12-1-122-121111-2-2-2-2-1-1-1-111-2-2-1-12211111111-1-1-1-1-2-200002200002000-200011-1-10000000000-1-1110000
χ3322-2-22i2i−2i−2i22-2-22i2i−2i−2i000000222-22-2-2-22i2i−2i−2i2i2i−2i−2i22-2-2000000002i2i−2i−2i000000002-200002i−2i0000000000002-20000000000002i−2i000000
χ3422-2-22i2i−2i−2i22-2-22i2i−2i−2i000000222-22-2-2-22i2i−2i−2i2i2i−2i−2i22-2-2000000002i2i−2i−2i00000000-220000−2i2i000000000000-22000000000000−2i2i000000
χ3522-2-22i2i−2i−2i22-2-22i2i−2i−2i000000-12-112-21-2−i−iii2i2i−2i−2i-1-111−i3i3003−300−i−iii−i3−i3i3i333−3−32-200002i−2i000000000000-11−i3i30000000000−ii3−30000
χ3622-2-22i2i−2i−2i22-2-22i2i−2i−2i000000-12-112-21-2−i−iii2i2i−2i−2i-1-111−i3i3003−300−i−iii−i3−i3i3i333−3−3-220000−2i2i0000000000001-1i3−i30000000000i−i−330000
χ3722-2-22i2i−2i−2i22-2-22i2i−2i−2i000000-12-112-21-2−i−iii2i2i−2i−2i-1-111i3−i300−3300−i−iiii3i3−i3−i3−3−3332-200002i−2i000000000000-11i3−i30000000000−ii−330000
χ3822-2-22i2i−2i−2i22-2-22i2i−2i−2i000000-12-112-21-2−i−iii2i2i−2i−2i-1-111i3−i300−3300−i−iiii3i3−i3−i3−3−333-220000−2i2i0000000000001-1−i3i30000000000i−i3−30000
χ3922-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000222-22-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-200000000−2i−2i2i2i000000002-20000−2i2i0000000000002-2000000000000−2i2i000000
χ4022-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000222-22-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-200000000−2i−2i2i2i00000000-2200002i−2i000000000000-220000000000002i−2i000000
χ4122-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000-12-112-21-2ii−i−i−2i−2i2i2i-1-111−i3i300−3300ii−i−i−i3−i3i3i3−3−3332-20000−2i2i000000000000-11−i3i30000000000i−i−330000
χ4222-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000-12-112-21-2ii−i−i−2i−2i2i2i-1-111−i3i300−3300ii−i−i−i3−i3i3i3−3−333-2200002i−2i0000000000001-1i3−i30000000000−ii3−30000
χ4322-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000-12-112-21-2ii−i−i−2i−2i2i2i-1-111i3−i3003−300ii−i−ii3i3−i3−i333−3−32-20000−2i2i000000000000-11i3−i30000000000i−i3−30000
χ4422-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000-12-112-21-2ii−i−i−2i−2i2i2i-1-111i3−i3003−300ii−i−ii3i3−i3−i333−3−3-2200002i−2i0000000000001-1−i3i30000000000−ii−330000
χ452-22-22i−2i2i−2i2-22-22i−2i2i−2i00000022-22-22-2-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i00000000002-200002i−2i000000000000002-20000000000002i−2i00
χ462-22-22i−2i2i−2i2-22-22i−2i2i−2i00000022-22-22-2-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i0000000000-220000−2i2i00000000000000-22000000000000−2i2i00
χ472-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-221-1-212i−2i2i−2i−ii−ii-11-11003−300−i3i3−ii−ii3−33−3−i3i3−i3i3002-200002i−2i00000000000000-11−i3i30000000000−ii3−3
χ482-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-221-1-212i−2i2i−2i−ii−ii-11-11003−300−i3i3−ii−ii3−33−3−i3i3−i3i300-220000−2i2i000000000000001-1i3−i30000000000i−i−33
χ492-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-221-1-212i−2i2i−2i−ii−ii-11-1100−3300i3−i3−ii−ii−33−33i3−i3i3−i3002-200002i−2i00000000000000-11i3−i30000000000−ii−33
χ502-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-221-1-212i−2i2i−2i−ii−ii-11-1100−3300i3−i3−ii−ii−33−33i3−i3i3−i300-220000−2i2i000000000000001-1−i3i30000000000i−i3−3
χ512-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i00000000002-20000−2i2i000000000000002-2000000000000−2i2i00
χ522-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i0000000000-2200002i−2i00000000000000-220000000000002i−2i00
χ532-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-221-1-21−2i2i−2i2ii−ii−i-11-11003−300i3−i3i−ii−i3−33−3i3−i3i3−i3002-20000−2i2i00000000000000-11i3−i30000000000i−i3−3
χ542-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-221-1-21−2i2i−2i2ii−ii−i-11-11003−300i3−i3i−ii−i3−33−3i3−i3i3−i300-2200002i−2i000000000000001-1−i3i30000000000−ii−33
χ552-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-221-1-21−2i2i−2i2ii−ii−i-11-1100−3300−i3i3i−ii−i−33−33−i3i3−i3i3002-20000−2i2i00000000000000-11−i3i30000000000i−i−33
χ562-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-221-1-21−2i2i−2i2ii−ii−i-11-1100−3300−i3i3i−ii−i−33−33−i3i3−i3i300-2200002i−2i000000000000001-1i3−i30000000000−ii3−3
χ572-2-222-2-222-2-222-2-2200000022-2-2-2-2222-2-222-2-222-2-22000000002-2-220000000000002-200002-20000002-2000000002-2000000000000
χ582-2-222-2-222-2-222-2-2200000022-2-2-2-2222-2-222-2-222-2-22000000002-2-22000000000000-220000-22000000-2200000000-22000000000000
χ592-2-22-222-22-2-22-222-200000022-2-2-2-222-222-2-222-22-2-2200000000-222-20000000000002-20000-220000002-200000000-22000000000000
χ602-2-22-222-22-2-22-222-200000022-2-2-2-222-222-2-222-22-2-2200000000-222-2000000000000-2200002-2000000-22000000002-2000000000000
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
χ634444-4-4-4-44444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-2222222221111-2-2-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000000000
χ644444-4-4-4-44444-4-4-4-4-44-4-444-2-2-2-2-2-2-2-22222222211112222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000000000
χ6544-4-44i4i−4i−4i44-4-44i4i−4i−4i0000004-24-4-22-424i4i−4i−4i−2i−2i2i2i-2-22200000000−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ6644-4-44i4i−4i−4i44-4-44i4i−4i−4i000000-2-2-22-2222−2i−2i2i2i−2i−2i2i2i11-1-1−2i32i30023−2300ii−i−ii3i3−i3−i3−3−333000000000000000000000000000000000000000000
χ6744-4-44i4i−4i−4i44-4-44i4i−4i−4i000000-2-2-22-2222−2i−2i2i2i−2i−2i2i2i11-1-12i3−2i300−232300ii−i−i−i3−i3i3i333−3−3000000000000000000000000000000000000000000
χ6844-4-4−4i−4i4i4i44-4-4−4i−4i4i4i0000004-24-4-22-42−4i−4i4i4i2i2i−2i−2i-2-222000000002i2i−2i−2i00000000000000000000000000000000000000000000000000
χ6944-4-4−4i−4i4i4i44-4-4−4i−4i4i4i000000-2-2-22-22222i2i−2i−2i2i2i−2i−2i11-1-1−2i32i300−232300−i−iiii3i3−i3−i333−3−3000000000000000000000000000000000000000000
χ7044-4-4−4i−4i4i4i44-4-4−4i−4i4i4i000000-2-2-22-22222i2i−2i−2i2i2i−2i−2i11-1-12i3−2i30023−2300−i−iii−i3−i3i3i3−3−333000000000000000000000000000000000000000000
χ714-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-242-2-442-4−2i2i−2i2i4i−4i4i−4i-22-2200000000−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ724-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-2-22-22-222−2i2i−2i2i−2i2i−2i2i1-11-10023−2300−2i32i3i−ii−i−33−33i3−i3i3−i3000000000000000000000000000000000000000000
χ734-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-2-22-22-222−2i2i−2i2i−2i2i−2i2i1-11-100−2323002i3−2i3i−ii−i3−33−3−i3i3−i3i3000000000000000000000000000000000000000000
χ744-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-242-2-442-42i−2i2i−2i−4i4i−4i4i-22-22000000002i−2i2i−2i00000000000000000000000000000000000000000000000000
χ754-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-2-22-22-2222i−2i2i−2i2i−2i2i−2i1-11-10023−23002i3−2i3−ii−ii−33−33−i3i3−i3i3000000000000000000000000000000000000000000
χ764-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-2-22-22-2222i−2i2i−2i2i−2i2i−2i1-11-100−232300−2i32i3−ii−ii3−33−3i3−i3i3−i3000000000000000000000000000000000000000000
χ774-4-444-4-444-4-444-4-440000004-2-4-4224-24-4-44-222-2-222-200000000-222-200000000000000000000000000000000000000000000000000
χ784-4-444-4-444-4-444-4-44000000-2422-4-4-24-222-24-4-44-222-200000000-222-200000000000000000000000000000000000000000000000000
χ794-4-444-4-444-4-444-4-44000000-2-22222-2-2-222-2-222-21-1-11000000001-1-113i−3i−3i3i−3i3i3i−3i000000000000000000000000000000000000000000
χ804-4-444-4-444-4-444-4-44000000-2-22222-2-2-222-2-222-21-1-11000000001-1-11−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000000000
χ814-4-44-444-44-4-44-444-40000004-2-4-4224-2-444-42-2-22-222-2000000002-2-2200000000000000000000000000000000000000000000000000
χ824-4-44-444-44-4-44-444-4000000-2422-4-4-242-2-22-444-4-222-2000000002-2-2200000000000000000000000000000000000000000000000000
χ834-4-44-444-44-4-44-444-4000000-2-22222-2-22-2-222-2-221-1-1100000000-111-13i−3i−3i3i3i−3i−3i3i000000000000000000000000000000000000000000
χ844-4-44-444-44-4-44-444-4000000-2-22222-2-22-2-222-2-221-1-1100000000-111-1−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000000022000022002200-1-100000000-1-1-1-1-1-100000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000-2-20000-2-200-2-200110000000011111100000000
χ8766666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000002200002200-2-200-1-100000000-1-1111100000000
χ8866666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000-2-20000-2-2002200110000000011-1-1-1-100000000
χ896666-6-6-6-6-3-3-3-333336-6-3-33300000000000000000000000000000000000000000000220000-2-2002-200-1-10000000011-1-11100000000
χ906666-6-6-6-6-3-3-3-333336-6-3-33300000000000000000000000000000000000000000000-2-200002200-22001100000000-1-111-1-100000000
χ916666-6-6-6-6-3-3-3-33333-6633-3-300000000000000000000000000000000000000000000220000-2-200-2200-1-1000000001111-1-100000000
χ926666-6-6-6-6-3-3-3-33333-6633-3-300000000000000000000000000000000000000000000-2-2000022002-2001100000000-1-1-1-11100000000
χ936-6-666-6-66-333-3-333-30033−3333−33000000000000000000000000000000000000000000002-200002-2000000-1100000000-113−33−300000000
χ946-6-666-6-66-333-3-333-30033−3333−3300000000000000000000000000000000000000000000-220000-220000001-1000000001-1−33−3300000000
χ956-6-666-6-66-333-3-333-300−3333−3333000000000000000000000000000000000000000000002-200002-2000000-1100000000-11−33−3300000000
χ966-6-666-6-66-333-3-333-300−3333−333300000000000000000000000000000000000000000000-220000-220000001-1000000001-13−33−300000000
χ976-6-66-666-6-333-33-3-330033−33−3333000000000000000000000000000000000000000000002-20000-22000000-11000000001-13−3−3300000000
χ986-6-66-666-6-333-33-3-330033−33−333300000000000000000000000000000000000000000000-2200002-20000001-100000000-11−333−300000000
χ996-6-66-666-6-333-33-3-3300−333333−33000000000000000000000000000000000000000000002-20000-22000000-11000000001-1−333−300000000
χ1006-6-66-666-6-333-33-3-3300−333333−3300000000000000000000000000000000000000000000-2200002-20000001-100000000-113−3−3300000000
χ1011212-12-1212i12i−12i−12i-6-666−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-12-12−12i−12i12i12i-6-6666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-1212-1212i−12i12i−12i-66-66−6i6i−6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-1212-12−12i12i−12i12i-66-666i−6i6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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