Finite Group Databasebeta

← Group #13150889

Character table — Group #13150889

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order12224444366612121212246612123366666612121212121212123666666666661212121212121212121212122222224444442444446666666612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-11111-111-1-1-1-1-1-111-1-111111111-1-1-1-1
χ71111111111111111-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-11-1-1111-1-11111-1-1-1-111-1-1-1-1111111-1-1
χ81111111111111111-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1-11-1-111-1-111-1-1111111-1-1-1-1-1-111
χ91111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-11-1111-1-11111-1-11111-1-111-1-1-1-1-1-1
χ101111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-11111-1-1-1-1-1-1-1-111-1-111-1-1111111
χ111111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11-1-1-11111-1-111-1-111-1-1-1-111-1-111
χ121111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1
χ131111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-11-11-11-111111111-1-1-1-1-1-111-1-111-1-1-1-1
χ141111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1111111-11-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111
χ151111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111-1-111-1-111-1-111-1-111-11-1-1-1-111-1-11111-1-11111-1-1-1-111
χ161111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1111111-1-1-11-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ1722222222222222222222222-122-1-12-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000022000022000220000000-1-100000000-1-1-1-100-1-1
χ1822222222222222222222222-122-1-12-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-20000-2-2000-2-20000000110000000011110011
χ192222222222222222222222-12-1-122-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10022000022000220000000-1-1000000-1-1-1-10000-1-100
χ202222222222222222222222-12-1-122-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100-2-20000-2-2000-2-2000000011000000111100001100
χ212222222222222222-2-2-2-2-2-22-122-1-12-12222-1-1-1-1-1-2-211-1-11111-1-2-211-1-1-1-11111000022000022000-2-20000000-1-100000000111100-1-1
χ222222222222222222-2-2-2-2-2-22-122-1-12-12222-1-1-1-1-1-2-211-1-11111-1-2-211-1-1-1-111110000-2-20000-2-20002200000001100000000-1-1-1-10011
χ232222222222222222-2-2-2-2-2-2-12-1-122-12-1-1-1-12222-111-2-2-1-11111-111-2-2-1-1-1-111110022000022000-2-20000000-1-100000011110000-1-100
χ242222222222222222-2-2-2-2-2-2-12-1-122-12-1-1-1-12222-111-2-2-1-11111-111-2-2-1-1-1-1111100-2-20000-2-200022000000011000000-1-1-1-100001100
χ252222-2-2-2-22222-2-2-2-22-222-2-22-122-1-12-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-211111111110000220000-2-20002-20000000-1-100000000-1-1110011
χ262222-2-2-2-22222-2-2-2-22-222-2-22-122-1-12-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-211111111110000-2-2000022000-220000000110000000011-1-100-1-1
χ272222-2-2-2-22222-2-2-2-22-222-2-2-12-1-122-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-21111111100220000-2-20002-20000000-1-1000000-1-11100001100
χ282222-2-2-2-22222-2-2-2-22-222-2-2-12-1-122-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-21111111100-2-2000022000-2200000001100000011-1-10000-1-100
χ292222-2-2-2-22222-2-2-2-2-22-2-2222-122-1-12-1-2-2-2-21111-1-2-211-1-11111-122-1-11111-1-1-1-10000220000-2-2000-220000000-1-10000000011-1-10011
χ302222-2-2-2-22222-2-2-2-2-22-2-2222-122-1-12-1-2-2-2-21111-1-2-211-1-11111-122-1-11111-1-1-1-10000-2-20000220002-200000001100000000-1-11100-1-1
χ312222-2-2-2-22222-2-2-2-2-22-2-222-12-1-122-121111-2-2-2-2-111-2-2-1-11111-1-1-1221111-1-1-1-100220000-2-2000-220000000-1-100000011-1-100001100
χ322222-2-2-2-22222-2-2-2-2-22-2-222-12-1-122-121111-2-2-2-2-111-2-2-1-11111-1-1-1221111-1-1-1-100-2-20000220002-2000000011000000-1-1110000-1-100
χ3322-2-22i2i−2i−2i22-2-22i2i−2i−2i000000222-22-2-2-22i2i−2i−2i2i2i−2i−2i200002-20000-200002i2i−2i−2i000000002-200002i−2i0000000000002-2000000000000002i−2i
χ3422-2-22i2i−2i−2i22-2-22i2i−2i−2i000000222-22-2-2-22i2i−2i−2i2i2i−2i−2i200002-20000-200002i2i−2i−2i00000000-220000−2i2i000000000000-2200000000000000−2i2i
χ3522-2-22i2i−2i−2i22-2-22i2i−2i−2i0000002-12-2-11-212i2i−2i−2i−i−iii-100−i3i3-11−i3−i3i3i31003−3−i−iii33−3−300002-200002i−2i000000000000-1100000000−i3i33−300−ii
χ3622-2-22i2i−2i−2i22-2-22i2i−2i−2i0000002-12-2-11-212i2i−2i−2i−i−iii-100−i3i3-11−i3−i3i3i31003−3−i−iii33−3−30000-220000−2i2i0000000000001-100000000i3−i3−3300i−i
χ3722-2-22i2i−2i−2i22-2-22i2i−2i−2i0000002-12-2-11-212i2i−2i−2i−i−iii-100i3−i3-11i3i3−i3−i3100−33−i−iii−3−33300002-200002i−2i000000000000-1100000000i3−i3−3300−ii
χ3822-2-22i2i−2i−2i22-2-22i2i−2i−2i0000002-12-2-11-212i2i−2i−2i−i−iii-100i3−i3-11i3i3−i3−i3100−33−i−iii−3−3330000-220000−2i2i0000000000001-100000000−i3i33−300i−i
χ3922-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000222-22-2-2-2−2i−2i2i2i−2i−2i2i2i200002-20000-20000−2i−2i2i2i000000002-20000−2i2i0000000000002-200000000000000−2i2i
χ4022-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000222-22-2-2-2−2i−2i2i2i−2i−2i2i2i200002-20000-20000−2i−2i2i2i00000000-2200002i−2i000000000000-22000000000000002i−2i
χ4122-2-2−2i−2i2i2i22-2-2−2i−2i2i2i0000002-12-2-11-21−2i−2i2i2iii−i−i-100−i3i3-11−i3−i3i3i3100−33ii−i−i−3−33300002-20000−2i2i000000000000-1100000000−i3i3−3300i−i
χ4222-2-2−2i−2i2i2i22-2-2−2i−2i2i2i0000002-12-2-11-21−2i−2i2i2iii−i−i-100−i3i3-11−i3−i3i3i3100−33ii−i−i−3−3330000-2200002i−2i0000000000001-100000000i3−i33−300−ii
χ4322-2-2−2i−2i2i2i22-2-2−2i−2i2i2i0000002-12-2-11-21−2i−2i2i2iii−i−i-100i3−i3-11i3i3−i3−i31003−3ii−i−i33−3−300002-20000−2i2i000000000000-1100000000i3−i33−300i−i
χ4422-2-2−2i−2i2i2i22-2-2−2i−2i2i2i0000002-12-2-11-21−2i−2i2i2iii−i−i-100i3−i3-11i3i3−i3−i31003−3ii−i−i33−3−30000-2200002i−2i0000000000001-100000000−i3i3−3300−ii
χ452-22-22i−2i2i−2i2-22-22i−2i2i−2i00000022-22-22-2-22i−2i2i−2i2i−2i2i−2i20000-220000-200002i−2i2i−2i0000002-200002i−2i0000000000002-2000000000000002i−2i00
χ462-22-22i−2i2i−2i2-22-22i−2i2i−2i00000022-22-22-2-22i−2i2i−2i2i−2i2i−2i20000-220000-200002i−2i2i−2i000000-220000−2i2i000000000000-2200000000000000−2i2i00
χ472-22-22i−2i2i−2i2-22-22i−2i2i−2i000000-121-1-221-2−ii−ii2i−2i2i−2i-1−i3i3001-1−i3i3−i3i313−300−ii−ii3−33−3002-200002i−2i000000000000-11000000−i3i33−30000−ii00
χ482-22-22i−2i2i−2i2-22-22i−2i2i−2i000000-121-1-221-2−ii−ii2i−2i2i−2i-1−i3i3001-1−i3i3−i3i313−300−ii−ii3−33−300-220000−2i2i0000000000001-1000000i3−i3−330000i−i00
χ492-22-22i−2i2i−2i2-22-22i−2i2i−2i000000-121-1-221-2−ii−ii2i−2i2i−2i-1i3−i3001-1i3−i3i3−i31−3300−ii−ii−33−33002-200002i−2i000000000000-11000000i3−i3−330000−ii00
χ502-22-22i−2i2i−2i2-22-22i−2i2i−2i000000-121-1-221-2−ii−ii2i−2i2i−2i-1i3−i3001-1i3−i3i3−i31−3300−ii−ii−33−3300-220000−2i2i0000000000001-1000000−i3i33−30000i−i00
χ512-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i20000-220000-20000−2i2i−2i2i0000002-20000−2i2i0000000000002-200000000000000−2i2i00
χ522-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i20000-220000-20000−2i2i−2i2i000000-2200002i−2i000000000000-22000000000000002i−2i00
χ532-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000-121-1-221-2i−ii−i−2i2i−2i2i-1−i3i3001-1−i3i3−i3i31−3300i−ii−i−33−33002-20000−2i2i000000000000-11000000−i3i3−330000i−i00
χ542-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000-121-1-221-2i−ii−i−2i2i−2i2i-1−i3i3001-1−i3i3−i3i31−3300i−ii−i−33−3300-2200002i−2i0000000000001-1000000i3−i33−30000−ii00
χ552-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000-121-1-221-2i−ii−i−2i2i−2i2i-1i3−i3001-1i3−i3i3−i313−300i−ii−i3−33−3002-20000−2i2i000000000000-11000000i3−i33−30000i−i00
χ562-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000-121-1-221-2i−ii−i−2i2i−2i2i-1i3−i3001-1i3−i3i3−i313−300i−ii−i3−33−300-2200002i−2i0000000000001-1000000−i3i3−330000−ii00
χ572-2-222-2-222-2-222-2-2200000022-2-2-2-2222-2-222-2-2220000-2-20000200002-2-2200002-200002-200000000002-20000002-200000000000000
χ582-2-222-2-222-2-222-2-2200000022-2-2-2-2222-2-222-2-2220000-2-20000200002-2-220000-220000-220000000000-22000000-2200000000000000
χ592-2-22-222-22-2-22-222-200000022-2-2-2-222-222-2-222-220000-2-2000020000-222-200002-20000-2200000000002-2000000-2200000000000000
χ602-2-22-222-22-2-22-222-200000022-2-2-2-222-222-2-222-220000-2-2000020000-222-20000-2200002-20000000000-220000002-200000000000000
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122221111-1-1-1-1000000000000000000000000000000000000000000
χ634444-4-4-4-44444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ644444-4-4-4-44444-4-4-4-4-44-4-444-2-2-2-2-2-2-2-2222222221222211-1-1-1-11-2-2-2-2-1-1-1-11111000000000000000000000000000000000000000000
χ6544-4-44i4i−4i−4i44-4-44i4i−4i−4i000000-24-224-42-4−2i−2i2i2i4i4i−4i−4i-20000-22000020000−2i−2i2i2i0000000000000000000000000000000000000000000000
χ6644-4-44i4i−4i−4i44-4-44i4i−4i−4i000000-2-2-22-2222−2i−2i2i2i−2i−2i2i2i100−2i32i31-1i3i3−i3−i3-10023−23ii−i−i−3−333000000000000000000000000000000000000000000
χ6744-4-44i4i−4i−4i44-4-44i4i−4i−4i000000-2-2-22-2222−2i−2i2i2i−2i−2i2i2i1002i3−2i31-1−i3−i3i3i3-100−2323ii−i−i33−3−3000000000000000000000000000000000000000000
χ6844-4-4−4i−4i4i4i44-4-4−4i−4i4i4i000000-24-224-42-42i2i−2i−2i−4i−4i4i4i-20000-220000200002i2i−2i−2i0000000000000000000000000000000000000000000000
χ6944-4-4−4i−4i4i4i44-4-4−4i−4i4i4i000000-2-2-22-22222i2i−2i−2i2i2i−2i−2i100−2i32i31-1i3i3−i3−i3-100−2323−i−iii33−3−3000000000000000000000000000000000000000000
χ7044-4-4−4i−4i4i4i44-4-4−4i−4i4i4i000000-2-2-22-22222i2i−2i−2i2i2i−2i−2i1002i3−2i31-1−i3−i3i3i3-10023−23−i−iii−3−333000000000000000000000000000000000000000000
χ714-44-44i−4i4i−4i4-44-44i−4i4i−4i0000004-2-442-2-424i−4i4i−4i−2i2i−2i2i-200002-2000020000−2i2i−2i2i0000000000000000000000000000000000000000000000
χ724-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-2-22-22-222−2i2i−2i2i−2i2i−2i2i1−2i32i300-11i3−i3i3−i3-123−2300i−ii−i−33−33000000000000000000000000000000000000000000
χ734-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-2-22-22-222−2i2i−2i2i−2i2i−2i2i12i3−2i300-11−i3i3−i3i3-1−232300i−ii−i3−33−3000000000000000000000000000000000000000000
χ744-44-4−4i4i−4i4i4-44-4−4i4i−4i4i0000004-2-442-2-42−4i4i−4i4i2i−2i2i−2i-200002-20000200002i−2i2i−2i0000000000000000000000000000000000000000000000
χ754-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-2-22-22-2222i−2i2i−2i2i−2i2i−2i1−2i32i300-11i3−i3i3−i3-1−232300−ii−ii3−33−3000000000000000000000000000000000000000000
χ764-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-2-22-22-2222i−2i2i−2i2i−2i2i−2i12i3−2i300-11−i3i3−i3i3-123−2300−ii−ii−33−33000000000000000000000000000000000000000000
χ774-4-444-4-444-4-444-4-440000004-2-4-4224-24-4-44-222-2-20000220000-20000-222-20000000000000000000000000000000000000000000000
χ784-4-444-4-444-4-444-4-44000000-2422-4-4-24-222-24-4-44-20000220000-20000-222-20000000000000000000000000000000000000000000000
χ794-4-444-4-444-4-444-4-44000000-2-22222-2-2-222-2-222-210000-1-13-3-33100001-1-113-3-33000000000000000000000000000000000000000000
χ804-4-444-4-444-4-444-4-44000000-2-22222-2-2-222-2-222-210000-1-1-333-3100001-1-11-333-3000000000000000000000000000000000000000000
χ814-4-44-444-44-4-44-444-40000004-2-4-4224-2-444-42-2-22-20000220000-200002-2-220000000000000000000000000000000000000000000000
χ824-4-44-444-44-4-44-444-4000000-2422-4-4-242-2-22-444-4-20000220000-200002-2-220000000000000000000000000000000000000000000000
χ834-4-44-444-44-4-44-444-4000000-2-22222-2-22-2-222-2-2210000-1-13-3-3310000-111-1-333-3000000000000000000000000000000000000000000
χ844-4-44-444-44-4-44-444-4000000-2-22222-2-22-2-222-2-2210000-1-1-333-310000-111-13-3-33000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000220000220000200002-1-1-1-10000-1-1-1-1000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-20000-2-20000-20000-2111100001111000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000220000220000-20000-2-1-1110000-1-111000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-20000-2-2000020000211-1-1000011-1-1000000000000
χ896666-6-6-6-6-3-3-3-333336-6-3-3330000000000000000000000000000000000000000220000-2-20000-200002-1-111000011-1-1000000000000
χ906666-6-6-6-6-3-3-3-333336-6-3-3330000000000000000000000000000000000000000-2-2000022000020000-211-1-10000-1-111000000000000
χ916666-6-6-6-6-3-3-3-33333-6633-3-30000000000000000000000000000000000000000220000-2-2000020000-2-1-1-1-100001111000000000000
χ926666-6-6-6-6-3-3-3-33333-6633-3-30000000000000000000000000000000000000000-2-20000220000-20000211110000-1-1-1-1000000000000
χ936-6-666-6-66-333-3-333-300−3i33i3−3i33i300000000000000000000000000000000000000002-200002-20000000000-11−i3i30000-11−i3i3000000000000
χ946-6-666-6-66-333-3-333-300−3i33i3−3i33i30000000000000000000000000000000000000000-220000-2200000000001-1i3−i300001-1i3−i3000000000000
χ956-6-666-6-66-333-3-333-3003i3−3i33i3−3i300000000000000000000000000000000000000002-200002-20000000000-11i3−i30000-11i3−i3000000000000
χ966-6-666-6-66-333-3-333-3003i3−3i33i3−3i30000000000000000000000000000000000000000-220000-2200000000001-1−i3i300001-1−i3i3000000000000
χ976-6-66-666-6-333-33-3-3300−3i33i33i3−3i300000000000000000000000000000000000000002-20000-220000000000-11i3−i300001-1−i3i3000000000000
χ986-6-66-666-6-333-33-3-3300−3i33i33i3−3i30000000000000000000000000000000000000000-2200002-200000000001-1−i3i30000-11i3−i3000000000000
χ996-6-66-666-6-333-33-3-33003i3−3i3−3i33i300000000000000000000000000000000000000002-20000-220000000000-11−i3i300001-1i3−i3000000000000
χ1006-6-66-666-6-333-33-3-33003i3−3i3−3i33i30000000000000000000000000000000000000000-2200002-200000000001-1i3−i30000-11−i3i3000000000000
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).