Finite Group Databasebeta

← Group #13178683

Character table — Group #13178683

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181836363636363636363636363636363636363636363636363672727272
order1222223336666666662333334666666666666666666666661212666666666666666666666612121212121212121212121244441212121222244444446666121212121212121212126121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-11
χ5111111111111111111-111111-111-1-11111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1
χ6111111111111111111-111111-111-1-11111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ7111111111111111111-111111-111-1-11111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ8111111111111111111-111111-111-1-11111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-111-111-1
χ91111-1-1111111111111111111-1-1-111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-11-11-11-11-111-1-1-1-111-1-1-1-11111-1-1
χ101111-1-1111111111111111111-1-1-111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-111-1-11-11-1-111-1-1-1-111-1-111-1-111
χ111111-1-1111111111111111111-1-1-111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-11-111-1-1111-1-111-1-11111-1-1-11-11
χ121111-1-1111111111111111111-1-1-111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11-111-1-1-1111111-1-111-1-11-11-1
χ131111-1-1111111111111-1111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111111-1-11-11-111-111-1-11111-1-1-1-1-1-1-1-111
χ141111-1-1111111111111-1111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-111-1-111-1-11-1-11111-1-111-1-1-1-111-1-1
χ151111-1-1111111111111-1111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11-11-11-1-11-1111-1-1-1-1-1-11111111-11-1
χ161111-1-1111111111111-1111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-11-111-11-11-1-1-111-1-111-1-11111-11-11
χ1722222222-122-12-1-122222-1-1-1-12222222-1-122-1-1-1-1-1-1-1-12-1-1-1-1222-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1000000002200002200-1-1-1-100000000000-1-10
χ1822222222-122-12-1-122222-1-1-1-12222222-1-122-1-1-1-1-1-1-1-12-1-1-1-1222-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-100000000-2-20000-2-200111100000000000110
χ1922222222-122-12-1-1222-22-1-1-1-1-222-2-222-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2122-1-1-1-1-1-1-1-1-2-2111111111-2-2-21111111100000000220000-2-200-1-1-1-100000000000110
χ2022222222-122-12-1-1222-22-1-1-1-1-222-2-222-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2122-1-1-1-1-1-1-1-1-2-2111111111-2-2-21111111100000000-2-200002200111100000000000-1-10
χ212222222-12-122222-1-122-12-1-1-122222-1-122-1-122-1-1-1-1-1-1-12-1-1-122-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1000000000022000022000000-1-1-1-10000-100-1
χ222222222-12-122222-1-122-12-1-1-122222-1-122-1-122-1-1-1-1-1-1-12-1-1-122-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-10000000000-2-20000-2-2000000111100001001
χ232222222-12-122222-1-12-2-12-1-1-1-222-2-2-1-122-1-122-1-1-1-1-1-1-12-1-1-1-2-21-2-1-122-1-1-1-1-1-111-2-2111111-2111-2-21111110000000000220000-2-200000011110000-100-1
χ242222222-12-122222-1-12-2-12-1-1-1-222-2-2-1-122-1-122-1-1-1-1-1-1-12-1-1-1-2-21-2-1-122-1-1-1-1-1-111-2-2111111-2111-2-21111110000000000-2-2000022000000-1-1-1-100001001
χ25222222-1222-12-12222-12-1-12-1-12-1-1-1-12222-1-1-1-122-1-1-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-100002200000000-1-10000-1-1-1-10000
χ26222222-1222-12-12222-12-1-12-1-12-1-1-1-12222-1-1-1-122-1-1-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-211110000-2-20000000011000011110000
χ27222222-1222-12-12222-1-2-1-12-1-1-2-1-1112222-1-1-1-122-1-1-1-1-1-12-1-111-2-2-1-1-1-122-1-1-1-11111-2-21111-2-21111-2-211112222-1-1-1-10000-2-200000000110000-1-1110000
χ28222222-1222-12-12222-1-2-1-12-1-1-2-1-1112222-1-1-1-122-1-1-1-1-1-12-1-111-2-2-1-1-1-122-1-1-1-11111-2-21111-2-21111-2-21111-2-2-2-2111100002200000000-1-1000011-1-10000
χ292222-2-222-122-12-1-122222-1-1-1-1-2-2-222-2-21122-1-1-1-1-1-1-1-12-1-1-1-1-2-22-1-2-21111111122-1-1-1-1-1-1-1-11-2-2-211111111000000002-200002-200-1-11100000000000-110
χ302222-2-222-122-12-1-122222-1-1-1-1-2-2-222-2-21122-1-1-1-1-1-1-1-12-1-1-1-1-2-22-1-2-21111111122-1-1-1-1-1-1-1-11-2-2-21111111100000000-220000-220011-1-1000000000001-10
χ312222-2-222-122-12-1-1222-22-1-1-1-12-2-2-2-2-2-21122-1-1-1-1-1-1-1-12-1-1-1-122-21-2-211111111-2-211111111-1222-1-1-1-1-1-1-1-1000000002-20000-2200-1-111000000000001-10
χ322222-2-222-122-12-1-1222-22-1-1-1-12-2-2-2-2-2-21122-1-1-1-1-1-1-1-12-1-1-1-122-21-2-211111111-2-211111111-1222-1-1-1-1-1-1-1-100000000-2200002-20011-1-100000000000-110
χ332222-2-22-12-122222-1-122-12-1-1-1-2-2-22211-2-2-1-122-1-1-1-1-1-1-12-1-1-1-2-2-1211-2-2111111-1-122-1-1-1-1-1-1-2111-2-211111100000000002-200002-2000000-1-1110000-1001
χ342222-2-22-12-122222-1-122-12-1-1-1-2-2-22211-2-2-1-122-1-1-1-1-1-1-12-1-1-1-2-2-1211-2-2111111-1-122-1-1-1-1-1-1-2111-2-21111110000000000-220000-2200000011-1-10000100-1
χ352222-2-22-12-122222-1-12-2-12-1-1-12-2-2-2-211-2-2-1-122-1-1-1-1-1-1-12-1-1-1221-211-2-211111111-2-21111112-1-1-122-1-1-1-1-1-100000000002-20000-2200000011-1-10000-1001
χ362222-2-22-12-122222-1-12-2-12-1-1-12-2-2-2-211-2-2-1-122-1-1-1-1-1-1-12-1-1-1221-211-2-211111111-2-21111112-1-1-122-1-1-1-1-1-10000000000-2200002-2000000-1-1110000100-1
χ372222-2-2-1222-12-12222-12-1-12-1-1-211-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-12-1-111221111-2-21111-1-1-1-122-1-1-1-1-2-21111-2-2111122-2-2-1-1-1-100002-20000000011000011-1-10000
χ382222-2-2-1222-12-12222-12-1-12-1-1-211-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-12-1-111221111-2-21111-1-1-1-122-1-1-1-1-2-21111-2-21111-2-22211110000-2200000000-1-10000-1-1110000
χ392222-2-2-1222-12-12222-1-2-1-12-1-121111-2-2-2-2-1-1-1-122-1-1-1-1-1-12-1-1-1-1-2-21111-2-211111111-2-2111122-1-1-1-122-1-1-1-122-2-2-1-1-1-10000-2200000000-1-1000011110000
χ402222-2-2-1222-12-12222-1-2-1-12-1-121111-2-2-2-2-1-1-1-122-1-1-1-1-1-12-1-1-1-1-2-21111-2-211111111-2-2111122-1-1-1-122-1-1-1-1-2-222111100002-200000000110000-1-1-1-10000
χ4122-2-22-2222-222-2-2-22-2-202222202-2002-22-2-2-2-2-2-2-2-2-2-2-22222200002-22-22-222-2-200000000000000000000002i−2i2i−2i2i2i−2i−2i000000000000000000002i−2i000000
χ4222-2-22-2222-222-2-2-22-2-202222202-2002-22-2-2-2-2-2-2-2-2-2-2-22222200002-22-22-222-2-20000000000000000000000−2i2i−2i2i−2i−2i2i2i00000000000000000000−2i2i000000
χ4322-2-22-2-122-2-121-2-22-210-1-12-1-10-11−i3i32-22-21111-2-21111-1-12-1-1−i3i300-11-112-2-1-111−i3i3−i3i300−i3−i3i3i300−i3i3−i3i300−i3−i3i3i32i−2i2i−2i−i−iii000000000000003−30000−ii3−30000
χ4422-2-22-2-122-2-121-2-22-210-1-12-1-10-11−i3i32-22-21111-2-21111-1-12-1-1−i3i300-11-112-2-1-111−i3i3−i3i300−i3−i3i3i300−i3i3−i3i300−i3−i3i3i3−2i2i−2i2iii−i−i00000000000000−330000i−i−330000
χ4522-2-22-2-122-2-121-2-22-210-1-12-1-10-11i3−i32-22-21111-2-21111-1-12-1-1i3−i300-11-112-2-1-111i3−i3i3−i300i3i3−i3−i300i3−i3i3−i300i3i3−i3−i32i−2i2i−2i−i−iii00000000000000−330000−ii−330000
χ4622-2-22-2-122-2-121-2-22-210-1-12-1-10-11i3−i32-22-21111-2-21111-1-12-1-1i3−i300-11-112-2-1-111i3−i3i3−i300i3i3−i3−i300i3−i3i3−i300i3i3−i3−i3−2i2i−2i2iii−i−i000000000000003−30000i−i3−30000
χ4722-2-2-22222-222-2-2-22-2-20222220-2200-22-22-2-2-2-2-2-2-2-2-2-2222220000-22-22-22-2-22200000000000000000000002i−2i−2i2i2i2i−2i−2i00000000000000000000−2i2i000000
χ4822-2-2-22222-222-2-2-22-2-20222220-2200-22-22-2-2-2-2-2-2-2-2-2-2222220000-22-22-22-2-2220000000000000000000000−2i2i2i−2i−2i−2i2i2i000000000000000000002i−2i000000
χ4922-2-2-22-122-2-121-2-22-210-1-12-1-101-1−i3i3-22-221111-2-21111-1-12-1-1i3−i3001-11-1-2211-1-1−i3i3−i3i300−i3−i3i3i300i3−i3i3−i300i3i3−i3−i32i−2i−2i2i−i−iii00000000000000−330000i−i3−30000
χ5022-2-2-22-122-2-121-2-22-210-1-12-1-101-1−i3i3-22-221111-2-21111-1-12-1-1i3−i3001-11-1-2211-1-1−i3i3−i3i300−i3−i3i3i300i3−i3i3−i300i3i3−i3−i3−2i2i2i−2iii−i−i000000000000003−30000−ii−330000
χ5122-2-2-22-122-2-121-2-22-210-1-12-1-101-1i3−i3-22-221111-2-21111-1-12-1-1−i3i3001-11-1-2211-1-1i3−i3i3−i300i3i3−i3−i300−i3i3−i3i300−i3−i3i3i32i−2i−2i2i−i−iii000000000000003−30000i−i−330000
χ5222-2-2-22-122-2-121-2-22-210-1-12-1-101-1i3−i3-22-221111-2-21111-1-12-1-1−i3i3001-11-1-2211-1-1i3−i3i3−i300i3i3−i3−i300−i3i3−i3i300−i3−i3i3i3−2i2i2i−2iii−i−i00000000000000−330000−ii3−30000
χ534444444-2-2-24-24-2-2-2-244-2-211144444-2-2-2-2-2-2-2-2111111-2-211144-2-2-2-2-2-2111111-2-2-2-2111111-2-2-2-2-2-2111111000000000000000000000000000000000000
χ544444444-2-2-24-24-2-2-2-24-4-2-2111-444-4-4-2-2-2-2-2-2-2-2111111-2-2111-4-422-2-2-2-21111112222-1-1-1-1-1-1222222-1-1-1-1-1-1000000000000000000000000000000000000
χ55444444-24-24-2-2-2-2-244-24-21-2114-2-2-2-244-2-2-2-211-2-21111-21-211-2-24-2-2-211-2-21111-2-211-2-21111-24-2-211-2-21111000000000000000000000000000000000000
χ56444444-24-24-2-2-2-2-244-2-4-21-211-4-2-22244-2-2-2-211-2-21111-21-21122-42-2-211-2-2111122-1-122-1-1-1-12-422-1-122-1-1-1-1000000000000000000000000000000000000
χ57444444-2-24-2-24-244-2-2-241-2-2114-2-2-2-2-2-24411-2-2-2-211111-2-211-2-2-2411-2-2-2-2111111-2-2-2-211114-211-2-2-2-21111000000000000000000000000000000000000
χ58444444-2-24-2-24-244-2-2-2-41-2-211-4-2-222-2-24411-2-2-2-211111-2-211222-411-2-2-2-21111-1-12222-1-1-1-1-42-1-12222-1-1-1-1000000000000000000000000000000000000
χ59444444-2-2-2-2-2-2-2-2-2-2-2-24111−1−3i32−1+3i324-2-2-2-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000000000
χ60444444-2-2-2-2-2-2-2-2-2-2-2-24111−1+3i32−1−3i324-2-2-2-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000000000
χ61444444-2-2-2-2-2-2-2-2-2-2-2-2-4111−1−3i32−1+3i32-4-2-222-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i322222111111−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000000
χ62444444-2-2-2-2-2-2-2-2-2-2-2-2-4111−1+3i32−1−3i32-4-2-222-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i322222111111−1+3i32−1−3i32−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000000000000
χ634444-4-44-2-2-24-24-2-2-2-244-2-2111-4-4-4442222-2-2-2-2111111-2-2111-4-4-2-22222-1-1-1-1-1-1-2-2-2-2111111222222-1-1-1-1-1-1000000000000000000000000000000000000
χ644444-4-44-2-2-24-24-2-2-2-24-4-2-21114-4-4-4-42222-2-2-2-2111111-2-211144222222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2111111000000000000000000000000000000000000
χ654444-4-4-24-24-2-2-2-2-244-24-21-211-422-2-2-4-422-2-211-2-21111-21-211224-222-1-122-1-1-1-1-2-211-2-211112-422-1-122-1-1-1-1000000000000000000000000000000000000
χ664444-4-4-24-24-2-2-2-2-244-2-4-21-21142222-4-422-2-211-2-21111-21-211-2-2-4222-1-122-1-1-1-122-1-122-1-1-1-1-24-2-211-2-21111000000000000000000000000000000000000
χ674444-4-4-2-24-2-24-244-2-2-241-2-211-422-2-222-4-411-2-2-2-211111-2-21122-24-1-12222-1-1-1-111-2-2-2-21111-42-1-12222-1-1-1-1000000000000000000000000000000000000
χ684444-4-4-2-24-2-24-244-2-2-2-41-2-2114222222-4-411-2-2-2-211111-2-211-2-22-4-1-12222-1-1-1-1-1-12222-1-1-1-14-211-2-2-2-21111000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).