Finite Group Databasebeta

← Group #13178775

Character table — Group #13178775

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size112222222222244444444444444444444444444444444448888888888888888888888888888888888181818181818363636363636363636363636363636363636363636727272727272
order122333446661212233333466666666661212121212121212121212121212121212666666666666666661212121212121212121212121212121212224488222224666666888121224242424666122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11-1-11-1-1-1-1-1-11-1-1-1-111111-1-11-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-111
χ51111111111111-111111-1111-1-111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-111
χ61111111111111-111111-1111-1-111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ71111111111111-111111-1111-1-111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-111111-1-1-1-11111-111-1-1-1
χ81111111111111-111111-1111-1-111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111-111-1-1-1-1-1-11-1-1111
χ911-1111-11111-1-1111111-1-1-1-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-11-11-1111-111-1-11-111-1-1-11-11-111-1-111-1-11-1
χ1011-1111-11111-1-1111111-1-1-1-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-11-11-1-1-11-1-1-1111-111-1-11-111-1-1-111-1-111-11
χ1111-1111-11111-1-1111111-1-1-1-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11-1111-111-11-1-11-1-111-1-11-1111-1-11-11-1-11
χ1211-1111-11111-1-1111111-1-1-1-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11-11-11-11-1-11111-1-11-1-111-11-111-1
χ1311-1111-11111-1-1-1111111-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-11-111-11-1-1111-1-1-111-11-11-111-1-1-1-1111-1
χ1411-1111-11111-1-1-1111111-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-11-1-1-1-1111-1-11-1-1-1111-111-1-1-11111-1-1-11
χ1511-1111-11111-1-1-1111111-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-11111-1-11-11-1111-1-1-1-11-1111-1-1-11-11-11
χ1611-1111-11111-1-1-1111111-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-11-1-11-11-11-1-1111-1-111-1-11-1-1111-11-11-1
χ17222222-2-2222-2-202222202220022222-2-2-200-2-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-200000000002-2-22000000002-20000000-220000000000
χ18222222-2-2222-2-202222202220022222-2-2-200-2-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-20000000000-222-200000000-2200000002-20000000000
χ1922222-12222-12222-1-1-1-1222-1-1-12-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1222200220000-1-1-1-1-1-1000-1-10000000000
χ2022222-12222-12222-1-1-1-1222-1-1-12-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200-2-20000111111000110000000000
χ2122222-12222-122-22-1-1-1-1-222-1112-1-1-1-12-1-11122-1-1-1-1-1-1-1-122-2-22-1-1-1-1-2-211111111-2-22-1-1-1-1-2-211111111222200-2-20000-1-11111000-1-10000000000
χ2222222-12222-122-22-1-1-1-1-222-1112-1-1-1-12-1-11122-1-1-1-1-1-1-1-122-2-22-1-1-1-1-2-211111111-2-22-1-1-1-1-2-211111111-2-2-2-20022000011-1-1-1-1000110000000000
χ2322222-1-2-222-1-2-202-1-1-1-1022-1−i3i32-1-1-1-1-211−i3i3-2-211111111-2-2002-1-1-1-100−i3−i3−i3−i3i3i3i3i300-2111100−i3−i3−i3−i3i3i3i3i32-2-2200000000-11−i3i3−i3i30001-10000000000
χ2422222-1-2-222-1-2-202-1-1-1-1022-1−i3i32-1-1-1-1-211−i3i3-2-211111111-2-2002-1-1-1-100−i3−i3−i3−i3i3i3i3i300-2111100−i3−i3−i3−i3i3i3i3i3-222-2000000001-1i3−i3i3−i3000-110000000000
χ2522222-1-2-222-1-2-202-1-1-1-1022-1i3−i32-1-1-1-1-211i3−i3-2-211111111-2-2002-1-1-1-100i3i3i3i3−i3−i3−i3−i300-2111100i3i3i3i3−i3−i3−i3−i32-2-2200000000-11i3−i3i3−i30001-10000000000
χ2622222-1-2-222-1-2-202-1-1-1-1022-1i3−i32-1-1-1-1-211i3−i3-2-211111111-2-2002-1-1-1-100i3i3i3i3−i3−i3−i3−i300-2111100i3i3i3i3−i3−i3−i3−i3-222-2000000001-1−i3i3−i3i3000-110000000000
χ272222-1222-122222-12-1-1-122-1222-12-1-1-1-12222-1-122-1-1-1-1-1-1-122-1-12-1-1-1-1-12-1-1-12-1-1-1-12-12-1-1-1-1-12-1-1-12-1-1-10000000002200000000220000000-1-10-1-1
χ282222-1222-122222-12-1-1-122-1222-12-1-1-1-12222-1-122-1-1-1-1-1-1-122-1-12-1-1-1-1-12-1-1-12-1-1-1-12-12-1-1-1-1-12-1-1-12-1-1-1000000000-2-200000000-2-2000000011011
χ292222-1222-12222-2-12-1-1-1-22-12-2-2-12-1-1-1-122-2-2-1-122-1-1-1-1-1-1-12-21-12-1-1-111-2111-21111-2-12-1-1-111-2111-21110000000002200000000-2-20000000-1-1011
χ302222-1222-12222-2-12-1-1-1-22-12-2-2-12-1-1-1-122-2-2-1-122-1-1-1-1-1-1-12-21-12-1-1-111-2111-21111-2-12-1-1-111-2111-2111000000000-2-200000000220000000110-1-1
χ31222-122222-12-1-12-1-12-1-12-12222-1-12-1-122222-1-1-1-122-1-1-1-12-1-12-1-12-1-1-1-1-12-1-1-12-1-12-1-1-12-1-1-1-1-12-1-1-12-1-100002200200200000020000-1-1-1-1-100-100
χ32222-122222-12-1-12-1-12-1-12-12222-1-12-1-122222-1-1-1-122-1-1-1-12-1-12-1-12-1-1-1-1-12-1-1-12-1-12-1-1-12-1-1-1-1-12-1-1-12-1-10000-2-200-200-2000000-200001111100100
χ33222-122222-12-1-1-2-1-12-1-1-2-122-2-2-1-12-1-1222-2-2-1-1-1-122-1-1-1-12-11-2-1-12-1-1111-2111-211-21-1-12-1-1111-2111-21100002200-200-200000020000-1-1-1-1100100
χ34222-122222-12-1-1-2-1-12-1-1-2-122-2-2-1-12-1-1222-2-2-1-1-1-122-1-1-1-12-11-2-1-12-1-1111-2111-211-21-1-12-1-1111-2111-2110000-2-2002002000000-200001111-100-100
χ3522-22222-2222220222220-2-2-200222222-22002222222222-2-200-2-2-2-2-2000000000000-2-2-2-2-2000000000022-2-200000000220000000-2-20000000000
χ3622-22222-2222220222220-2-2-200222222-22002222222222-2-200-2-2-2-2-2000000000000-2-2-2-2-20000000000-2-22200000000-2-20000000220000000000
χ3722-222-12-222-12202-1-1-1-10-2-21−i3i32-1-1-1-121-1i3−i322-1-1-1-1-1-1-1-1-2-200-2111100−i3−i3−i3−i3i3i3i3i300-2111100i3i3i3i3−i3−i3−i3−i322-2-200000000-1-1−i3i3i3−i3000110000000000
χ3822-222-12-222-12202-1-1-1-10-2-21−i3i32-1-1-1-121-1i3−i322-1-1-1-1-1-1-1-1-2-200-2111100−i3−i3−i3−i3i3i3i3i300-2111100i3i3i3i3−i3−i3−i3−i3-2-2220000000011i3−i3−i3i3000-1-10000000000
χ3922-222-12-222-12202-1-1-1-10-2-21i3−i32-1-1-1-121-1−i3i322-1-1-1-1-1-1-1-1-2-200-2111100i3i3i3i3−i3−i3−i3−i300-2111100−i3−i3−i3−i3i3i3i3i322-2-200000000-1-1i3−i3−i3i3000110000000000
χ4022-222-12-222-12202-1-1-1-10-2-21i3−i32-1-1-1-121-1−i3i322-1-1-1-1-1-1-1-1-2-200-2111100i3i3i3i3−i3−i3−i3−i300-2111100−i3−i3−i3−i3i3i3i3i3-2-2220000000011−i3i3i3−i3000-1-10000000000
χ4122-222-1-2222-1-2-222-1-1-1-1-2-2-21-1-12-1-1-1-1-2-1111-2-2111111112222-2111122-1-1-1-1-1-1-1-1-2-22-1-1-1-1-2-2111111112-22-2002-20000-11-1-111000-110000000000
χ4222-222-1-2222-1-2-222-1-1-1-1-2-2-21-1-12-1-1-1-1-2-1111-2-2111111112222-2111122-1-1-1-1-1-1-1-1-2-22-1-1-1-1-2-211111111-22-2200-2200001-111-1-10001-10000000000
χ4322-222-1-2222-1-2-2-22-1-1-1-12-2-21112-1-1-1-1-2-11-1-1-2-21111111122-2-2-21111-2-211111111222-1-1-1-122-1-1-1-1-1-1-1-12-22-200-220000-1111-1-1000-110000000000
χ4422-222-1-2222-1-2-2-22-1-1-1-12-2-21112-1-1-1-1-2-11-1-1-2-21111111122-2-2-21111-2-211111111222-1-1-1-122-1-1-1-1-1-1-1-1-22-22002-200001-1-1-1110001-10000000000
χ4522-22-12-22-122-2-22-12-1-1-1-2-21-222-12-1-1-112-2-2-211-2-2111111-122-11-2111-1-12-1-1-12-1-1-11-2-12-1-1-111-2111-21110000000002-2000000002-20000000-110-11
χ4622-22-12-22-122-2-22-12-1-1-1-2-21-222-12-1-1-112-2-2-211-2-2111111-122-11-2111-1-12-1-1-12-1-1-11-2-12-1-1-111-2111-2111000000000-2200000000-2200000001-101-1
χ4722-22-12-22-122-2-2-2-12-1-1-12-21-2-2-2-12-1-1-112-22211-2-2111111-12-211-211111-2111-2111-12-12-1-1-1-1-12-1-1-12-1-1-10000000002-200000000-220000000-1101-1
χ4822-22-12-22-122-2-2-2-12-1-1-12-21-2-2-2-12-1-1-112-22211-2-2111111-12-211-211111-2111-2111-12-12-1-1-1-1-12-1-1-12-1-1-1000000000-22000000002-200000001-10-11
χ4922-2-122-222-12112-1-12-1-1-21-2-222-1-12-1-1-22-2-2-21111-2-211112-1-1211-211-1-1-12-1-1-12-1-1-21-1-12-1-1111-2111-21100002200200-2000000-20000-1-111-100100
χ5022-2-122-222-12112-1-12-1-1-21-2-222-1-12-1-1-22-2-2-21111-2-211112-1-1211-211-1-1-12-1-1-12-1-1-21-1-12-1-1111-2111-2110000-2-200-20020000002000011-1-1100-100
χ5122-2-122-222-1211-2-1-12-1-121-2-2-2-2-1-12-1-1-22-2221111-2-211112-11-211-211111-2111-2112-1-1-12-1-1-1-1-12-1-1-12-1-100002200-2002000000-20000-1-111100-100
χ5222-2-122-222-1211-2-1-12-1-121-2-2-2-2-1-12-1-1-22-2221111-2-211112-11-211-211111-2111-2112-1-1-12-1-1-1-1-12-1-1-12-1-10000-2-200200-20000002000011-1-1-100100
χ534444-24-4-4-244-4-40-24-2-2-204-2400-24-2-2-22-4-40022-4-42222222-400-24-2-2-20000000000002-42220000000000000000000000000000000000000000000
χ544444-2-244-24-2444-2-211144-2-2-2-2-2-2111-2-2-2-2-2-2-2-2-2111111-244-2-2-2111-2-2-2111-2111-24-2-2111-2-2-2111-2111000000000000000000000000000000000
χ554444-2-244-24-244-4-2-2111-44-2-222-2-2111-2-2-222-2-2-2-2111111-24-42-2-2111222-1-1-12-1-1-12-4-2-2111222-1-1-12-1-1-1000000000000000000000000000000000
χ564444-2-2-4-4-24-2-4-40-2-211104-2-2−2i32i3-2-2111222−2i32i32222-1-1-1-1-1-12-400-2-211100−2i3i3i3i32i3−i3−i3−i30022-1-1-100−2i3i3i3i32i3−i3−i3−i3000000000000000000000000000000000
χ574444-2-2-4-4-24-2-4-40-2-211104-2-22i3−2i3-2-21112222i3−2i32222-1-1-1-1-1-12-400-2-2111002i3−i3−i3−i3−2i3i3i3i30022-1-1-1002i3−i3−i3−i3−2i3i3i3i3000000000000000000000000000000000
χ58444-244-4-44-24220-2-24-2-20-24400-2-24-2-2-4-4-4002222-4-42222-4200-2-24-2-200000000000022-4220000000000000000000000000000000000000000000
χ59444-24-2444-2-2-2-24-21-2114-24-2-2-2-21-2114-2-2-2-2-2-211-2-211114-2-24-21-211-2-21-2111-2114-2-21-211-2-21-2111-211000000000000000000000000000000000
χ60444-24-2444-2-2-2-2-4-21-211-4-24-222-21-2114-2-222-2-211-2-211114-22-4-21-21122-12-1-1-12-1-1-42-21-21122-12-1-1-12-1-1000000000000000000000000000000000
χ61444-24-2-4-44-2-2220-21-2110-24-2−2i32i3-21-211-422−2i32i322-1-122-1-1-1-1-4200-21-21100i3−2i3i3i3−i32i3−i3−i3002-12-1-100i3−2i3i3i3−i32i3−i3−i3000000000000000000000000000000000
χ62444-24-2-4-44-2-2220-21-2110-24-22i3−2i3-21-211-4222i3−2i322-1-122-1-1-1-1-4200-21-21100−i32i3−i3−i3i3−2i3i3i3002-12-1-100−i32i3−i3−i3i3−2i3i3i3000000000000000000000000000000000
χ63444-2-2444-2-24-2-241-2-2114-2-24441-2-211-2444411-2-2-2-21111-2-2-2-21-2-21111-2-211-2-211-2-21-2-21111-2-211-2-211000000000000000000000000000000000
χ64444-2-2444-2-24-2-2-41-2-211-4-2-24-4-41-2-211-244-4-411-2-2-2-21111-2-2221-2-211-1-122-1-122-1-1221-2-211-1-122-1-122-1-1000000000000000000000000000000000
χ65444-2-24-4-4-2-242201-2-2110-2-24001-2-2112-4-400-1-12222-1-1-1-122001-2-2113-3003-3003-300-122-1-13-3003-3003-3000000000000000000000000000000000
χ66444-2-24-4-4-2-242201-2-2110-2-24001-2-2112-4-400-1-12222-1-1-1-122001-2-211-3300-3300-3300-122-1-1-3300-3300-33000000000000000000000000000000000
χ67444-2-2-244-2-2-2-2-24111−1−3i32−1+3i324-2-2-2-2-2111−1−3i32−1+3i32-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-2111−1−3i32−1+3i321111−1−3i32−1+3i3211−1+3i32−1−3i32-2-2111−1−3i32−1+3i321111−1−3i32−1+3i3211−1+3i32−1−3i32000000000000000000000000000000000
χ68444-2-2-244-2-2-2-2-24111−1+3i32−1−3i324-2-2-2-2-2111−1+3i32−1−3i32-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2111−1+3i32−1−3i321111−1+3i32−1−3i3211−1−3i32−1+3i32-2-2111−1+3i32−1−3i321111−1+3i32−1−3i3211−1−3i32−1+3i32000000000000000000000000000000000
χ69444-2-2-244-2-2-2-2-2-4111−1−3i32−1+3i32-4-2-2-222111−1−3i32−1+3i32-2-2-222111111−1−3i32−1−3i32−1+3i32−1+3i32-2-222111−1−3i32−1+3i32-1-1-1-11+3i321−3i32-1-11−3i321+3i3222111−1−3i32−1+3i32-1-1-1-11+3i321−3i32-1-11−3i321+3i32000000000000000000000000000000000
χ70444-2-2-244-2-2-2-2-2-4111−1+3i32−1−3i32-4-2-2-222111−1+3i32−1−3i32-2-2-222111111−1+3i32−1+3i32−1−3i32−1−3i32-2-222111−1+3i32−1−3i32-1-1-1-11−3i321+3i32-1-11+3i321−3i3222111−1+3i32−1−3i32-1-1-1-11−3i321+3i32-1-11+3i321−3i32000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.