Finite Group Databasebeta

← Group #13162040

Character table — Group #13162040

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222222244444444444444444444444444444444448888888888888888888888888888888888181818181818363636363636363636727272727272727272727272
order12233344666121223333346666666666121212121212121212121212121212121266666666666666666121212121212121212121212121212121288242424248882424242424242266668824242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-111
χ51111111111111-111111-11-1-11111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111-111111-11-1-11111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111-111111-11-1-11111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-111-1-1-11-1-111
χ81111111111111-111111-11-1-11111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-1-1111-111-1-1
χ9222222-2-2222-2-202222202002222222-2-2-200-2-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-2000000000000000002i−2i002i2i−2i−2i000000000000
χ10222222-2-2222-2-202222202002222222-2-2-200-2-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-200000000000000000−2i2i00−2i−2i2i2i000000000000
χ1122222-12222-12222-1-1-1-122222-12-1-1-1-122-12222-1-1-1-1-1-1-1-12-12-12-1-1-1-122-1-1-1-1-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-10000000000000000200-1-10200-1-1
χ1222222-12222-12222-1-1-1-122222-12-1-1-1-122-12222-1-1-1-1-1-1-1-12-12-12-1-1-1-122-1-1-1-1-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-10000000000000000-200110-20011
χ1322222-12222-122-22-1-1-1-1-22-2-22-12-1-1-1-122-1-2-222-1-1-1-1-1-1-1-12-1-212-1-1-1-1-2-211111111-212-1-1-1-1-2-2111111110000000000000000200-1-10-20011
χ1422222-12222-122-22-1-1-1-1-22-2-22-12-1-1-1-122-1-2-222-1-1-1-1-1-1-1-12-1-212-1-1-1-1-2-211111111-212-1-1-1-1-2-2111111110000000000000000-200110200-1-1
χ152222-12222-12222-12-1-1-12222-12-12-1-1-12-1222-1-122-1-1-1-1-1-1-12-12-12-1-1-1-1-122-1-1-1-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-100000000000000020-1-10020-1-100
χ162222-12222-12222-12-1-1-12222-12-12-1-1-12-1222-1-122-1-1-1-1-1-1-12-12-12-1-1-1-1-122-1-1-1-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1000000000000000-201100-201100
χ172222-12222-1222-2-12-1-1-1-22-2-2-12-12-1-1-12-12-2-2-1-122-1-1-1-1-1-1-121-2-12-1-1-111-2-21111111-2-12-1-1-111-2-211111100000000000000020-1-100-201100
χ182222-12222-1222-2-12-1-1-1-22-2-2-12-12-1-1-12-12-2-2-1-122-1-1-1-1-1-1-121-2-12-1-1-111-2-21111111-2-12-1-1-111-2-2111111000000000000000-20110020-1-100
χ19222-12222-122-1-12-1-12-1-12-1-1-122-1-12-1-1-122-1-1-1-1-1-122-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-122-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1222-1-1-1-1-1-1000000000000
χ20222-12222-122-1-12-1-12-1-12-1-1-122-1-12-1-1-122-1-1-1-1-1-122-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-122-1-12-1-1-1-1-1-122-1-1-1-1-2-21111-2-2-2111111000000000000
χ21222-12222-122-1-1-2-1-12-1-1-2-11122-1-12-1-1-12211-1-1-1-122-1-1-1-122-2-2-1-12-1-11111-2-21111-2-2-1-12-1-11111-2-2111122-1-1-1-12-2-2-1-11111000000000000
χ22222-12222-122-1-1-2-1-12-1-1-2-11122-1-12-1-1-12211-1-1-1-122-1-1-1-122-2-2-1-12-1-11111-2-21111-2-2-1-12-1-11111-2-21111-2-21111-22211-1-1-1-1000000000000
χ23222-122-2-2-122110-1-12-1-10-1−i3i322-1-12-1-11-2-2−i3i31111-2-21111-2-200-1-12-1-1−i3i3−i3i300−i3−i3i3i30011-211−i3i3−i3i300−i3−i3i3i30033−3−302i−2i3−3−i−iii000000000000
χ24222-122-2-2-122110-1-12-1-10-1−i3i322-1-12-1-11-2-2−i3i31111-2-21111-2-200-1-12-1-1−i3i3−i3i300−i3−i3i3i30011-211−i3i3−i3i300−i3−i3i3i300−3−3330−2i2i−33ii−i−i000000000000
χ25222-122-2-2-122110-1-12-1-10-1i3−i322-1-12-1-11-2-2i3−i31111-2-21111-2-200-1-12-1-1i3−i3i3−i300i3i3−i3−i30011-211i3−i3i3−i300i3i3−i3−i30033−3−30−2i2i3−3ii−i−i000000000000
χ26222-122-2-2-122110-1-12-1-10-1i3−i322-1-12-1-11-2-2i3−i31111-2-21111-2-200-1-12-1-1i3−i3i3−i300i3i3−i3−i30011-211i3−i3i3−i300i3i3−i3−i300−3−33302i−2i−33−i−iii000000000000
χ2722-22222-2222220222220-200-2-222222-222002222222222-2-200-2-2-2-2-2000000000000-2-2-2-2-20000000000222222-200-2-20000000000000000
χ2822-22222-2222220222220-200-2-222222-222002222222222-2-200-2-2-2-2-2000000000000-2-2-2-2-20000000000-2-2-2-2-2-2200220000000000000000
χ2922-2222-22222-2-2222222-2-222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-22222222222-2-222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000
χ3022-2222-22222-2-2-2222222-2-2-2-2-2222222-2-222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222000000000000000000000000000
χ3122-222-1-2222-1-2-222-1-1-1-1-2-222-212-1-1-1-12-21-2-2-2-2111111112-12-1-2111122-1-1-1-1-1-1-1-1-212-1-1-1-1-2-2111111110000000000000000000−i3i30000−i3i3
χ3222-222-1-2222-1-2-222-1-1-1-1-2-222-212-1-1-1-12-21-2-2-2-2111111112-12-1-2111122-1-1-1-1-1-1-1-1-212-1-1-1-1-2-2111111110000000000000000000i3−i30000i3−i3
χ3322-222-1-2222-1-2-2-22-1-1-1-12-2-2-2-212-1-1-1-12-2122-2-2111111112-1-21-21111-2-2111111112-12-1-1-1-122-1-1-1-1-1-1-1-10000000000000000000−i3i30000i3−i3
χ3422-222-1-2222-1-2-2-22-1-1-1-12-2-2-2-212-1-1-1-12-2122-2-2111111112-1-21-21111-2-2111111112-12-1-1-1-122-1-1-1-1-1-1-1-10000000000000000000i3−i30000−i3i3
χ3522-22-12-222-12-2-22-12-1-1-1-2-2221-2-12-1-1-121-2-2-211-2-2111111-12-121-2111-1-122-1-1-1-1-1-11-2-12-1-1-111-2-211111100000000000000000−i3i30000−i3i300
χ3622-22-12-222-12-2-22-12-1-1-1-2-2221-2-12-1-1-121-2-2-211-2-2111111-12-121-2111-1-122-1-1-1-1-1-11-2-12-1-1-111-2-211111100000000000000000i3−i30000i3−i300
χ3722-22-12-222-12-2-2-2-12-1-1-12-2-2-21-2-12-1-1-121-22211-2-2111111-121-21-211111-2-2111111-12-12-1-1-1-1-122-1-1-1-1-1-100000000000000000−i3i30000i3−i300
χ3822-22-12-222-12-2-2-2-12-1-1-12-2-2-21-2-12-1-1-121-22211-2-2111111-121-21-211111-2-2111111-12-12-1-1-1-1-122-1-1-1-1-1-100000000000000000i3−i30000−i3i300
χ3922-2-1222-2-122-1-10-1-12-1-101−i3i3-2-2-1-12-1-1122i3−i3-1-1-1-122-1-1-1-1-2-20011-211−i3i3−i3i300−i3−i3i3i30011-211i3−i3i3−i300i3i3−i3−i322-1-1-1-1-20011−i3i3−i3i3000000000000
χ4022-2-1222-2-122-1-10-1-12-1-101−i3i3-2-2-1-12-1-1122i3−i3-1-1-1-122-1-1-1-1-2-20011-211−i3i3−i3i300−i3−i3i3i30011-211i3−i3i3−i300i3i3−i3−i3-2-21111200-1-1i3−i3i3−i3000000000000
χ4122-2-1222-2-122-1-10-1-12-1-101i3−i3-2-2-1-12-1-1122−i3i3-1-1-1-122-1-1-1-1-2-20011-211i3−i3i3−i300i3i3−i3−i30011-211−i3i3−i3i300−i3−i3i3i322-1-1-1-1-20011i3−i3i3−i3000000000000
χ4222-2-1222-2-122-1-10-1-12-1-101i3−i3-2-2-1-12-1-1122−i3i3-1-1-1-122-1-1-1-1-2-20011-211i3−i3i3−i300i3i3−i3−i30011-211−i3i3−i3i300−i3−i3i3i3-2-21111200-1-1−i3i3−i3i3000000000000
χ4322-2-122-22-122112-1-12-1-1-21-1-1-2-2-1-12-1-1-1-2-2111111-2-21111222211-211-1-1-1-122-1-1-1-1-2-2-1-12-1-11111-2-211110033−3−3000−333−3−33000000000000
χ4422-2-122-22-122112-1-12-1-1-21-1-1-2-2-1-12-1-1-1-2-2111111-2-21111222211-211-1-1-1-122-1-1-1-1-2-2-1-12-1-11111-2-2111100−3−3330003−3−333−3000000000000
χ4522-2-122-22-12211-2-1-12-1-12111-2-2-1-12-1-1-1-2-2-1-11111-2-2111122-2-211-2111111-2-2111122-1-12-1-1-1-1-1-122-1-1-1-10033−3−3000−33−333−3000000000000
χ4622-2-122-22-12211-2-1-12-1-12111-2-2-1-12-1-1-1-2-2-1-11111-2-2111122-2-211-2111111-2-2111122-1-12-1-1-1-1-1-122-1-1-1-100−3−3330003−33−3−33000000000000
χ4744444-2-4-444-2-4-404-2-2-2-204004-24-2-2-2-2-4-4200-4-422222222-42004-2-2-2-2000000000000-422220000000000000000000000000000000000000
χ484444-24-4-44-24-4-40-24-2-2-20400-24-24-2-2-2-42-40022-4-42222222-400-24-2-2-20000000000002-42220000000000000000000000000000000000000
χ494444-2-2444-2-2444-2-21114444-2-2-2-21114-2-244-2-2-2-2111111-2-2-2-2-2-2111-2-2-2-2111111-2-2-2-2111-2-2-2-2111111000000000000000000000000000
χ504444-2-2444-2-244-4-2-2111-44-4-4-2-2-2-21114-2-2-4-4-2-2-2-2111111-2-222-2-21112222-1-1-1-1-1-122-2-21112222-1-1-1-1-1-1000000000000000000000000000
χ514444-2-2-4-44-2-2-4-40-2-21110400-2-2-2-2111-422002222-1-1-1-1-1-12200-2-211100003-33-33-30022-1-1-100003-33-33-3000000000000000000000000000
χ524444-2-2-4-44-2-2-4-40-2-21110400-2-2-2-2111-422002222-1-1-1-1-1-12200-2-21110000-33-33-330022-1-1-10000-33-33-33000000000000000000000000000
χ53444-24-244-24-2-2-24-21-2114-2-2-24-2-21-211-24-2-2-2-2-211-2-211114-24-2-21-211-2-211-2-211114-2-21-211-2-211-2-21111000000000000000000000000000
χ54444-24-244-24-2-2-2-4-21-211-4-2224-2-21-211-24-222-2-211-2-211114-2-42-21-21122-1-122-1-1-1-1-42-21-21122-1-122-1-1-1-1000000000000000000000000000
χ55444-24-2-4-4-24-2220-21-2110-2−2i32i34-2-21-2112-42−2i32i322-1-122-1-1-1-1-4200-21-211−2i32i3i3−i300i3i3−i3−i3002-12-1-1−2i32i3i3−i300i3i3−i3−i3000000000000000000000000000
χ56444-24-2-4-4-24-2220-21-2110-22i3−2i34-2-21-2112-422i3−2i322-1-122-1-1-1-1-4200-21-2112i3−2i3−i3i300−i3−i3i3i3002-12-1-12i3−2i3−i3i300−i3−i3i3i3000000000000000000000000000
χ57444-2-2444-2-24-2-241-2-2114-2-2-2-241-2-211-2-24-2-211-2-2-2-21111-24-241-2-21111-2-2-2-21111-241-2-21111-2-2-2-21111000000000000000000000000000
χ58444-2-2444-2-24-2-2-41-2-211-4-222-241-2-211-2-242211-2-2-2-21111-242-41-2-211-1-12222-1-1-1-12-41-2-211-1-12222-1-1-1-1000000000000000000000000000
χ59444-2-24-4-4-2-242201-2-2110-2−2i32i3-241-2-21122-4−2i32i3-1-12222-1-1-1-12-4001-2-211i3−i3−2i32i300i3i3−i3−i300-122-1-1i3−i3−2i32i300i3i3−i3−i3000000000000000000000000000
χ60444-2-24-4-4-2-242201-2-2110-22i3−2i3-241-2-21122-42i3−2i3-1-12222-1-1-1-12-4001-2-211−i3i32i3−2i300−i3−i3i3i300-122-1-1−i3i32i3−2i300−i3−i3i3i3000000000000000000000000000
χ61444-2-2-244-2-2-2-2-24111−1−3i32−1+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+3i32111111−1−3i32−1+3i32−1+3i32−1−3i32-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1+3i32−1−3i32000000000000000000000000000
χ62444-2-2-244-2-2-2-2-24111−1+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+3i32−1−3i32111111−1+3i32−1−3i32−1−3i32−1+3i32-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1−3i32−1+3i32000000000000000000000000000
χ63444-2-2-244-2-2-2-2-2-4111−1−3i32−1+3i32-4-222-2-2111−1−3i32−1+3i32-2-2-222111111−1−3i32−1−3i32−1+3i32−1+3i32-2-222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321−3i321+3i3222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321−3i321+3i32000000000000000000000000000
χ64444-2-2-244-2-2-2-2-2-4111−1+3i32−1−3i32-4-222-2-2111−1+3i32−1−3i32-2-2-222111111−1+3i32−1+3i32−1−3i32−1−3i32-2-222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321+3i321−3i3222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321+3i321−3i32000000000000000000000000000
χ65444-2-2-2-4-4-2-2-2220111−1−3i32−1+3i320-2−2i32i3-2-2111−1−3i32−1+3i32222−2i32i3-1-1-1-1-1-11+3i321+3i321−3i321−3i322200111−1−3i32−1+3i32i3−i3i3−i33-3−3−i323−i32−3+i323+i3200-1-1-11+3i321−3i32i3−i3i3−i33-3−3−i323−i32−3+i323+i32000000000000000000000000000
χ66444-2-2-2-4-4-2-2-2220111−1−3i32−1+3i320-22i3−2i3-2-2111−1−3i32−1+3i322222i3−2i3-1-1-1-1-1-11+3i321+3i321−3i321−3i322200111−1−3i32−1+3i32−i3i3−i3i3-333+i32−3+i323−i32−3−i3200-1-1-11+3i321−3i32−i3i3−i3i3-333+i32−3+i323−i32−3−i32000000000000000000000000000
χ67444-2-2-2-4-4-2-2-2220111−1+3i32−1−3i320-2−2i32i3-2-2111−1+3i32−1−3i32222−2i32i3-1-1-1-1-1-11−3i321−3i321+3i321+3i322200111−1+3i32−1−3i32i3−i3i3−i3-333−i32−3−i323+i32−3+i3200-1-1-11−3i321+3i32i3−i3i3−i3-333−i32−3−i323+i32−3+i32000000000000000000000000000
χ68444-2-2-2-4-4-2-2-2220111−1+3i32−1−3i320-22i3−2i3-2-2111−1+3i32−1−3i322222i3−2i3-1-1-1-1-1-11−3i321−3i321+3i321+3i322200111−1+3i32−1−3i32−i3i3−i3i33-3−3+i323+i32−3−i323−i3200-1-1-11−3i321+3i32−i3i3−i3i33-3−3+i323+i32−3−i323−i32000000000000000000000000000
χ6944-444-24-444-24404-2-2-2-20-400-424-2-2-2-2-44-20044-2-2-2-2-2-2-2-2-4200-42222000000000000-422220000000000000000000000000000000000000
χ7044-44-244-44-24440-24-2-2-20-4002-4-24-2-2-2-4-2400-2-244-2-2-2-2-2-22-4002-42220000000000002-42220000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.