Finite Group Databasebeta

← Group #13155505

Character table — Group #13155505

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order1244233346666612121212121212123336666666661212121212121212121212122244661212366661212121212666666688881212121212121224242424242424242424242424242424242424242424242424248888882424242424242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111-1-1111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911-1-1-11111-1-1111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-111-1-1111-1-11-11-111-1-11-1-1-11111-1-11-1-111-1-1i−i1-111-111-1-1ii−i−i11-1-1111111-1-1-1-1-1-1i−iii−i−ii−ii−i1-1ii−i−i11-1-1i−ii−i
χ1011-1-1-11111-1-1111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-111-1-1111-1-11-11-111-1-11-1-1-11111-1-11-1-111-1-1i−i-1111-111-1-1ii−i−i-1-111-1-1-1-1-1-1111111i−iii−i−ii−i−ii-11ii−i−i-1-111−ii−ii
χ1111-1-1-11111-1-1111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-111-1-1111-1-11-11-111-1-11-1-1-11111-1-11-1-111-1-1−ii1-111-111-1-1−i−iii11-1-1111111-1-1-1-1-1-1−ii−i−iii−ii−ii1-1−i−iii11-1-1−ii−ii
χ1211-1-1-11111-1-1111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-111-1-1111-1-11-11-111-1-11-1-1-11111-1-11-1-111-1-1−ii-1111-111-1-1−i−iii-1-111-1-1-1-1-1-1111111−ii−i−iii−iii−i-11−i−iii-1-111i−ii−i
χ1311-1-1-11111-1-1111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-111-1-1111-1-1-11-11-1-1111-1-1-11111-1-1-111-1-111i−i1-1-1-11-1-111ii−i−i11-1-1111111-1-1-1-1-1-1i−iii−i−i−iii−i-11−i−iii-1-111i−i−ii
χ1411-1-1-11111-1-1111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-111-1-1111-1-1-11-11-1-1111-1-1-11111-1-1-111-1-111i−i-11-1-11-1-111ii−i−i-1-111-1-1-1-1-1-1111111i−iii−i−i−ii−ii1-1−i−iii11-1-1−iii−i
χ1511-1-1-11111-1-1111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-111-1-1111-1-1-11-11-1-1111-1-1-11111-1-1-111-1-111−ii1-1-1-11-1-111−i−iii11-1-1111111-1-1-1-1-1-1−ii−i−iiii−i−ii-11ii−i−i-1-111−iii−i
χ1611-1-1-11111-1-1111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-111-1-1111-1-1-11-11-1-1111-1-1-11111-1-1-111-1-111−ii-11-1-11-1-111−i−iii-1-111-1-1-1-1-1-1111111−ii−i−iiii−ii−i1-1ii−i−i11-1-1i−i−ii
χ172222222-122222-1222222-1-12-1-12-122-1-12-1-1-122-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-122002-12-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1220000-1-1-1-100000000
χ182222222-122222-1222222-1-12-1-12-122-1-12-1-1-122-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-2-2002-12-1-1-1-111110000000000000000-2-21111-2-20000111100000000
χ192222222-122222-1222222-1-12-1-12-122-1-12-1-1-122-1-1-1-1222-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-2111112200-21-21111-1-1-1-1000000000000000022-1-1-1-1-2-20000111100000000
χ202222222-122222-1222222-1-12-1-12-122-1-12-1-1-122-1-1-1-1222-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-211111-2-200-21-2111111110000000000000000-2-21111220000-1-1-1-100000000
χ21222222-122-1-12-12-1-122-1-122-12-122-1-1-1-1-12-12-1-1-1-1-1-12-1-12222222222-12-1-1-12-1-1-1-1-1-12-1-1-1-10022-12-1-1-1-1-10000-1-1-1-122-1-1-1-122-1-1-1-10000000000220000-1-1-1-10000
χ22222222-122-1-12-12-1-122-1-122-12-122-1-1-1-1-12-12-1-1-1-1-1-12-1-12222222222-12-1-1-12-1-1-1-1-1-12-1-1-1-100-2-2-12-1-1-1-1-100001111-2-21111-2-211110000000000-2-2000011110000
χ23222222-122-1-12-12-1-122-1-122-12-122-1-1-1-1-12-12-1-1-1-1-1-12-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-111-2111100221-2111110000-1-1-1-122-1-1-1-122-1-1-1-10000000000-2-2000011110000
χ24222222-122-1-12-12-1-122-1-122-12-122-1-1-1-1-12-12-1-1-1-1-1-12-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-111-2111100-2-21-21111100001111-2-21111-2-211110000000000220000-1-1-1-10000
χ2522222-122222-12222-1-12222-1-12-12-1-122-1-122-1-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-100000002222000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100220000000000-1-100
χ2622222-122222-12222-1-12222-1-12-12-1-122-1-122-1-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000022-2-200000002222-2-2-2-2111111111111-1-1-1-1-1-100-2-200000000001100
χ2722222-122222-12222-1-12222-1-12-12-1-122-1-122-1-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000-2-2220000000-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-111111100-2-200000000001100
χ2822222-122222-12222-1-12222-1-12-12-1-122-1-122-1-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000-2-2-2-20000000-2-2-2-2-2-2-2-211111111111111111100220000000000-1-100
χ292222-2222-2-2-22222222-2-222222-2-2-2-2-2-2222-222-2-222-2-2-2222-2-2222222-2-2-22-2-2-2222-2-222-2-20000-2-22-2-22200000000000000000000000000000000000000000000
χ302222-2222-2-2-22222222-2-222222-2-2-2-2-2-2222-222-2-222-2-2-222-222-2-2-2-2-22-2-2-22-2-2-222-222-2-222000022-222-2-200000000000000000000000000000000000000000000
χ312222-222-1-2-2-222-12222-2-2-1-12-1-1-21-2-2112-1-112211-1-1-2-2-2-1-12-2-22-1-1-1-1-1111-1111-1-12-21-1-1110000-21211-1-1−i3i3−i3i3000000000000000000−i3i3−i3i3000000−i3i3−i3i300000000
χ322222-222-1-2-2-222-12222-2-2-1-12-1-1-21-2-2112-1-112211-1-1-2-2-2-1-12-2-22-1-1-1-1-1111-1111-1-12-21-1-1110000-21211-1-1i3−i3i3−i3000000000000000000i3−i3i3−i3000000i3−i3i3−i300000000
χ332222-222-1-2-2-222-12222-2-2-1-12-1-1-21-2-2112-1-112211-1-1-2-2-2-1-1-222-21111-1111-1111-1-1-22-111-1-100002-1-2-1-111−i3i3−i3i3000000000000000000−i3i3−i3i3000000i3−i3i3−i300000000
χ342222-222-1-2-2-222-12222-2-2-1-12-1-1-21-2-2112-1-112211-1-1-2-2-2-1-1-222-21111-1111-1111-1-1-22-111-1-100002-1-2-1-111i3−i3i3−i3000000000000000000i3−i3i3−i3000000−i3i3−i3i300000000
χ352222-22-12-2112-12-1-1221122-12-1-2-21111-12-1-2-1-111-1-1-211222-2-222222-1-211-1-211-1-1-11-2-1-11100001-2-111-1-100003−33−30033−3−30033−3−300000000000000003−33−30000
χ362222-22-12-2112-12-1-1221122-12-1-2-21111-12-1-2-1-111-1-1-211222-2-222222-1-211-1-211-1-1-11-2-1-11100001-2-111-1-10000−33−3300−3−33300−3−3330000000000000000−33−330000
χ372222-22-12-2112-12-1-1221122-12-1-2-21111-12-1-2-1-111-1-1-21122-222-2-2-2-2-2-1-211-1-211-1-11-1211-1-10000-121-1-11100003−33−30033−3−30033−3−30000000000000000−33−330000
χ382222-22-12-2112-12-1-1221122-12-1-2-21111-12-1-2-1-111-1-1-21122-222-2-2-2-2-2-1-211-1-211-1-11-1211-1-10000-121-1-1110000−33−3300−3−33300−3−33300000000000000003−33−30000
χ3922-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222222-2-2-2-2-222222220000-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ4022-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-20000222222200000000000000000000000000000000000000000000
χ4122-2-2222-1-22222-1-2-2-2-2-2-2112-1-12-122-1-12-1-11-2-21111-2-2-21122-2-2-1-111-1-1-1-1-11111122-1-1-1-1-10000-21-211113−3−330000000000000000003−3−330000003−3−3300000000
χ4222-2-2222-1-22222-1-2-2-2-2-2-2112-1-12-122-1-12-1-11-2-21111-2-2-21122-2-2-1-111-1-1-1-1-11111122-1-1-1-1-10000-21-21111−333−3000000000000000000−333−3000000−333−300000000
χ4322-2-2222-1-22222-1-2-2-2-2-2-2112-1-12-122-1-12-1-11-2-21111-2-2-211-2-22211-1-1-1-1-1-1-111111-2-21111100002-12-1-1-1-13−3−330000000000000000003−3−33000000−333−300000000
χ4422-2-2222-1-22222-1-2-2-2-2-2-2112-1-12-122-1-12-1-11-2-21111-2-2-211-2-22211-1-1-1-1-1-1-111111-2-21111100002-12-1-1-1-1−333−3000000000000000000−333−30000003−3−3300000000
χ4522-2-222-12-2-1-12-1211-2-211-2-2-12-122-1-1-1-1-12-1-2111111-211-2-222-2-222-2-2-12-1-1-1-21111-1-12-1-1-1-100001-21111100003−3−330033−3−300−3−33300000000000000003−3−330000
χ4622-2-222-12-2-1-12-1211-2-211-2-2-12-122-1-1-1-1-12-1-2111111-211-2-222-2-222-2-2-12-1-1-1-21111-1-12-1-1-1-100001-2111110000−333−300−3−3330033−3−30000000000000000−333−30000
χ4722-2-222-12-2-1-12-1211-2-211-2-2-12-122-1-1-1-1-12-1-2111111-211-2-2-2-222-2-222-12-1-1-1-2111111-211110000-12-1-1-1-1-100003−3−330033−3−300−3−3330000000000000000−333−30000
χ4822-2-222-12-2-1-12-1211-2-211-2-2-12-122-1-1-1-1-12-1-2111111-211-2-2-2-222-2-222-12-1-1-1-2111111-211110000-12-1-1-1-1-10000−333−300−3−3330033−3−300000000000000003−3−330000
χ4922-2-2-222-12-2-222-1-2-2-2-222112-1-1-21-2-2112-1-1-1-2-2-1-111222112-22-2-1-111-1111-1-1-1-1112-21-1-1112i−2i002-1-2-1-111−i−iii00000000000000002i−2i−i−iii2i−2i0000−i−iii00000000
χ5022-2-2-222-12-2-222-1-2-2-2-222112-1-1-21-2-2112-1-1-1-2-2-1-111222112-22-2-1-111-1111-1-1-1-1112-21-1-111−2i2i002-1-2-1-111ii−i−i0000000000000000−2i2iii−i−i−2i2i0000ii−i−i00000000
χ5122-2-2-222-12-2-222-1-2-2-2-222112-1-1-21-2-2112-1-1-1-2-2-1-11122211-22-2211-1-1-1111-1-1-1-111-22-111-1-12i−2i00-21211-1-1−i−iii00000000000000002i−2i−i−iii−2i2i0000ii−i−i00000000
χ5222-2-2-222-12-2-222-1-2-2-2-222112-1-1-21-2-2112-1-1-1-2-2-1-11122211-22-2211-1-1-1111-1-1-1-111-22-111-1-1−2i2i00-21211-1-1ii−i−i0000000000000000−2i2iii−i−i2i−2i0000−i−iii00000000
χ5322-2-2-22-122112-1211-2-2-1-1-2-2-12-1-2-21111-12-1211-1-1112-1-1-2-22-22-222-2-2-1-211-12-1-111-11-2-1-111002-2-121-1-1110000-1-11122-1-1-1-1-2-2111100000000002-20000-1-1110000
χ5422-2-2-22-122112-1211-2-2-1-1-2-2-12-1-2-21111-12-1211-1-1112-1-1-2-22-22-222-2-2-1-211-12-1-111-11-2-1-11100-22-121-1-111000011-1-1-2-2111122-1-1-1-10000000000-22000011-1-10000
χ5522-2-2-22-122112-1211-2-2-1-1-2-2-12-1-2-21111-12-1211-1-1112-1-1-2-2-22-22-2-222-1-211-12-1-1111-1211-1-1002-21-2-111-1-10000-1-11122-1-1-1-1-2-211110000000000-22000011-1-10000
χ5622-2-2-22-122112-1211-2-2-1-1-2-2-12-1-2-21111-12-1211-1-1112-1-1-2-2-22-22-2-222-1-211-12-1-1111-1211-1-100-221-2-111-1-1000011-1-1-2-2111122-1-1-1-100000000002-20000-1-1110000
χ5722-2-2-2-1222-2-2-122-2-21122-2-2-1-121-211-2-2-1-1221122-2-2-1-1-11100000000-1111-1-1-1-11100000002i−2i2-200000002i2i−2i−2i22-2-2-1-1-1-1-1-1111111−ii−i−iii002i−2i0000000000−ii00
χ5822-2-2-2-1222-2-2-122-2-21122-2-2-1-121-211-2-2-1-1221122-2-2-1-1-11100000000-1111-1-1-1-11100000002i−2i-2200000002i2i−2i−2i-2-222111111-1-1-1-1-1-1−ii−i−iii00−2i2i0000000000i−i00
χ5922-2-2-2-1222-2-2-122-2-21122-2-2-1-121-211-2-2-1-1221122-2-2-1-1-11100000000-1111-1-1-1-1110000000−2i2i2-20000000−2i−2i2i2i22-2-2-1-1-1-1-1-1111111i−iii−i−i00−2i2i0000000000i−i00
χ6022-2-2-2-1222-2-2-122-2-21122-2-2-1-121-211-2-2-1-1221122-2-2-1-1-11100000000-1111-1-1-1-1110000000−2i2i-220000000−2i−2i2i2i-2-222111111-1-1-1-1-1-1i−iii−i−i002i−2i0000000000−ii00
χ61444444-2-24-2-24-2-2-2-244-2-2-2-2-2-214-2-2-211-2-21-2-2-211114-2-2-2-24444-2-2-2-21-2111-21111-2-2-211110000-2-2-2111100000000000000000000000000000000000000000000
χ62444444-2-24-2-24-2-2-2-244-2-2-2-2-2-214-2-2-211-2-21-2-2-211114-2-2-2-2-4-4-4-422221-2111-21111222-1-1-1-10000222-1-1-1-100000000000000000000000000000000000000000000
χ6344444-24-2444-24-244-2-244-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-211000000001111111111000000044000000000-2-2-2-20000000000000000-2-21111000000000000000000
χ6444444-24-2444-24-244-2-244-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2110000000011111111110000000-4-40000000002222000000000000000022-1-1-1-1000000000000000000
χ6544444-2-244-2-2-2-24-2-2-2-2-2-2441-2-2-2411-2-21-2-2411-2-2-2-2-211-2-2000000001-2111-211110000000004400000000000-2-2-2-2-2-21111-2-21111000000000000000000000000
χ6644444-2-244-2-2-2-24-2-2-2-2-2-2441-2-2-2411-2-21-2-2411-2-2-2-2-211-2-2000000001-2111-21111000000000-4-400000000000222222-1-1-1-122-1-1-1-1000000000000000000000000
χ674444-44-2-2-4224-2-2-2-24422-2-2-2-21-4222-1-1-2-212-2-2-1-111-422-2-24-4-44-2-2-2-212-1-112-1-111-22211-1-1000022-2-1-11100000000000000000000000000000000000000000000
χ684444-44-2-2-4224-2-2-2-24422-2-2-2-21-4222-1-1-2-212-2-2-1-111-422-2-2-444-4222212-1-112-1-1112-2-2-1-1110000-2-2211-1-100000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.