Finite Group Databasebeta

← Group #13155752

Character table — Group #13155752

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order12442333466666121212121212121233366666666612121212121212121212121288882424242436666121212121224446612121212121212121212121212121212121224242424242424242424242424246661212128888882424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
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
χ911-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111111-1-1-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-11-1i−i11ii−i−i-1-1iiiiii−i−i−i−i−i−iii−i−ii−iiiii−i−i−i−i111-1-1-1i−ii−i1-111-1-1ii−i−ii−i1-1
χ1011-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111111-1-1-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-11-1−ii11−i−iii-1-1−i−i−i−i−i−iiiiiiiii−i−ii−iiiii−i−i−i−i111-1-1-1i−i−ii-11-1-111ii−i−i−ii-11
χ1111-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111111-1-1-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-1-11i−i-1-1ii−i−i11iiiiii−i−i−i−i−i−iii−i−ii−iiiii−i−i−i−i-1-1-1111−ii−ii1-111-1-1−i−iii−ii-11
χ1211-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111111-1-1-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-1-11−ii-1-1−i−iii11−i−i−i−i−i−iiiiiiiii−i−ii−iiiii−i−i−i−i-1-1-1111−iii−i-11-1-111−i−iiii−i1-1
χ1311-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111111-1-1-1-1-1-1−i−iii−i−iii1-1-1-11111-1-11-1i−i11ii−i−i-1-1iiiiii−i−i−i−i−i−i−i−iii−ii−i−i−i−iiiii111-1-1-1−iii−i-11-1-111−i−iiii−i-11
χ1411-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111111-1-1-1-1-1-1−i−iii−i−iii1-1-1-11111-1-11-1−ii11−i−iii-1-1−i−i−i−i−i−iiiiiii−i−iii−ii−i−i−i−iiiii111-1-1-1−ii−ii1-111-1-1−i−iii−ii1-1
χ1511-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111111-1-1-1-1-1-1−i−iii−i−iii1-1-1-11111-1-1-11i−i-1-1ii−i−i11iiiiii−i−i−i−i−i−i−i−iii−ii−i−i−i−iiiii-1-1-1111i−i−ii-11-1-111ii−i−i−ii1-1
χ1611-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111111-1-1-1-1-1-1−i−iii−i−iii1-1-1-11111-1-1-11−ii-1-1−i−iii11−i−i−i−i−i−iiiiiii−i−iii−ii−i−i−i−iiiii-1-1-1111i−ii−i1-111-1-1ii−i−ii−i-11
χ172222222-122222-1222222-1-12-1-1-1-1-12-1222-12-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-1-10000-1-10000000000002222-1-1-1-1-1-1-1-1-1-12-1-12-1-12200000000-1-1-1-10000
χ182222222-122222-1222222-1-12-1-1-1-1-12-1222-12-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200110000110000000000002222-1-1-1-1-1-1-1-1-1-1-211-211-2-20000000011110000
χ192222222-122222-1222222-1-12-1-1-1-1-12-1222-12-122-1-122-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-12200-1-10000-1-1000000000000-2-2-2-211111111112-1-12-1-1-2-20000000011110000
χ202222222-122222-1222222-1-12-1-1-1-1-12-1222-12-122-1-122-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-20011000011000000000000-2-2-2-21111111111-211-2112200000000-1-1-1-10000
χ21222222-122222-122222-1-122-12-1222-12-1-1-1-1-12-1-122-1-1-1-12200000000-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-100000000000000-1-1-1-1-1-100220000000000-1-100
χ22222222-122222-122222-1-122-12-1222-12-1-1-1-1-12-1-122-1-1-1-12200000000-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-22211111111111100000000000000-1-1-1-1-1-100-2-200000000001100
χ23222222-122222-122222-1-122-12-1222-12-1-1-1-1-12-1-122-1-1-1-12200000000-1-1-1-1-1-1-1-1-1-1-2-222-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-10000000000000011111100-2-200000000001100
χ24222222-122222-122222-1-122-12-1222-12-1-1-1-1-12-1-122-1-1-1-12200000000-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000011111100220000000000-1-100
χ2522222-1222-1-1-122-1-1-1-12222-1-122-1-1-1-12-1-1222-1-1-1-1-1-122-1-122222222-12-1-1-12-1-1-1-1002200-1-1-1-10022-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000022-1-1-1-100000000
χ2622222-1222-1-1-122-1-1-1-12222-1-122-1-1-1-12-1-1222-1-1-1-1-1-122-1-122222222-12-1-1-12-1-1-1-100-2-200111100-2-21111-2-21111-1-1-1-122-1-1-1-1-1-1-1-10000000000-2-2111100000000
χ2722222-1222-1-1-122-1-1-1-12222-1-122-1-1-1-12-1-1222-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-1002200-1-1-1-10022-1-1-1-122-1-1-1-11111-2-2111111110000000000-2-2111100000000
χ2822222-1222-1-1-122-1-1-1-12222-1-122-1-1-1-12-1-1222-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-100-2-200111100-2-21111-2-211111111-2-211111111000000000022-1-1-1-100000000
χ292222-2222-22-2-22222-2-22222222-2-2-222-2-2-22-2-2-2-2-2-22222222-22-222222-2-2-22-2-2-2220000000000000000000000002-22-2-2-222-2-222-2-2000000000000000000000000
χ302222-2222-22-2-22222-2-22222222-2-2-222-2-2-22-2-2-2-2-2-2222222-22-22-2-2-2-22-2-2-22-2-2-222000000000000000000000000-22-2222-2-222-2-222000000000000000000000000
χ312222-222-1-22-2-22-122-2-222-1-12-1-11112-1-2-2-2-1-21-2-21122-1-1-1-12-22-2-1-1-1-1-1111-1111-1-10000−i3i30000−i3i30000000000002-22-211-1-111-1-1110−i3i30−i3i30000000000−i3i3−i3i30000
χ322222-222-1-22-2-22-122-2-222-1-12-1-11112-1-2-2-2-1-21-2-21122-1-1-1-12-22-2-1-1-1-1-1111-1111-1-10000i3−i30000i3−i30000000000002-22-211-1-111-1-1110i3−i30i3−i30000000000i3−i3i3−i30000
χ332222-222-1-22-2-22-122-2-222-1-12-1-11112-1-2-2-2-1-21-2-21122-1-1-1-1-22-221111-1111-1111-1-10000−i3i30000−i3i3000000000000-22-22-1-111-1-111-1-10−i3i30−i3i30000000000i3−i3i3−i30000
χ342222-222-1-22-2-22-122-2-222-1-12-1-11112-1-2-2-2-1-21-2-21122-1-1-1-1-22-221111-1111-1111-1-10000i3−i30000i3−i3000000000000-22-22-1-111-1-111-1-10i3−i30i3−i30000000000−i3i3−i3i30000
χ352222-2-122-2-11122-1-1112222-1-12-211-1-1-2112-2-21111-1-122-1-12-22-22222-1-211-1-211-1-10000003−33−3000033−3−30033−3−3-11-11-2-2-1-111-1-1110000000000003−33−300000000
χ362222-2-122-2-11122-1-1112222-1-12-211-1-1-2112-2-21111-1-122-1-12-22-22222-1-211-1-211-1-1000000−33−330000−3−33300−3−333-11-11-2-2-1-111-1-111000000000000−33−3300000000
χ372222-2-122-2-11122-1-1112222-1-12-211-1-1-2112-2-21111-1-122-1-1-22-22-2-2-2-2-1-211-1-211-1-10000003−33−3000033−3−30033−3−31-11-12211-1-111-1-1000000000000−33−3300000000
χ382222-2-122-2-11122-1-1112222-1-12-211-1-1-2112-2-21111-1-122-1-1-22-22-2-2-2-2-1-211-1-211-1-1000000−33−330000−3−33300−3−3331-11-12211-1-111-1-10000000000003−33−300000000
χ3922-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22i−2i−2i2i2i2i−2i−2i22222-2-2-2-2-20000000000000000000000002i−2i−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ4022-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2−2i2i2i−2i−2i−2i2i2i22222-2-2-2-2-2000000000000000000000000−2i2i2i−2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ4122-2-2222-1-22222-1-2-2-2-2-2-2112-1-1-1-1-12-1222-1-21-2-211-2-211112i−2i−2i2i−i−iii-1-1-1-1-1111110000−i3i30000i3−i30000000000002i−2i−2i2ii−i−i−iiiii−i−i0−i3i30i3−i300000000003−3−330000
χ4222-2-2222-1-22222-1-2-2-2-2-2-2112-1-1-1-1-12-1222-1-21-2-211-2-211112i−2i−2i2i−i−iii-1-1-1-1-1111110000i3−i30000−i3i30000000000002i−2i−2i2ii−i−i−iiiii−i−i0i3−i30−i3i30000000000−333−30000
χ4322-2-2222-1-22222-1-2-2-2-2-2-2112-1-1-1-1-12-1222-1-21-2-211-2-21111−2i2i2i−2iii−i−i-1-1-1-1-1111110000−i3i30000i3−i3000000000000−2i2i2i−2i−iiii−i−i−i−iii0−i3i30i3−i30000000000−333−30000
χ4422-2-2222-1-22222-1-2-2-2-2-2-2112-1-1-1-1-12-1222-1-21-2-211-2-21111−2i2i2i−2iii−i−i-1-1-1-1-1111110000i3−i30000−i3i3000000000000−2i2i2i−2i−iiii−i−i−i−iii0i3−i30−i3i300000000003−3−330000
χ4522-2-22-122-2-1-1-1221111-2-2-2-2-1-122-1-1-1-12-1-12-2-2111111-2-2112i−2i−2i2i2i2i−2i−2i-12-1-1-1-21111000000−i3i3i3−i30000−i3−i3i3i300i3i3−i3−i3−iii−i−2i2i−i−iiiii−i−i000000000000−333−300000000
χ4622-2-22-122-2-1-1-1221111-2-2-2-2-1-122-1-1-1-12-1-12-2-2111111-2-2112i−2i−2i2i2i2i−2i−2i-12-1-1-1-21111000000i3−i3−i3i30000i3i3−i3−i300−i3−i3i3i3−iii−i−2i2i−i−iiiii−i−i0000000000003−3−3300000000
χ4722-2-22-122-2-1-1-1221111-2-2-2-2-1-122-1-1-1-12-1-12-2-2111111-2-211−2i2i2i−2i−2i−2i2i2i-12-1-1-1-21111000000−i3i3i3−i30000−i3−i3i3i300i3i3−i3−i3i−i−ii2i−2iii−i−i−i−iii0000000000003−3−3300000000
χ4822-2-22-122-2-1-1-1221111-2-2-2-2-1-122-1-1-1-12-1-12-2-2111111-2-211−2i2i2i−2i−2i−2i2i2i-12-1-1-1-21111000000i3−i3−i3i30000i3i3−i3−i300−i3−i3i3i3i−i−ii2i−2iii−i−i−i−iii000000000000−333−300000000
χ4922-2-2-222-122-2-22-1-2-222-2-2112-1-11112-1-2-2-2-12-122-1-1-2-211112i2i−2i−2i−i−iii-1111-1-1-1-1112-200-1-10000110000000000002i2i−2i−2i−ii−i−i−i−iiiii2-1-1-2112i−2i00000000−i−iii0000
χ5022-2-2-222-122-2-22-1-2-222-2-2112-1-11112-1-2-2-2-12-122-1-1-2-211112i2i−2i−2i−i−iii-1111-1-1-1-111-2200110000-1-10000000000002i2i−2i−2i−ii−i−i−i−iiiii-2112-1-1−2i2i00000000ii−i−i0000
χ5122-2-2-222-122-2-22-1-2-222-2-2112-1-11112-1-2-2-2-12-122-1-1-2-21111−2i−2i2i2iii−i−i-1111-1-1-1-1112-200-1-1000011000000000000−2i−2i2i2ii−iiiii−i−i−i−i2-1-1-211−2i2i00000000ii−i−i0000
χ5222-2-2-222-122-2-22-1-2-222-2-2112-1-11112-1-2-2-2-12-122-1-1-2-21111−2i−2i2i2iii−i−i-1111-1-1-1-111-2200110000-1-1000000000000−2i−2i2i2ii−iiiii−i−i−i−i-2112-1-12i−2i00000000−i−iii0000
χ5322-2-2-22-1222-2-2-12-2-22211-2-2-12-1-2-2-2-12111-1-12-1-1221111-2-200000000-1111-1-1-1-1112-22i−2i222i2i−2i−2i-2-2−i−i−i−i−i−iiiiiii00000000000000-1-1-1111002i−2i0000000000−ii00
χ5422-2-2-22-1222-2-2-12-2-22211-2-2-12-1-2-2-2-12111-1-12-1-1221111-2-200000000-1111-1-1-1-1112-2−2i2i22−2i−2i2i2i-2-2iiiiii−i−i−i−i−i−i00000000000000-1-1-111100−2i2i0000000000i−i00
χ5522-2-2-22-1222-2-2-12-2-22211-2-2-12-1-2-2-2-12111-1-12-1-1221111-2-200000000-1111-1-1-1-111-222i−2i-2-22i2i−2i−2i22−i−i−i−i−i−iiiiiii00000000000000111-1-1-100−2i2i0000000000i−i00
χ5622-2-2-22-1222-2-2-12-2-22211-2-2-12-1-2-2-2-12111-1-12-1-1221111-2-200000000-1111-1-1-1-111-22−2i2i-2-2−2i−2i2i2i22iiiiii−i−i−i−i−i−i00000000000000111-1-1-1002i−2i0000000000−ii00
χ5722-2-2-2-1222-1112211-1-1-2-2-2-2-1-12-211-1-1-211222-1-1-1-111-2-2112i2i−2i−2i2i2i−2i−2i-1-211-12-1-111002i−2i00−i−iii002i2i−i−i−i−i−2i−2iiiii−i−iii2i−2i−i−i−i−iiiii00000000002-2-1-11100000000
χ5822-2-2-2-1222-1112211-1-1-2-2-2-2-1-12-211-1-1-211222-1-1-1-111-2-2112i2i−2i−2i2i2i−2i−2i-1-211-12-1-11100−2i2i00ii−i−i00−2i−2iiiii2i2i−i−i−i−i−i−iii2i−2i−i−i−i−iiiii0000000000-2211-1-100000000
χ5922-2-2-2-1222-1112211-1-1-2-2-2-2-1-12-211-1-1-211222-1-1-1-111-2-211−2i−2i2i2i−2i−2i2i2i-1-211-12-1-111002i−2i00−i−iii002i2i−i−i−i−i−2i−2iiiiiii−i−i−2i2iiiii−i−i−i−i0000000000-2211-1-100000000
χ6022-2-2-2-1222-1112211-1-1-2-2-2-2-1-12-211-1-1-211222-1-1-1-111-2-211−2i−2i2i2i−2i−2i2i2i-1-211-12-1-11100−2i2i00ii−i−i00−2i−2iiiii2i2i−i−i−i−iii−i−i−2i2iiiii−i−i−i−i00000000002-2-1-11100000000
χ61444444-2-24444-2-24444-2-2-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-211-2-20000000011111111114400-2-20000-2-200000000000000000000000000-211-211000000000000000000
χ62444444-2-24444-2-24444-2-2-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-211-2-2000000001111111111-4-40022000022000000000000000000000000002-1-12-1-1000000000000000000
χ6344444-24-24-2-2-24-2-2-2-2-244-2-2-21-2-211-214-2-2-24-2-2-211-2-2-2-2114444-2-2-2-21-2111-21111000000000000000000000000-2-2-2-2-2-211111111000000000000000000000000
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χ1258-8−8i8i0-4-4-404−4i34i3444i−4i−43434i−4i4i−4i22202i3−2i3-2-202i3−2i3-20023−2323−23−2i2i−2i2i−2i2i00000000-10−i3i310−33i−i00000000000000000000000000000000000000000000000000000000000000
χ1268-8−8i8i0-4-4-4044i3−4i3444i−4i43−434i−4i4i−4i2220−2i32i3-2-20−2i32i3-200−2323−2323−2i2i−2i2i−2i2i00000000-10i3−i3103−3i−i00000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.