Finite Group Databasebeta

← Group #13166798

Character table — Group #13166798

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135
size111122444444444444881212121212121212121212121818242424242424363636363611112244444444444488121212121212121212121212181824242424242436363636361111224444444444448812121212121212121212121218182424242424243636363636
order122244336666661212121212122244666612121212444412121212288883666121233666666121212121212661212666612121212121212121212121262424242436661212336666661212121212126612126666121212121212121212121212624242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111
χ51111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-111-1-1-111-1-11111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-111-1-1-111-1-11111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-111-1-1-111-1-1
χ61111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-1-1-1111111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-1-1-1111111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-1-1-111
χ71111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-1-1-1-111
χ81111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-11-1-111-111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-11-1-111-111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-11-1-111-111-1-1
χ922222222222222222222000000000000-2-2000000-2000022222222222222222222000000000000-2-2000000-2000022222222222222222222000000000000-2-2000000-20000
χ102222-2-222222222-2-2-2-2-2-2000000000000-2-2000000200002222-2-222222222-2-2-2-2-2-2000000000000-2-2000000200002222-2-222222222-2-2-2-2-2-2000000000000-2-200000020000
χ112-22-22i−2i22-22-22-2-22i2i−2i−2i2i−2i0000000000000000000002−2−i2i22-22-22i−2i22-22-22-2-22i2i−2i−2i2i−2i0000000000000000000002−2−i2i22-22-22i−2i22-22-22-2-22i2i−2i−2i2i−2i0000000000000000000002−2−i2i2
χ122-22-22i−2i22-22-22-2-22i2i−2i−2i2i−2i000000000000000000000−22i2−i22-22-22i−2i22-22-22-2-22i2i−2i−2i2i−2i000000000000000000000−22i2−i22-22-22i−2i22-22-22-2-22i2i−2i−2i2i−2i000000000000000000000−22i2−i2
χ132-22-2−2i2i22-22-22-2-2−2i−2i2i2i−2i2i0000000000000000000002−2i2−i22-22-2−2i2i22-22-22-2-2−2i−2i2i2i−2i2i0000000000000000000002−2i2−i22-22-2−2i2i22-22-22-2-2−2i−2i2i2i−2i2i0000000000000000000002−2i2−i2
χ142-22-2−2i2i22-22-22-2-2−2i−2i2i2i−2i2i000000000000000000000−22−i2i22-22-2−2i2i22-22-22-2-2−2i−2i2i2i−2i2i000000000000000000000−22−i2i22-22-2−2i2i22-22-22-2-2−2i−2i2i2i−2i2i000000000000000000000−22−i2i2
χ152-2-220022-2-2-2-222000000002-2000022-2-22-2000000000002-2-220022-2-2-2-222000000002-2000022-2-22-2000000000002-2-220022-2-2-2-222000000002-2000022-2-22-200000000000
χ162-2-220022-2-2-2-22200000000-220000-2-2222-2000000000002-2-220022-2-2-2-22200000000-220000-2-2222-2000000000002-2-220022-2-2-2-22200000000-220000-2-2222-200000000000
χ172-2-220022-2-2-2-2220000002-20022-2-20000-22000000000002-2-220022-2-2-2-2220000002-20022-2-20000-22000000000002-2-220022-2-2-2-2220000002-20022-2-20000-2200000000000
χ182-2-220022-2-2-2-222000000-2200-2-2220000-22000000000002-2-220022-2-2-2-222000000-2200-2-2220000-22000000000002-2-220022-2-2-2-222000000-2200-2-2220000-2200000000000
χ194444441-21-2-211-2-2-2-2-2110000000000000022-1-1-1-1000004444441-21-2-211-2-2-2-2-2110000000000000022-1-1-1-1000004444441-21-2-211-2-2-2-2-2110000000000000022-1-1-1-100000
χ204444441-21-2-211-2-2-2-2-21100000000000000-2-21111000004444441-21-2-211-2-2-2-2-21100000000000000-2-21111000004444441-21-2-211-2-2-2-2-21100000000000000-2-2111100000
χ21444444-21-211-2-211111-2-22222-1-1-1-1-1-1-1-10000000000000444444-21-211-2-211111-2-22222-1-1-1-1-1-1-1-10000000000000444444-21-211-2-211111-2-22222-1-1-1-1-1-1-1-10000000000000
χ22444444-21-211-2-211111-2-2-2-2-2-2111111110000000000000444444-21-211-2-211111-2-2-2-2-2-2111111110000000000000444444-21-211-2-211111-2-2-2-2-2-2111111110000000000000
χ234444-4-41-21-2-211-22222-1-1000000000000002-2-1-111000004444-4-41-21-2-211-22222-1-1000000000000002-2-1-111000004444-4-41-21-2-211-22222-1-1000000000000002-2-1-11100000
χ244444-4-41-21-2-211-22222-1-100000000000000-2211-1-1000004444-4-41-21-2-211-22222-1-100000000000000-2211-1-1000004444-4-41-21-2-211-22222-1-100000000000000-2211-1-100000
χ254444-4-4-21-211-2-21-1-1-1-12222-2-2-1-1-1-1111100000000000004444-4-4-21-211-2-21-1-1-1-12222-2-2-1-1-1-1111100000000000004444-4-4-21-211-2-21-1-1-1-12222-2-2-1-1-1-111110000000000000
χ264444-4-4-21-211-2-21-1-1-1-122-2-2221111-1-1-1-100000000000004444-4-4-21-211-2-21-1-1-1-122-2-2221111-1-1-1-100000000000004444-4-4-21-211-2-21-1-1-1-122-2-2221111-1-1-1-10000000000000
χ2744-4-400444-44-4-4-4000000000000000000000000000000044-4-400444-44-4-4-4000000000000000000000000000000044-4-400444-44-4-4-40000000000000000000000000000000
χ2844-4-400-21-2-1122-13i−3i3i−3i000000−i3i3−i3i33−33−3000000000000044-4-400-21-2-1122-13i−3i3i−3i000000−i3i3−i3i33−33−3000000000000044-4-400-21-2-1122-13i−3i3i−3i000000−i3i3−i3i33−33−30000000000000
χ2944-4-400-21-2-1122-13i−3i3i−3i000000i3−i3i3−i3−33−33000000000000044-4-400-21-2-1122-13i−3i3i−3i000000i3−i3i3−i3−33−33000000000000044-4-400-21-2-1122-13i−3i3i−3i000000i3−i3i3−i3−33−330000000000000
χ3044-4-400-21-2-1122-1−3i3i−3i3i000000−i3i3−i3i3−33−33000000000000044-4-400-21-2-1122-1−3i3i−3i3i000000−i3i3−i3i3−33−33000000000000044-4-400-21-2-1122-1−3i3i−3i3i000000−i3i3−i3i3−33−330000000000000
χ3144-4-400-21-2-1122-1−3i3i−3i3i000000i3−i3i3−i33−33−3000000000000044-4-400-21-2-1122-1−3i3i−3i3i000000i3−i3i3−i33−33−3000000000000044-4-400-21-2-1122-1−3i3i−3i3i000000i3−i3i3−i33−33−30000000000000
χ324-44-44i−4i1-2-1-221-12−2i−2i2i2ii−i0000000000000000−i3i33−3000004-44-44i−4i1-2-1-221-12−2i−2i2i2ii−i0000000000000000−i3i33−3000004-44-44i−4i1-2-1-221-12−2i−2i2i2ii−i0000000000000000−i3i33−300000
χ334-44-44i−4i1-2-1-221-12−2i−2i2i2ii−i0000000000000000i3−i3−33000004-44-44i−4i1-2-1-221-12−2i−2i2i2ii−i0000000000000000i3−i3−33000004-44-44i−4i1-2-1-221-12−2i−2i2i2ii−i0000000000000000i3−i3−3300000
χ344-44-44i−4i-2121-1-22-1ii−i−i−2i2i0000−i3i3i3−i33−3−3300000000000004-44-44i−4i-2121-1-22-1ii−i−i−2i2i0000−i3i3i3−i33−3−3300000000000004-44-44i−4i-2121-1-22-1ii−i−i−2i2i0000−i3i3i3−i33−3−330000000000000
χ354-44-44i−4i-2121-1-22-1ii−i−i−2i2i0000i3−i3−i3i3−333−300000000000004-44-44i−4i-2121-1-22-1ii−i−i−2i2i0000i3−i3−i3i3−333−300000000000004-44-44i−4i-2121-1-22-1ii−i−i−2i2i0000i3−i3−i3i3−333−30000000000000
χ364-44-4−4i4i1-2-1-221-122i2i−2i−2i−ii0000000000000000−i3i3−33000004-44-4−4i4i1-2-1-221-122i2i−2i−2i−ii0000000000000000−i3i3−33000004-44-4−4i4i1-2-1-221-122i2i−2i−2i−ii0000000000000000−i3i3−3300000
χ374-44-4−4i4i1-2-1-221-122i2i−2i−2i−ii0000000000000000i3−i33−3000004-44-4−4i4i1-2-1-221-122i2i−2i−2i−ii0000000000000000i3−i33−3000004-44-4−4i4i1-2-1-221-122i2i−2i−2i−ii0000000000000000i3−i33−300000
χ384-44-4−4i4i-2121-1-22-1−i−iii2i−2i0000−i3i3i3−i3−333−300000000000004-44-4−4i4i-2121-1-22-1−i−iii2i−2i0000−i3i3i3−i3−333−300000000000004-44-4−4i4i-2121-1-22-1−i−iii2i−2i0000−i3i3i3−i3−333−30000000000000
χ394-44-4−4i4i-2121-1-22-1−i−iii2i−2i0000i3−i3−i3i33−3−3300000000000004-44-4−4i4i-2121-1-22-1−i−iii2i−2i0000i3−i3−i3i33−3−3300000000000004-44-4−4i4i-2121-1-22-1−i−iii2i−2i0000i3−i3−i3i33−3−330000000000000
χ404-4-4400-212-1-12-213-3-33002-22-2-1-111-1-11100000000000004-4-4400-212-1-12-213-3-33002-22-2-1-111-1-11100000000000004-4-4400-212-1-12-213-3-33002-22-2-1-111-1-1110000000000000
χ414-4-4400-212-1-12-213-3-3300-22-2211-1-111-1-100000000000004-4-4400-212-1-12-213-3-3300-22-2211-1-111-1-100000000000004-4-4400-212-1-12-213-3-3300-22-2211-1-111-1-10000000000000
χ424-4-4400-212-1-12-21-333-3002-2-22-1-11111-1-100000000000004-4-4400-212-1-12-21-333-3002-2-22-1-11111-1-100000000000004-4-4400-212-1-12-21-333-3002-2-22-1-11111-1-10000000000000
χ434-4-4400-212-1-12-21-333-300-222-211-1-1-1-11100000000000004-4-4400-212-1-12-21-333-300-222-211-1-1-1-11100000000000004-4-4400-212-1-12-21-333-300-222-211-1-1-1-1110000000000000
χ4488-8-8002-424-4-2-24000000000000000000000000000000088-8-8002-424-4-2-24000000000000000000000000000000088-8-8002-424-4-2-240000000000000000000000000000000
χ458-8-88002-4-244-22-400000000000000000000000000000008-8-88002-4-244-22-400000000000000000000000000000008-8-88002-4-244-22-40000000000000000000000000000000
χ46111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ471111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i321+i321+i321+i32
χ4811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ4911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ501111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-111-1-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ511111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32
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χ1324-4-4400-212-1-12-21-333-3002-2-22-1-11111-1-10000000000000−2−2i32+2i32+2i3−2−2i3001+i3−1−i32−1−i31+i321+i32−1−i31+i3−1−i323+3i32−3−3i32−3−3i323+3i3200−1−i31+i31+i3−1−i31+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i320000000000000−2+2i32−2i32−2i3−2+2i3001−i3−1+i32−1+i31−i321−i32−1+i31−i3−1+i323−3i32−3+3i32−3+3i323−3i3200−1+i31−i31−i3−1+i31−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i320000000000000
χ1334-4-4400-212-1-12-21-333-300-222-211-1-1-1-1110000000000000−2−2i32+2i32+2i3−2−2i3001+i3−1−i32−1−i31+i321+i32−1−i31+i3−1−i323+3i32−3−3i32−3−3i323+3i32001+i3−1−i3−1−i31+i3−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i320000000000000−2+2i32−2i32−2i3−2+2i3001−i3−1+i32−1+i31−i321−i32−1+i31−i3−1+i323−3i32−3+3i32−3+3i323−3i32001−i3−1+i3−1+i31−i3−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i320000000000000
χ13488-8-8002-424-4-2-240000000000000000000000000000000−4−4i3−4−4i34+4i34+4i300−1−i32+2i3−1−i3−2−2i32+2i31+i31+i3−2−2i30000000000000000000000000000000−4+4i3−4+4i34−4i34−4i300−1+i32−2i3−1+i3−2+2i32−2i31−i31−i3−2+2i30000000000000000000000000000000
χ1358-8-88002-4-244-22-40000000000000000000000000000000−4−4i34+4i34+4i3−4−4i300−1−i32+2i31+i3−2−2i3−2−2i31+i3−1−i32+2i30000000000000000000000000000000−4+4i34−4i34−4i3−4+4i300−1+i32−2i31−i3−2+2i3−2+2i31−i3−1+i32−2i30000000000000000000000000000000

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