Finite Group Databasebeta

← Group #13180944

Character table — Group #13180944

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size12888999181818272727271288899918181827272727241616161818183636365454545424161616181818363636545454542416161618181836363654545454
order1333324461212888826666244612128888412121212444121212888841212121244412121288884121212124441212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111-1-1-1-111111111111-1-1-1-111111111111-1-1-1-111111111111-1-1-1-111111111111-1-1-1-1
χ3111111-1-11-1-1ii−i−i111111-1-11-1-1ii−i−i111111-1-11-1-1ii−i−i111111-1-11-1-1ii−i−i111111-1-11-1-1ii−i−i
χ4111111-1-11-1-1−i−iii111111-1-11-1-1−i−iii111111-1-11-1-1−i−iii111111-1-11-1-1−i−iii111111-1-11-1-1−i−iii
χ511111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ611111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ711111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ811111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ92-12-1-1222-1-1-100002-12-1-1222-1-1-100002-12-1-1222-1-1-100002-12-1-1222-1-1-100002-12-1-1222-1-1-10000
χ102-12-1-12-2-2-11100002-12-1-12-2-2-11100002-12-1-12-2-2-11100002-12-1-12-2-2-11100002-12-1-12-2-2-1110000
χ112-12-1-1-22i−2i1−ii00002-12-1-1-22i−2i1−ii00002-12-1-1-22i−2i1−ii00002-12-1-1-22i−2i1−ii00002-12-1-1-22i−2i1−ii0000
χ122-12-1-1-2−2i2i1i−i00002-12-1-1-2−2i2i1i−i00002-12-1-1-2−2i2i1i−i00002-12-1-1-2−2i2i1i−i00002-12-1-1-2−2i2i1i−i0000
χ1388-1-1-1000000000088-1-1-1000000000088-1-1-1000000000088-1-1-1000000000088-1-1-10000000000
χ148-4-11−3i321+3i3200000000008-4-11−3i321+3i3200000000008-4-11−3i321+3i3200000000008-4-11−3i321+3i3200000000008-4-11−3i321+3i320000000000
χ158-4-11+3i321−3i3200000000008-4-11+3i321−3i3200000000008-4-11+3i321−3i3200000000008-4-11+3i321−3i3200000000008-4-11+3i321−3i320000000000
χ16111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1711111111111-1-1-1-111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111
χ18111111-1-11-1-1ii−i−i111111-1-11-1-1ii−i−i111111-1-11-1-1ii−i−i-1-1-1-1-1-111-111−i−iii-1-1-1-1-1-111-111−i−iii
χ19111111-1-11-1-1−i−iii111111-1-11-1-1−i−iii111111-1-11-1-1−i−iii-1-1-1-1-1-111-111ii−i−i-1-1-1-1-1-111-111ii−i−i
χ2011111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-1-1-1-11−ii1−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-1-1-1-11−ii1−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ2111111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-1-1-1-11−ii1−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-1-1-1-11−ii1−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ2211111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-1-1-1-11i−i1i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-1-1-1-11i−i1i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-1-1-1-11i−i1i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-1-1-1-11i−i1i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ242-12-1-1222-1-1-100002-12-1-1222-1-1-100002-12-1-1222-1-1-10000-21-211-2-2-21110000-21-211-2-2-21110000
χ252-12-1-12-2-2-11100002-12-1-12-2-2-11100002-12-1-12-2-2-1110000-21-211-2221-1-10000-21-211-2221-1-10000
χ262-12-1-1-22i−2i1−ii00002-12-1-1-22i−2i1−ii00002-12-1-1-22i−2i1−ii0000-21-2112−2i2i-1i−i0000-21-2112−2i2i-1i−i0000
χ272-12-1-1-2−2i2i1i−i00002-12-1-1-2−2i2i1i−i00002-12-1-1-2−2i2i1i−i0000-21-21122i−2i-1−ii0000-21-21122i−2i-1−ii0000
χ2888-1-1-1000000000088-1-1-1000000000088-1-1-10000000000-8-81110000000000-8-81110000000000
χ298-4-11−3i321+3i3200000000008-4-11−3i321+3i3200000000008-4-11−3i321+3i320000000000-841−1+3i32−1−3i320000000000-841−1+3i32−1−3i320000000000
χ308-4-11+3i321−3i3200000000008-4-11+3i321−3i3200000000008-4-11+3i321−3i320000000000-841−1−3i32−1+3i320000000000-841−1−3i32−1+3i320000000000
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3211111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ33111111-1-11-1-1ii−i−i111111-1-11-1-1ii−i−i-1-1-1-1-1-111-111−i−iii111111-1-11-1-1ii−i−i-1-1-1-1-1-111-111−i−iii
χ34111111-1-11-1-1−i−iii111111-1-11-1-1−i−iii-1-1-1-1-1-111-111ii−i−i111111-1-11-1-1−i−iii-1-1-1-1-1-111-111ii−i−i
χ3511111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-1-1-1-11−ii1−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-1-1-1-11−ii1−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ3611111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-1-1-1-11−ii1−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-1-1-1-11−ii1−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ3711111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-1-1-1-11i−i1i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-1-1-1-11i−i1i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ3811111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-1-1-1-11i−i1i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-1-1-1-11i−i1i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ392-12-1-1222-1-1-100002-12-1-1222-1-1-10000-21-211-2-2-211100002-12-1-1222-1-1-10000-21-211-2-2-21110000
χ402-12-1-12-2-2-11100002-12-1-12-2-2-1110000-21-211-2221-1-100002-12-1-12-2-2-1110000-21-211-2221-1-10000
χ412-12-1-1-22i−2i1−ii00002-12-1-1-22i−2i1−ii0000-21-2112−2i2i-1i−i00002-12-1-1-22i−2i1−ii0000-21-2112−2i2i-1i−i0000
χ422-12-1-1-2−2i2i1i−i00002-12-1-1-2−2i2i1i−i0000-21-21122i−2i-1−ii00002-12-1-1-2−2i2i1i−i0000-21-21122i−2i-1−ii0000
χ4388-1-1-1000000000088-1-1-10000000000-8-8111000000000088-1-1-10000000000-8-81110000000000
χ448-4-11−3i321+3i3200000000008-4-11−3i321+3i320000000000-841−1+3i32−1−3i3200000000008-4-11−3i321+3i320000000000-841−1+3i32−1−3i320000000000
χ458-4-11+3i321−3i3200000000008-4-11+3i321−3i320000000000-841−1−3i32−1+3i3200000000008-4-11+3i321−3i320000000000-841−1−3i32−1+3i320000000000
χ46111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111
χ4711111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1
χ48111111-1-11-1-1ii−i−i111111-1-11-1-1ii−i−i-1-1-1-1-1-111-111−i−iii-1-1-1-1-1-111-111−i−iii111111-1-11-1-1ii−i−i
χ49111111-1-11-1-1−i−iii111111-1-11-1-1−i−iii-1-1-1-1-1-111-111ii−i−i-1-1-1-1-1-111-111ii−i−i111111-1-11-1-1−i−iii
χ5011111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-1-1-1-11−ii1−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-1-1-1-11−ii1−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311111-1i−i-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ5111111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-1-1-1-11−ii1−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-1-1-1-11−ii1−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311111-1i−i-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ5211111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-1-1-1-11i−i1i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-1-1-1-11i−i1i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311111-1−ii-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ5311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-1-1-1-11i−i1i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-1-1-1-11i−i1i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311111-1−ii-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ542-12-1-1222-1-1-100002-12-1-1222-1-1-10000-21-211-2-2-21110000-21-211-2-2-211100002-12-1-1222-1-1-10000
χ552-12-1-12-2-2-11100002-12-1-12-2-2-1110000-21-211-2221-1-10000-21-211-2221-1-100002-12-1-12-2-2-1110000
χ562-12-1-1-22i−2i1−ii00002-12-1-1-22i−2i1−ii0000-21-2112−2i2i-1i−i0000-21-2112−2i2i-1i−i00002-12-1-1-22i−2i1−ii0000
χ572-12-1-1-2−2i2i1i−i00002-12-1-1-2−2i2i1i−i0000-21-21122i−2i-1−ii0000-21-21122i−2i-1−ii00002-12-1-1-2−2i2i1i−i0000
χ5888-1-1-1000000000088-1-1-10000000000-8-81110000000000-8-8111000000000088-1-1-10000000000
χ598-4-11−3i321+3i3200000000008-4-11−3i321+3i320000000000-841−1+3i32−1−3i320000000000-841−1+3i32−1−3i3200000000008-4-11−3i321+3i320000000000
χ608-4-11+3i321−3i3200000000008-4-11+3i321−3i320000000000-841−1−3i32−1+3i320000000000-841−1−3i32−1+3i3200000000008-4-11+3i321−3i320000000000
χ61222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000
χ6222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000
χ63222222-2-22-2-22i2i−2i−2i-2-2-2-2-2-222-222−2i−2i2i2i000000000000000000000000000000000000000000000
χ64222222-2-22-2-2−2i−2i2i2i-2-2-2-2-2-222-2222i2i−2i−2i000000000000000000000000000000000000000000000
χ6522222-22i−2i-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-2-2-2-2-22−2i2i2−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000000000000000000000
χ6622222-22i−2i-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-2-2-2-2-22−2i2i2−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000000000000000000000
χ6722222-2−2i2i-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-2-2-2-2-222i−2i22i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000000000000000000000
χ6822222-2−2i2i-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-2-2-2-2-222i−2i22i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000000000000000000
χ694-24-2-2444-2-2-20000-42-422-4-4-42220000000000000000000000000000000000000000000000000
χ704-24-2-24-4-4-2220000-42-422-4442-2-20000000000000000000000000000000000000000000000000
χ714-24-2-2-44i−4i2−2i2i0000-42-4224−4i4i-22i−2i0000000000000000000000000000000000000000000000000
χ724-24-2-2-4−4i4i22i−2i0000-42-42244i−4i-2−2i2i0000000000000000000000000000000000000000000000000
χ731616-2-2-20000000000-16-162220000000000000000000000000000000000000000000000000000000
χ7416-8-21−3i31+3i30000000000-1682−1+3i3−1−3i30000000000000000000000000000000000000000000000000000000
χ7516-8-21+3i31−3i30000000000-1682−1−3i3−1+3i30000000000000000000000000000000000000000000000000000000

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