Finite Group Databasebeta

← Group #13162037

Character table — Group #13162037

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181836363636363636363636363636363636363636363636363672727272
order1244233346661212121212122333334666666666612121212121212121212121212121266666666666666666121212121212121212121212121212121222446612122444446668888121212121212121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-11111-1-111
χ5111111111111111111-111111-11-1-11111111111-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-111111-1-1-1-1-1-11-1-111111111-1-1-1-1
χ6111111111111111111-111111-11-1-11111111111-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-111111-11-1-11111111111-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-1111111-1-1-1-1-1-111
χ8111111111111111111-111111-11-1-11111111111-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11111-1-1-111-1-1-1-1111111-1-1
χ911-1-1-11111111-1-1-1-1-1-1111111-1-11111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-11-11-111-1-11-1i−ii−i-111i−ii−i1-1-1ii−i−iii−i−ii−ii−i
χ1011-1-1-11111111-1-1-1-1-1-1111111-1-11111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-11-11-111-1-11-1−ii−ii-111−ii−ii1-1-1−i−iii−i−iii−ii−ii
χ1111-1-1-11111111-1-1-1-1-1-1111111-1-11111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11i−i−ii1-1-1i−i−ii-111ii−i−i−i−iiii−i−ii
χ1211-1-1-11111111-1-1-1-1-1-1111111-1-11111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11−iii−i1-1-1−iii−i-111−i−iiiii−i−i−iii−i
χ1311-1-1-11111111-1-1-1-1-1-1-1111111-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-11-111-1-1-11i−ii−i-1-1-1−ii−ii111ii−i−iii−i−i−ii−ii
χ1411-1-1-11111111-1-1-1-1-1-1-1111111-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-11-111-1-1-11−ii−ii-1-1-1i−ii−i111−i−iii−i−iiii−ii−i
χ1511-1-1-11111111-1-1-1-1-1-1-1111111-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-11-1-1111-1i−i−ii111−iii−i-1-1-1ii−i−i−i−iii−iii−i
χ1611-1-1-11111111-1-1-1-1-1-1-1111111-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-11-1-1111-1−iii−i111i−i−ii-1-1-1−i−iiiii−i−ii−i−ii
χ172222222-1222-1-1-1222222-1-1-1-12-1-1-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1220000-1-1-10000-1-1-1000000000000
χ182222222-1222-1-1-1222222-1-1-1-12-1-1-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-2-200001110000111000000000000
χ192222222-1222-1-1-12222-22-1-1-1-1-2-1112-1-1-1-12222-11122-1-1-1-1-1-1-1-1-2-22-1-1-1-1-2-211111111-2-22-1-1-1-1-2-2111111112222-1-1-1-1-2-20000-1110000-111000000000000
χ202222222-1222-1-1-12222-22-1-1-1-1-2-1112-1-1-1-12222-11122-1-1-1-1-1-1-1-1-2-22-1-1-1-1-2-211111111-2-22-1-1-1-1-2-211111111-2-2-2-211112200001-1-100001-1-1000000000000
χ21222222-1222-122222-1-12-12-1-1-12222-12-1-1-12-12-1222-1-122-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-10000000000002200000220000000-1-1-1-100-1-1
χ22222222-1222-122222-1-12-12-1-1-12222-12-1-1-12-12-1222-1-122-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-1000000000000-2-200000-2-2000000011110011
χ23222222-1222-122222-1-1-2-12-1-1-1-22-2-2-12-1-1-12-12-12-2-2-1-122-1-1-1-1-1-1-21-12-1-1-111-2-2111111-21-12-1-1-111-2-21111110000000000002200000-2-20000000-1-1-1-10011
χ24222222-1222-122222-1-1-2-12-1-1-1-22-2-2-12-1-1-12-12-12-2-2-1-122-1-1-1-1-1-1-21-12-1-1-111-2-2111111-21-12-1-1-111-2-2111111000000000000-2-200000220000000111100-1-1
χ2522222-1222-12222-1-1222-1-12-1-12222-1-12-1-1-12-12222-1-1-1-122-1-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-1000000000022000002200000-1-1-1-10000-1-100
χ2622222-1222-12222-1-1222-1-12-1-12222-1-12-1-1-12-12222-1-1-1-122-1-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-10000000000-2-200000-2-200000111100001100
χ2722222-1222-12222-1-122-2-1-12-1-1-22-2-2-1-12-1-1-12-122-2-2-1-1-1-122-1-1-1-11-2-1-12-1-11111-2-211111-2-1-12-1-11111-2-2111100000000002200000-2-200000-1-1-1-100001100
χ2822222-1222-12222-1-122-2-1-12-1-1-22-2-2-1-12-1-1-12-122-2-2-1-1-1-122-1-1-1-11-2-1-12-1-11111-2-211111-2-1-12-1-11111-2-211110000000000-2-200000220000011110000-1-100
χ292222-2222-22222222220222220-20022222-2-2-2-2-200222222222200-2-2-2-2-2000000000000-2-2-2-2-200000000002-2-222222000000-2000000-200000000000000
χ302222-2222-22222222220222220-20022222-2-2-2-2-200222222222200-2-2-2-2-2000000000000-2-2-2-2-20000000000-222-2-2-2-2-20000002000000200000000000000
χ312222-222-1-222-1-1-1222202-1-1-1-101−i3i32-1-1-1-1-2-2-2-21−i3i322-1-1-1-1-1-1-1-100-2111100−i3i3−i3i3−i3−i3i3i300-2111100−i3i3−i3i3−i3−i3i3i32-2-22-1-1-1-10000001−i3i300001−i3i3000000000000
χ322222-222-1-222-1-1-1222202-1-1-1-101−i3i32-1-1-1-1-2-2-2-21−i3i322-1-1-1-1-1-1-1-100-2111100−i3i3−i3i3−i3−i3i3i300-2111100−i3i3−i3i3−i3−i3i3i3-222-21111000000-1i3−i30000-1i3−i3000000000000
χ332222-222-1-222-1-1-1222202-1-1-1-101i3−i32-1-1-1-1-2-2-2-21i3−i322-1-1-1-1-1-1-1-100-2111100i3−i3i3−i3i3i3−i3−i300-2111100i3−i3i3−i3i3i3−i3−i32-2-22-1-1-1-10000001i3−i300001i3−i3000000000000
χ342222-222-1-222-1-1-1222202-1-1-1-101i3−i32-1-1-1-1-2-2-2-21i3−i322-1-1-1-1-1-1-1-100-2111100i3−i3i3−i3i3i3−i3−i300-2111100i3−i3i3−i3i3i3−i3−i3-222-21111000000-1−i3i30000-1−i3i3000000000000
χ3522-2-22222-2222-2-2-2-2-2-202222202002222222-2-2-200-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-2000000000022-2-222-2-20000002000000-200000000000000
χ3622-2-22222-2222-2-2-2-2-2-202222202002222222-2-2-200-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-20000000000-2-222-2-222000000-2000000200000000000000
χ3722-2-2222-1-222-111-2-2-2-202-1-1-1-10-1−i3i32-1-1-1-122-2-21i3−i3-2-211111111002-1-1-1-100−i3i3−i3i3−i3−i3i3i300-2111100i3−i3i3−i3i3i3−i3−i322-2-2-1-111000000-1−i3i300001i3−i3000000000000
χ3822-2-2222-1-222-111-2-2-2-202-1-1-1-10-1−i3i32-1-1-1-122-2-21i3−i3-2-211111111002-1-1-1-100−i3i3−i3i3−i3−i3i3i300-2111100i3−i3i3−i3i3i3−i3−i3-2-22211-1-10000001i3−i30000-1−i3i3000000000000
χ3922-2-2222-1-222-111-2-2-2-202-1-1-1-10-1i3−i32-1-1-1-122-2-21−i3i3-2-211111111002-1-1-1-100i3−i3i3−i3i3i3−i3−i300-2111100−i3i3−i3i3−i3−i3i3i322-2-2-1-111000000-1i3−i300001−i3i3000000000000
χ4022-2-2222-1-222-111-2-2-2-202-1-1-1-10-1i3−i32-1-1-1-122-2-21−i3i3-2-211111111002-1-1-1-100i3−i3i3−i3i3i3−i3−i300-2111100−i3i3−i3i3−i3−i3i3i3-2-22211-1-10000001−i3i30000-1i3−i3000000000000
χ4122-2-2-222-1222-111-2-2-2-222-1-1-1-1-21-1-12-1-1-1-1-2-222-111-2-21111111122-2111122-1-1-1-1-1-1-1-1-2-22-1-1-1-1-2-2111111112-22-2-1-1112-200001-1-10000-111000000000000
χ4222-2-2-222-1222-111-2-2-2-222-1-1-1-1-21-1-12-1-1-1-1-2-222-111-2-21111111122-2111122-1-1-1-1-1-1-1-1-2-22-1-1-1-1-2-211111111-22-2211-1-1-220000-11100001-1-1000000000000
χ4322-2-2-222-1222-111-2-2-2-2-22-1-1-1-121112-1-1-1-1-2-222-1-1-1-2-211111111-2-2-21111-2-211111111222-1-1-1-122-1-1-1-1-1-1-1-12-22-2-1-111-2200001110000-1-1-1000000000000
χ4422-2-2-222-1222-111-2-2-2-2-22-1-1-1-121112-1-1-1-1-2-222-1-1-1-2-211111111-2-2-21111-2-211111111222-1-1-1-122-1-1-1-1-1-1-1-1-22-2211-1-12-20000-1-1-10000111000000000000
χ4522-2-2-22-1222-12-2-2-2-2112-12-1-1-1-2-222-12-1-1-1-212-12-2-211-2-21111112-11-2111-1-122-1-1-1-1-1-1-21-12-1-1-111-2-21111110000000000002i−2i000002i−2i0000000−i−iii00−ii
χ4622-2-2-22-1222-12-2-2-2-2112-12-1-1-1-2-222-12-1-1-1-212-12-2-211-2-21111112-11-2111-1-122-1-1-1-1-1-1-21-12-1-1-111-2-2111111000000000000−2i2i00000−2i2i0000000ii−i−i00i−i
χ4722-2-2-22-1222-12-2-2-2-211-2-12-1-1-12-2-2-2-12-1-1-1-212-122211-2-2111111-211-211111-2-21111112-1-12-1-1-1-1-122-1-1-1-1-1-10000000000002i−2i00000−2i2i0000000−i−iii00i−i
χ4822-2-2-22-1222-12-2-2-2-211-2-12-1-1-12-2-2-2-12-1-1-1-212-122211-2-2111111-211-211111-2-21111112-1-12-1-1-1-1-122-1-1-1-1-1-1000000000000−2i2i000002i−2i0000000ii−i−i00−ii
χ4922-2-2-2-1222-122-2-211-2-22-1-12-1-1-2-222-1-12-1-11-2-122-2-21111-2-21111-1211-211-1-1-1-122-1-1-1-11-2-1-12-1-11111-2-2111100000000002i−2i000002i−2i00000−i−iii0000−ii00
χ5022-2-2-2-1222-122-2-211-2-22-1-12-1-1-2-222-1-12-1-11-2-122-2-21111-2-21111-1211-211-1-1-1-122-1-1-1-11-2-1-12-1-11111-2-211110000000000−2i2i00000−2i2i00000ii−i−i0000i−i00
χ5122-2-2-2-1222-122-2-211-2-2-2-1-12-1-12-2-2-2-1-12-1-11-2-122221111-2-211111-211-2111111-2-21111-12-1-12-1-1-1-1-1-122-1-1-1-100000000002i−2i00000−2i2i00000−i−iii0000i−i00
χ5222-2-2-2-1222-122-2-211-2-2-2-1-12-1-12-2-2-2-1-12-1-11-2-122221111-2-211111-211-2111111-2-21111-12-1-12-1-1-1-1-1-122-1-1-1-10000000000−2i2i000002i−2i00000ii−i−i0000−ii00
χ53444444-2-244-2-2-2-244-2-24-2-21114-2-2-2-2-21114-24-2-2-2-2-2-2-2-21111114-2-2-2111-2-2-2-21111114-2-2-2111-2-2-2-2111111000000000000000000000000000000000000
χ54444444-2-244-2-2-2-244-2-2-4-2-2111-4-222-2-21114-24-2-222-2-2-2-2111111-42-2-21112222-1-1-1-1-1-1-42-2-21112222-1-1-1-1-1-1000000000000000000000000000000000000
χ5544444-24-24-24-2-2-2-2-2444-21-2114-2-2-2-21-211-24-24-2-2-2-2-211-2-21111-24-21-211-2-211-2-21111-24-21-211-2-211-2-21111000000000000000000000000000000000000
χ5644444-24-24-24-2-2-2-2-244-4-21-211-4-222-21-211-24-24-222-2-211-2-211112-4-21-21122-1-122-1-1-1-12-4-21-21122-1-122-1-1-1-1000000000000000000000000000000000000
χ5744444-2-244-2-2444-2-2-2-241-2-21144441-2-211-2-2-2-244411-2-2-2-21111-2-21-2-21111-2-2-2-21111-2-21-2-21111-2-2-2-21111000000000000000000000000000000000000
χ5844444-2-244-2-2444-2-2-2-2-41-2-211-44-4-41-2-211-2-2-2-24-4-411-2-2-2-21111221-2-211-1-12222-1-1-1-1221-2-211-1-12222-1-1-1-1000000000000000000000000000000000000
χ5944444-2-2-24-2-2-2-2-2-2-2-2-24111−1−3i32−1+3i324-2-2-2111−1−3i32−1+3i32-2-2-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000000000
χ6044444-2-2-24-2-2-2-2-2-2-2-2-24111−1+3i32−1−3i324-2-2-2111−1+3i32−1−3i32-2-2-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000000000
χ6144444-2-2-24-2-2-2-2-2-2-2-2-2-4111−1−3i32−1+3i32-4-222111−1−3i32−1+3i32-2-2-2-2-222111111−1−3i32−1−3i32−1+3i32−1+3i3222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i3222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000000
χ6244444-2-2-24-2-2-2-2-2-2-2-2-2-4111−1+3i32−1−3i32-4-222111−1+3i32−1−3i32-2-2-2-2-222111111−1+3i32−1+3i32−1−3i32−1−3i3222111−1+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+3i32000000000000000000000000000000000000
χ634444-44-24-44-244444-2-20-24-2-2-20-400-24-2-2-2-42-42-400-2-244-2-2-2-2-2-2002-42220000000000002-42220000000000000000000000000000000000000000000000
χ644444-44-2-2-44-2-2-2-244-2-20-2-211102−2i32i3-2-2111-42-422−2i32i3-2-2-2-21111110022-1-1-100−2i32i3i3−i3i3i3−i3−i30022-1-1-100−2i32i3i3−i3i3i3−i3−i3000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.