Finite Group Databasebeta

← Group #72710

Character table — Group #72710

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222444444444444888888881111111122224444444444448888888811111111222244444444444488888888
order1222444422444444444444444444888836661212121266121212121212121212121212121212121212242424243666121212126612121212121212121212121212121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-11111-1-1-1-111-1-111-1-1111111111111-1-1-1-11111-1-1-1-111-1-111-1-1111111111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111-1-1-1-11111-1-1-1-1-1-111-1-111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ7111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ8111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ91111-1-1-1-1-1-11111-1-1ii−i−iii−i−i1-11-1i−ii−i1111-1-1-1-1-1-11111-1-1ii−i−iii−i−i1-11-1i−ii−i1111-1-1-1-1-1-11111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ101111-1-1-1-1-1-11111-1-1ii−i−iii−i−i-11-11−ii−ii1111-1-1-1-1-1-11111-1-1ii−i−iii−i−i-11-11−ii−ii1111-1-1-1-1-1-11111-1-1ii−i−iii−i−i-11-11−ii−ii
χ111111-1-1-1-1-1-11111-1-1−i−iii−i−iii1-11-1−ii−ii1111-1-1-1-1-1-11111-1-1−i−iii−i−iii1-11-1−ii−ii1111-1-1-1-1-1-11111-1-1−i−iii−i−iii1-11-1−ii−ii
χ121111-1-1-1-1-1-11111-1-1−i−iii−i−iii-11-11i−ii−i1111-1-1-1-1-1-11111-1-1−i−iii−i−iii-11-11i−ii−i1111-1-1-1-1-1-11111-1-1−i−iii−i−iii-11-11i−ii−i
χ131111-1-1-1-1-1-111-1-111ii−i−i−i−iii1-1-11i−i−ii1111-1-1-1-1-1-111-1-111ii−i−i−i−iii1-1-11i−i−ii1111-1-1-1-1-1-111-1-111ii−i−i−i−iii1-1-11i−i−ii
χ141111-1-1-1-1-1-111-1-111ii−i−i−i−iii-111-1−iii−i1111-1-1-1-1-1-111-1-111ii−i−i−i−iii-111-1−iii−i1111-1-1-1-1-1-111-1-111ii−i−i−i−iii-111-1−iii−i
χ151111-1-1-1-1-1-111-1-111−i−iiiii−i−i1-1-11−iii−i1111-1-1-1-1-1-111-1-111−i−iiiii−i−i1-1-11−iii−i1111-1-1-1-1-1-111-1-111−i−iiiii−i−i1-1-11−iii−i
χ161111-1-1-1-1-1-111-1-111−i−iiiii−i−i-111-1i−i−ii1111-1-1-1-1-1-111-1-111−i−iiiii−i−i-111-1i−i−ii1111-1-1-1-1-1-111-1-111−i−iiiii−i−i-111-1i−i−ii
χ1722222222-2-2-2-22-22-2000000000000000022222222-2-2-2-22-22-2000000000000000022222222-2-2-2-22-22-20000000000000000
χ1822222222-2-2-2-2-22-22000000000000000022222222-2-2-2-2-22-22000000000000000022222222-2-2-2-2-22-220000000000000000
χ192222-2-2-2-222-2-22-2-2200000000000000002222-2-2-2-222-2-22-2-2200000000000000002222-2-2-2-222-2-22-2-220000000000000000
χ202222-2-2-2-222-2-2-222-200000000000000002222-2-2-2-222-2-2-222-200000000000000002222-2-2-2-222-2-2-222-20000000000000000
χ2122-2-222-2-22-22-2000000002-22-20000000022-2-222-2-22-22-2000000002-22-20000000022-2-222-2-22-22-2000000002-22-200000000
χ2222-2-222-2-22-22-200000000-22-220000000022-2-222-2-22-22-200000000-22-220000000022-2-222-2-22-22-200000000-22-2200000000
χ2322-2-222-2-2-22-2200002-22-200000000000022-2-222-2-2-22-2200002-22-200000000000022-2-222-2-2-22-2200002-22-2000000000000
χ2422-2-222-2-2-22-220000-22-2200000000000022-2-222-2-2-22-220000-22-2200000000000022-2-222-2-2-22-220000-22-22000000000000
χ2522-2-2-2-2222-2-2200002i−2i−2i2i00000000000022-2-2-2-2222-2-2200002i−2i−2i2i00000000000022-2-2-2-2222-2-2200002i−2i−2i2i000000000000
χ2622-2-2-2-2222-2-220000−2i2i2i−2i00000000000022-2-2-2-2222-2-220000−2i2i2i−2i00000000000022-2-2-2-2222-2-220000−2i2i2i−2i000000000000
χ2722-2-2-2-222-222-2000000002i−2i−2i2i0000000022-2-2-2-222-222-2000000002i−2i−2i2i0000000022-2-2-2-222-222-2000000002i−2i−2i2i00000000
χ2822-2-2-2-222-222-200000000−2i2i2i−2i0000000022-2-2-2-222-222-200000000−2i2i2i−2i0000000022-2-2-2-222-222-200000000−2i2i2i−2i00000000
χ294-44-44i−4i4i−4i0000000000000000000000004-44-44i−4i4i−4i0000000000000000000000004-44-44i−4i4i−4i000000000000000000000000
χ304-44-4−4i4i−4i4i0000000000000000000000004-44-4−4i4i−4i4i0000000000000000000000004-44-4−4i4i−4i4i000000000000000000000000
χ314-4-444i−4i−4i4i0000000000000000000000004-4-444i−4i−4i4i0000000000000000000000004-4-444i−4i−4i4i000000000000000000000000
χ324-4-44−4i4i4i−4i0000000000000000000000004-4-44−4i4i4i−4i0000000000000000000000004-4-44−4i4i4i−4i000000000000000000000000
χ3311111111111111111111111111111111−1+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
χ34111111111111111111111111-1-1-1-1-1-1-1-1−1+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+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−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+i32
χ351111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−1+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+i321−i321−i321−i321−i321−i321−i321−i321−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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ361111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−1+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−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
χ37111111111111-1-1-1-11111-1-1-1-111-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ38111111111111-1-1-1-11111-1-1-1-1-1-111-1-111−1+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−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−i32−1−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−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ39111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111−1+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−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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ40111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ411111-1-1-1-1-1-11111-1-1ii−i−iii−i−i1-11-1i−ii−i−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11
χ421111-1-1-1-1-1-11111-1-1ii−i−iii−i−i-11-11−ii−ii−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11
χ431111-1-1-1-1-1-11111-1-1−i−iii−i−iii1-11-1−ii−ii−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11
χ441111-1-1-1-1-1-11111-1-1−i−iii−i−iii-11-11i−ii−i−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11
χ451111-1-1-1-1-1-111-1-111ii−i−i−i−iii1-1-11i−i−ii−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11
χ461111-1-1-1-1-1-111-1-111ii−i−i−i−iii-111-1−iii−i−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ71−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ111+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11
χ471111-1-1-1-1-1-111-1-111−i−iiiii−i−i1-1-11−iii−i−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11
χ481111-1-1-1-1-1-111-1-111−i−iiiii−i−i-111-1i−i−ii−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ71−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ111+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11
χ4922222222-2-2-2-22-22-20000000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i31−i3−1+i31−i30000000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i31+i3−1−i31+i30000000000000000
χ5022222222-2-2-2-2-22-220000000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i3−1+i31−i3−1+i30000000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i3−1−i31+i3−1−i30000000000000000
χ512222-2-2-2-222-2-22-2-220000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i30000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i30000000000000000
χ522222-2-2-2-222-2-2-222-20000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i30000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i30000000000000000
χ5322-2-222-2-22-22-2000000002-22-200000000−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i300000000−1+i31−i3−1+i31−i300000000−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i300000000−1−i31+i3−1−i31+i300000000
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χ9122-2-2-2-222-222-2000000002i−2i−2i2i00000000−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i3−1−i3−1−i31+i3000000002ζ11−2ζ11−2ζ112ζ1100000000−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i3−1+i3−1+i31−i3000000002ζ7−2ζ7−2ζ72ζ700000000
χ9222-2-2-2-222-222-200000000−2i2i2i−2i00000000−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i3−1−i3−1−i31+i300000000−2ζ112ζ112ζ11−2ζ1100000000−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i3−1+i3−1+i31−i300000000−2ζ72ζ72ζ7−2ζ700000000
χ934-44-44i−4i4i−4i000000000000000000000000−2−2i32+2i3−2−2i32+2i34ζ11−4ζ114ζ11−4ζ11000000000000000000000000−2+2i32−2i3−2+2i32−2i34ζ7−4ζ74ζ7−4ζ7000000000000000000000000
χ944-44-4−4i4i−4i4i000000000000000000000000−2−2i32+2i3−2−2i32+2i3−4ζ114ζ11−4ζ114ζ11000000000000000000000000−2+2i32−2i3−2+2i32−2i3−4ζ74ζ7−4ζ74ζ7000000000000000000000000
χ954-4-444i−4i−4i4i000000000000000000000000−2−2i32+2i32+2i3−2−2i34ζ11−4ζ11−4ζ114ζ11000000000000000000000000−2+2i32−2i32−2i3−2+2i34ζ7−4ζ7−4ζ74ζ7000000000000000000000000
χ964-4-44−4i4i4i−4i000000000000000000000000−2−2i32+2i32+2i3−2−2i3−4ζ114ζ114ζ11−4ζ11000000000000000000000000−2+2i32−2i32−2i3−2+2i3−4ζ74ζ74ζ7−4ζ7000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.