Finite Group Databasebeta

← Group #4584

Character table — Group #4584

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222244444444444411112222224444444444441111222222444444444444
order1244222444444444448888361212666121212121212121212121224242424361212666121212121212121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ41111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111
χ511111-1-1-1-11ii−i−iii−i−i11-1-111111-1-1-1-11ii−i−iii−i−i11-1-111111-1-1-1-11ii−i−iii−i−i11-1-1
χ611111-1-1-1-11ii−i−i−i−iii-1-11111111-1-1-1-11ii−i−i−i−iii-1-11111111-1-1-1-11ii−i−i−i−iii-1-111
χ711111-1-1-1-11−i−iiiii−i−i-1-11111111-1-1-1-11−i−iiiii−i−i-1-11111111-1-1-1-11−i−iiiii−i−i-1-111
χ811111-1-1-1-11−i−iii−i−iii11-1-111111-1-1-1-11−i−iii−i−iii11-1-111111-1-1-1-11−i−iii−i−iii11-1-1
χ91111-11-11-1-11-11-1i−ii−ii−ii−i1111-11-11-1-11-11-1i−ii−ii−ii−i1111-11-11-1-11-11-1i−ii−ii−ii−i
χ101111-11-11-1-11-11-1−ii−ii−ii−ii1111-11-11-1-11-11-1−ii−ii−ii−ii1111-11-11-1-11-11-1−ii−ii−ii−ii
χ111111-11-11-1-1-11-11i−ii−i−ii−ii1111-11-11-1-1-11-11i−ii−i−ii−ii1111-11-11-1-1-11-11i−ii−i−ii−ii
χ121111-11-11-1-1-11-11−ii−iii−ii−i1111-11-11-1-1-11-11−ii−iii−ii−i1111-11-11-1-1-11-11−ii−iii−ii−i
χ131111-1-11-11-1i−i−ii1-1-11−iii−i1111-1-11-11-1i−i−ii1-1-11−iii−i1111-1-11-11-1i−i−ii1-1-11−iii−i
χ141111-1-11-11-1i−i−ii-111-1i−i−ii1111-1-11-11-1i−i−ii-111-1i−i−ii1111-1-11-11-1i−i−ii-111-1i−i−ii
χ151111-1-11-11-1−iii−i1-1-11i−i−ii1111-1-11-11-1−iii−i1-1-11i−i−ii1111-1-11-11-1−iii−i1-1-11i−i−ii
χ161111-1-11-11-1−iii−i-111-1−iii−i1111-1-11-11-1−iii−i-111-1−iii−i1111-1-11-11-1−iii−i-111-1−iii−i
χ1722-2-2222-2-2-200000000000022-2-2222-2-2-200000000000022-2-2222-2-2-2000000000000
χ1822-2-22-2-222-200000000000022-2-22-2-222-200000000000022-2-22-2-222-2000000000000
χ1922-2-2-22-2-22200000000000022-2-2-22-2-22200000000000022-2-2-22-2-222000000000000
χ2022-2-2-2-222-2200000000000022-2-2-2-222-2200000000000022-2-2-2-222-22000000000000
χ214-44i−4i0000000000000000004-44i−4i0000000000000000004-44i−4i000000000000000000
χ224-4−4i4i0000000000000000004-4−4i4i0000000000000000004-4−4i4i000000000000000000
χ231111111111111111111111−1+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
χ2411111111111111-1-1-1-1-1-1-1-1−1+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+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−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ251111111111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ261111111111-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ2711111-1-1-1-11ii−i−iii−i−i11-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1−i32−1−i321+i321+i32
χ2811111-1-1-1-11ii−i−i−i−iii-1-111−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ71−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ111+i321+i32−1−i32−1−i32
χ2911111-1-1-1-11−i−iiiii−i−i-1-111−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ71−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ111+i321+i32−1−i32−1−i32
χ3011111-1-1-1-11−i−iii−i−iii11-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1−i32−1−i321+i321+i32
χ311111-11-11-1-11-11-1i−ii−ii−ii−i−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11
χ321111-11-11-1-11-11-1−ii−ii−ii−ii−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11
χ331111-11-11-1-1-11-11i−ii−i−ii−ii−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11
χ341111-11-11-1-1-11-11−ii−iii−ii−i−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ11
χ351111-1-11-11-1i−i−ii1-1-11−iii−i−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11
χ361111-1-11-11-1i−i−ii-111-1i−i−ii−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11
χ371111-1-11-11-1−iii−i1-1-11i−i−ii−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11
χ381111-1-11-11-1−iii−i-111-1−iii−i−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11
χ3922-2-2222-2-2-2000000000000−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i31−i3000000000000−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i31+i3000000000000
χ4022-2-22-2-222-2000000000000−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i31−i3000000000000−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i31+i3000000000000
χ4122-2-2-22-2-222000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i31−i3−1+i3−1+i3000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i31+i3−1−i3−1−i3000000000000
χ4222-2-2-2-222-22000000000000−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i3−1+i3000000000000−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i3−1−i3000000000000
χ434-44i−4i000000000000000000−2+2i32−2i34ζ7−4ζ7000000000000000000−2−2i32+2i34ζ11−4ζ11000000000000000000
χ444-4−4i4i000000000000000000−2+2i32−2i3−4ζ74ζ7000000000000000000−2−2i32+2i3−4ζ114ζ11000000000000000000
χ451111111111111111111111−1−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
χ4611111111111111-1-1-1-1-1-1-1-1−1−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−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+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ471111111111-1-1-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ481111111111-1-1-1-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ4911111-1-1-1-11ii−i−iii−i−i11-1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1+i32−1+i321−i321−i32
χ5011111-1-1-1-11ii−i−i−i−iii-1-111−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ111+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ71−i321−i32−1+i32−1+i32
χ5111111-1-1-1-11−i−iiiii−i−i-1-111−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ111+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ71−i321−i32−1+i32−1+i32
χ5211111-1-1-1-11−i−iii−i−iii11-1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1+i32−1+i321−i321−i32
χ531111-11-11-1-11-11-1i−ii−ii−ii−i−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7
χ541111-11-11-1-11-11-1−ii−ii−ii−ii−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7
χ551111-11-11-1-1-11-11i−ii−i−ii−ii−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7
χ561111-11-11-1-1-11-11−ii−iii−ii−i−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ11−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ7
χ571111-1-11-11-1i−i−ii1-1-11−iii−i−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7
χ581111-1-11-11-1i−i−ii-111-1i−i−ii−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7
χ591111-1-11-11-1−iii−i1-1-11i−i−ii−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7
χ601111-1-11-11-1−iii−i-111-1−iii−i−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7
χ6122-2-2222-2-2-2000000000000−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i31+i3000000000000−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i31−i3000000000000
χ6222-2-22-2-222-2000000000000−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i31+i3000000000000−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i31−i3000000000000
χ6322-2-2-22-2-222000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i31+i3−1−i3−1−i3000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i31−i3−1+i3−1+i3000000000000
χ6422-2-2-2-222-22000000000000−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i3−1−i3000000000000−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i3−1+i3000000000000
χ654-44i−4i000000000000000000−2−2i32+2i34ζ11−4ζ11000000000000000000−2+2i32−2i34ζ7−4ζ7000000000000000000
χ664-4−4i4i000000000000000000−2−2i32+2i3−4ζ114ζ11000000000000000000−2+2i32−2i3−4ζ74ζ7000000000000000000

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