Finite Group Databasebeta

← Group #4591

Character table — Group #4591

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222244444444444411112222224444444444441111222222444444444444
order1244222444444488888888361212666121212121212122424242424242424361212666121212121212122424242424242424
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
χ511111-1-11-1-1ii−i−i11-1-1ii−i−i11111-1-11-1-1ii−i−i11-1-1ii−i−i11111-1-11-1-1ii−i−i11-1-1ii−i−i
χ611111-1-11-1-1ii−i−i-1-111−i−iii11111-1-11-1-1ii−i−i-1-111−i−iii11111-1-11-1-1ii−i−i-1-111−i−iii
χ711111-1-11-1-1−i−iii11-1-1−i−iii11111-1-11-1-1−i−iii11-1-1−i−iii11111-1-11-1-1−i−iii11-1-1−i−iii
χ811111-1-11-1-1−i−iii-1-111ii−i−i11111-1-11-1-1−i−iii-1-111ii−i−i11111-1-11-1-1−i−iii-1-111ii−i−i
χ911-1-1111-1-1-11-11-1i−ii−ii−ii−i11-1-1111-1-1-11-11-1i−ii−ii−ii−i11-1-1111-1-1-11-11-1i−ii−ii−ii−i
χ1011-1-1111-1-1-11-11-1−ii−ii−ii−ii11-1-1111-1-1-11-11-1−ii−ii−ii−ii11-1-1111-1-1-11-11-1−ii−ii−ii−ii
χ1111-1-1111-1-1-1-11-11i−ii−i−ii−ii11-1-1111-1-1-1-11-11i−ii−i−ii−ii11-1-1111-1-1-1-11-11i−ii−i−ii−ii
χ1211-1-1111-1-1-1-11-11−ii−iii−ii−i11-1-1111-1-1-1-11-11−ii−iii−ii−i11-1-1111-1-1-1-11-11−ii−iii−ii−i
χ1311-1-11-1-1-111i−i−iii−i−ii-111-111-1-11-1-1-111i−i−iii−i−ii-111-111-1-11-1-1-111i−i−iii−i−ii-111-1
χ1411-1-11-1-1-111i−i−ii−iii−i1-1-1111-1-11-1-1-111i−i−ii−iii−i1-1-1111-1-11-1-1-111i−i−ii−iii−i1-1-11
χ1511-1-11-1-1-111−iii−ii−i−ii1-1-1111-1-11-1-1-111−iii−ii−i−ii1-1-1111-1-11-1-1-111−iii−ii−i−ii1-1-11
χ1611-1-11-1-1-111−iii−i−iii−i-111-111-1-11-1-1-111−iii−i−iii−i-111-111-1-11-1-1-111−iii−i−iii−i-111-1
χ172222-22-2-2-220000000000002222-22-2-2-220000000000002222-22-2-2-22000000000000
χ182222-2-22-22-20000000000002222-2-22-22-20000000000002222-2-22-22-2000000000000
χ1922-2-2-22-222-200000000000022-2-2-22-222-200000000000022-2-2-22-222-2000000000000
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
χ2711111-1-11-1-1ii−i−i11-1-1ii−i−i−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11
χ2811111-1-11-1-1ii−i−i-1-111−i−iii−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ71−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ111+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11
χ2911111-1-11-1-1−i−iii11-1-1−i−iii−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11
χ3011111-1-11-1-1−i−iii-1-111ii−i−i−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ71−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ111+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11
χ3111-1-1111-1-1-11-11-1i−ii−ii−ii−i−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11
χ3211-1-1111-1-1-11-11-1−ii−ii−ii−ii−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11
χ3311-1-1111-1-1-1-11-11i−ii−i−ii−ii−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11
χ3411-1-1111-1-1-1-11-11−ii−iii−ii−i−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ7−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ11
χ3511-1-11-1-1-111i−i−iii−i−ii-111-1−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32
χ3611-1-11-1-1-111i−i−ii−iii−i1-1-11−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32
χ3711-1-11-1-1-111−iii−ii−i−ii1-1-11−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32
χ3811-1-11-1-1-111−iii−i−iii−i-111-1−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32
χ392222-22-2-2-22000000000000−1+i3−1+i3−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3000000000000−1−i3−1−i3−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3000000000000
χ402222-2-22-22-2000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i3000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i3000000000000
χ4122-2-2-22-222-2000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i3−1+i3−1+i31−i3000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i3−1−i3−1−i31+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
χ4911111-1-11-1-1ii−i−i11-1-1ii−i−i−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7
χ5011111-1-11-1-1ii−i−i-1-111−i−iii−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ111+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ71−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7
χ5111111-1-11-1-1−i−iii11-1-1−i−iii−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7
χ5211111-1-11-1-1−i−iii-1-111ii−i−i−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ111+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ71−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7
χ5311-1-1111-1-1-11-11-1i−ii−ii−ii−i−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7
χ5411-1-1111-1-1-11-11-1−ii−ii−ii−ii−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7
χ5511-1-1111-1-1-1-11-11i−ii−i−ii−ii−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7
χ5611-1-1111-1-1-1-11-11−ii−iii−ii−i−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ11−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ7
χ5711-1-11-1-1-111i−i−iii−i−ii-111-1−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32
χ5811-1-11-1-1-111i−i−ii−iii−i1-1-11−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32
χ5911-1-11-1-1-111−iii−ii−i−ii1-1-11−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32
χ6011-1-11-1-1-111−iii−i−iii−i-111-1−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32
χ612222-22-2-2-22000000000000−1−i3−1−i3−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3000000000000−1+i3−1+i3−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3000000000000
χ622222-2-22-22-2000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i3000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i3000000000000
χ6322-2-2-22-222-2000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i3−1−i3−1−i31+i3000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i3−1+i3−1+i31−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.