Finite Group Databasebeta

← Group #4589

Character table — Group #4589

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222244444444444411112222224444444444441111222222444444444444
order122222222244444444444436666666661212121212121212121212123666666666121212121212121212121212
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
χ5111111-1-1-1-111-1-1ii−i−iii−i−i111111-1-1-1-111-1-1ii−i−iii−i−i111111-1-1-1-111-1-1ii−i−iii−i−i
χ6111111-1-1-1-111-1-1−i−iii−i−iii111111-1-1-1-111-1-1−i−iii−i−iii111111-1-1-1-111-1-1−i−iii−i−iii
χ7111111-1-1-1-1-1-111ii−i−i−i−iii111111-1-1-1-1-1-111ii−i−i−i−iii111111-1-1-1-1-1-111ii−i−i−i−iii
χ8111111-1-1-1-1-1-111−i−iiiii−i−i111111-1-1-1-1-1-111−i−iiiii−i−i111111-1-1-1-1-1-111−i−iiiii−i−i
χ911-1-11-11-11-1i−ii−i1-11-1i−ii−i11-1-11-11-11-1i−ii−i1-11-1i−ii−i11-1-11-11-11-1i−ii−i1-11-1i−ii−i
χ1011-1-11-11-11-1i−ii−i-11-11−ii−ii11-1-11-11-11-1i−ii−i-11-11−ii−ii11-1-11-11-11-1i−ii−i-11-11−ii−ii
χ1111-1-11-11-11-1−ii−ii1-11-1−ii−ii11-1-11-11-11-1−ii−ii1-11-1−ii−ii11-1-11-11-11-1−ii−ii1-11-1−ii−ii
χ1211-1-11-11-11-1−ii−ii-11-11i−ii−i11-1-11-11-11-1−ii−ii-11-11i−ii−i11-1-11-11-11-1−ii−ii-11-11i−ii−i
χ1311-1-11-1-11-11i−i−iii−i−ii-111-111-1-11-1-11-11i−i−iii−i−ii-111-111-1-11-1-11-11i−i−iii−i−ii-111-1
χ1411-1-11-1-11-11i−i−ii−iii−i1-1-1111-1-11-1-11-11i−i−ii−iii−i1-1-1111-1-11-1-11-11i−i−ii−iii−i1-1-11
χ1511-1-11-1-11-11−iii−ii−i−ii1-1-1111-1-11-1-11-11−iii−ii−i−ii1-1-1111-1-11-1-11-11−iii−ii−i−ii1-1-11
χ1611-1-11-1-11-11−iii−i−iii−i-111-111-1-11-1-11-11−iii−i−iii−i-111-111-1-11-1-11-11−iii−i−iii−i-111-1
χ172222-2-22-2-220000000000002222-2-22-2-220000000000002222-2-22-2-22000000000000
χ182222-2-2-222-20000000000002222-2-2-222-20000000000002222-2-2-222-2000000000000
χ1922-2-2-2222-2-200000000000022-2-2-2222-2-200000000000022-2-2-2222-2-2000000000000
χ2022-2-2-22-2-22200000000000022-2-2-22-2-22200000000000022-2-2-22-2-222000000000000
χ214-44-40000000000000000004-44-40000000000000000004-44-4000000000000000000
χ224-4-440000000000000000004-4-440000000000000000004-4-44000000000000000000
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
χ27111111-1-1-1-111-1-1ii−i−iii−i−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11
χ28111111-1-1-1-111-1-1−i−iii−i−iii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11
χ29111111-1-1-1-1-1-111ii−i−i−i−iii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11
χ30111111-1-1-1-1-1-111−i−iiiii−i−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11
χ3111-1-11-11-11-1i−ii−i1-11-1i−ii−i−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11
χ3211-1-11-11-11-1i−ii−i-11-11−ii−ii−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11
χ3311-1-11-11-11-1−ii−ii1-11-1−ii−ii−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11
χ3411-1-11-11-11-1−ii−ii-11-11i−ii−i−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11
χ3511-1-11-1-11-11i−i−iii−i−ii-111-1−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32
χ3611-1-11-1-11-11i−i−ii−iii−i1-1-11−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32
χ3711-1-11-1-11-11−iii−ii−i−ii1-1-11−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32
χ3811-1-11-1-11-11−iii−i−iii−i-111-1−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32
χ392222-2-22-2-22000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3000000000000
χ402222-2-2-222-2000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i3000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i3000000000000
χ4122-2-2-2222-2-2000000000000−1+i3−1+i31−i31−i31−i3−1+i3−1+i3−1+i31−i31−i3000000000000−1−i3−1−i31+i31+i31+i3−1−i3−1−i3−1−i31+i31+i3000000000000
χ4222-2-2-22-2-222000000000000−1+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
χ434-44-4000000000000000000−2+2i32−2i3−2+2i32−2i3000000000000000000−2−2i32+2i3−2−2i32+2i3000000000000000000
χ444-4-44000000000000000000−2+2i32−2i32−2i3−2+2i3000000000000000000−2−2i32+2i32+2i3−2−2i3000000000000000000
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
χ49111111-1-1-1-111-1-1ii−i−iii−i−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7
χ50111111-1-1-1-111-1-1−i−iii−i−iii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7
χ51111111-1-1-1-1-1-111ii−i−i−i−iii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7
χ52111111-1-1-1-1-1-111−i−iiiii−i−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7
χ5311-1-11-11-11-1i−ii−i1-11-1i−ii−i−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7
χ5411-1-11-11-11-1i−ii−i-11-11−ii−ii−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7
χ5511-1-11-11-11-1−ii−ii1-11-1−ii−ii−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7
χ5611-1-11-11-11-1−ii−ii-11-11i−ii−i−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7
χ5711-1-11-1-11-11i−i−iii−i−ii-111-1−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32
χ5811-1-11-1-11-11i−i−ii−iii−i1-1-11−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32
χ5911-1-11-1-11-11−iii−ii−i−ii1-1-11−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32
χ6011-1-11-1-11-11−iii−i−iii−i-111-1−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32
χ612222-2-22-2-22000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3000000000000
χ622222-2-2-222-2000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i3000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i3000000000000
χ6322-2-2-2222-2-2000000000000−1−i3−1−i31+i31+i31+i3−1−i3−1−i3−1−i31+i31+i3000000000000−1+i3−1+i31−i31−i31−i3−1+i3−1+i3−1+i31−i31−i3000000000000
χ6422-2-2-22-2-222000000000000−1−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
χ654-44-4000000000000000000−2−2i32+2i3−2−2i32+2i3000000000000000000−2+2i32−2i3−2+2i32−2i3000000000000000000
χ664-4-44000000000000000000−2−2i32+2i32+2i3−2−2i3000000000000000000−2+2i32−2i32−2i3−2+2i3000000000000000000

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