Finite Group Databasebeta

← Group #5285

Character table — Group #5285

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112224444441122244444411222444444112224444441122244444411222444444
order122442288883661212662424242436612126624242424222442288886661212662424242466612126624242424
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111-1-1-1-11111111-1-1-1-11111111-1-1-1-11111111-1-1-1-11111111-1-1-1-11111111-1-1-1-1
χ311111-1-111-1-111111-1-111-1-111111-1-111-1-111111-1-111-1-111111-1-111-1-111111-1-111-1-1
χ411111-1-1-1-11111111-1-1-1-11111111-1-1-1-11111111-1-1-1-11111111-1-1-1-11111111-1-1-1-111
χ5111-1-11-1i−ii−i111-1-11-1i−ii−i111-1-11-1i−ii−i111-1-11-1i−ii−i111-1-11-1i−ii−i111-1-11-1i−ii−i
χ6111-1-11-1−ii−ii111-1-11-1−ii−ii111-1-11-1−ii−ii111-1-11-1−ii−ii111-1-11-1−ii−ii111-1-11-1−ii−ii
χ7111-1-1-11i−i−ii111-1-1-11i−i−ii111-1-1-11i−i−ii111-1-1-11i−i−ii111-1-1-11i−i−ii111-1-1-11i−i−ii
χ8111-1-1-11−iii−i111-1-1-11−iii−i111-1-1-11−iii−i111-1-1-11−iii−i111-1-1-11−iii−i111-1-1-11−iii−i
χ922-22-200000022-22-200000022-22-200000022-22-200000022-22-200000022-22-2000000
χ1022-2-2200000022-2-2200000022-2-2200000022-2-2200000022-2-2200000022-2-22000000
χ114-40000000004-40000000004-40000000004-40000000004-40000000004-4000000000
χ1211111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ131111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ1411111-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i3211111-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ1511111-1-1-1-111−1+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−i321+i321+i321+i321+i32−1−i32−1−i3211111-1-1-1-111−1+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−i321+i321+i321+i321+i32−1−i32−1−i32
χ16111-1-11-1i−ii−i−1+i32−1+i32−1+i321−i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i321+i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11111-1-11-1i−ii−i−1+i32−1+i32−1+i321−i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i321+i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11
χ17111-1-11-1−ii−ii−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11111-1-11-1−ii−ii−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11
χ18111-1-1-11i−i−ii−1+i32−1+i32−1+i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11111-1-1-11i−i−ii−1+i32−1+i32−1+i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11
χ19111-1-1-11−iii−i−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11111-1-1-11−iii−i−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11
χ2022-22-2000000−1+i3−1+i31−i3−1+i31−i3000000−1−i3−1−i31+i3−1−i31+i300000022-22-2000000−1+i3−1+i31−i3−1+i31−i3000000−1−i3−1−i31+i3−1−i31+i3000000
χ2122-2-22000000−1+i3−1+i31−i31−i3−1+i3000000−1−i3−1−i31+i31+i3−1−i300000022-2-22000000−1+i3−1+i31−i31−i3−1+i3000000−1−i3−1−i31+i31+i3−1−i3000000
χ224-4000000000−2+2i32−2i3000000000−2−2i32+2i30000000004-4000000000−2+2i32−2i3000000000−2−2i32+2i3000000000
χ2311111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ241111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ2511111-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i3211111-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ2611111-1-1-1-111−1−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+i321−i321−i321−i321−i32−1+i32−1+i3211111-1-1-1-111−1−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+i321−i321−i321−i321−i32−1+i32−1+i32
χ27111-1-11-1i−ii−i−1−i32−1−i32−1−i321+i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i32−1+i32−1+i321−i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7111-1-11-1i−ii−i−1−i32−1−i32−1−i321+i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i32−1+i32−1+i321−i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7
χ28111-1-11-1−ii−ii−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7111-1-11-1−ii−ii−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7
χ29111-1-1-11i−i−ii−1−i32−1−i32−1−i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−1+i32−1+i32−1+i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7111-1-1-11i−i−ii−1−i32−1−i32−1−i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−1+i32−1+i32−1+i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7
χ30111-1-1-11−iii−i−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7111-1-1-11−iii−i−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7
χ3122-22-2000000−1−i3−1−i31+i3−1−i31+i3000000−1+i3−1+i31−i3−1+i31−i300000022-22-2000000−1−i3−1−i31+i3−1−i31+i3000000−1+i3−1+i31−i3−1+i31−i3000000
χ3222-2-22000000−1−i3−1−i31+i31+i3−1−i3000000−1+i3−1+i31−i31−i3−1+i300000022-2-22000000−1−i3−1−i31+i31+i3−1−i3000000−1+i3−1+i31−i31−i3−1+i3000000
χ334-4000000000−2−2i32+2i3000000000−2+2i32−2i30000000004-4000000000−2−2i32+2i3000000000−2+2i32−2i3000000000
χ34111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ351111111-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111
χ3611111-1-111-1-111111-1-111-1-111111-1-111-1-1-1-1-1-1-111-1-111-1-1-1-1-111-1-111-1-1-1-1-111-1-111
χ3711111-1-1-1-11111111-1-1-1-11111111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1
χ38111-1-11-1i−ii−i111-1-11-1i−ii−i111-1-11-1i−ii−i-1-1-111-11−ii−ii-1-1-111-11−ii−ii-1-1-111-11−ii−ii
χ39111-1-11-1−ii−ii111-1-11-1−ii−ii111-1-11-1−ii−ii-1-1-111-11i−ii−i-1-1-111-11i−ii−i-1-1-111-11i−ii−i
χ40111-1-1-11i−i−ii111-1-1-11i−i−ii111-1-1-11i−i−ii-1-1-1111-1−iii−i-1-1-1111-1−iii−i-1-1-1111-1−iii−i
χ41111-1-1-11−iii−i111-1-1-11−iii−i111-1-1-11−iii−i-1-1-1111-1i−i−ii-1-1-1111-1i−i−ii-1-1-1111-1i−i−ii
χ4222-22-200000022-22-200000022-22-2000000-2-22-22000000-2-22-22000000-2-22-22000000
χ4322-2-2200000022-2-2200000022-2-22000000-2-222-2000000-2-222-2000000-2-222-2000000
χ444-40000000004-40000000004-4000000000-44000000000-44000000000-44000000000
χ4511111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32
χ461111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32-1-1-1-1-1-1-111111−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ4711111-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32-1-1-1-1-111-1-1111−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ4811111-1-1-1-111−1+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−i321+i321+i321+i321+i32−1−i32−1−i32-1-1-1-1-11111-1-11−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ49111-1-11-1i−ii−i−1+i32−1+i32−1+i321−i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i321+i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11-1-1-111-11−ii−ii1−i321−i321−i32−1+i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ71+i321+i321+i32−1−i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11
χ50111-1-11-1−ii−ii−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11-1-1-111-11i−ii−i1−i321−i321−i32−1+i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ71+i321+i321+i32−1−i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11
χ51111-1-1-11i−i−ii−1+i32−1+i32−1+i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11-1-1-1111-1−iii−i1−i321−i321−i32−1+i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ71+i321+i321+i32−1−i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11
χ52111-1-1-11−iii−i−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11-1-1-1111-1i−i−ii1−i321−i321−i32−1+i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ71+i321+i321+i32−1−i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11
χ5322-22-2000000−1+i3−1+i31−i3−1+i31−i3000000−1−i3−1−i31+i3−1−i31+i3000000-2-22-220000001−i31−i3−1+i31−i3−1+i30000001+i31+i3−1−i31+i3−1−i3000000
χ5422-2-22000000−1+i3−1+i31−i31−i3−1+i3000000−1−i3−1−i31+i31+i3−1−i3000000-2-222-20000001−i31−i3−1+i3−1+i31−i30000001+i31+i3−1−i3−1−i31+i3000000
χ554-4000000000−2+2i32−2i3000000000−2−2i32+2i3000000000-440000000002−2i3−2+2i30000000002+2i3−2−2i3000000000
χ5611111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32
χ571111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32-1-1-1-1-1-1-111111+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ5811111-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32-1-1-1-1-111-1-1111+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ5911111-1-1-1-111−1−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+i321−i321−i321−i321−i32−1+i32−1+i32-1-1-1-1-11111-1-11+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ60111-1-11-1i−ii−i−1−i32−1−i32−1−i321+i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i32−1+i32−1+i321−i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7-1-1-111-11−ii−ii1+i321+i321+i32−1−i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ111−i321−i321−i32−1+i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7
χ61111-1-11-1−ii−ii−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7-1-1-111-11i−ii−i1+i321+i321+i32−1−i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ111−i321−i321−i32−1+i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7
χ62111-1-1-11i−i−ii−1−i32−1−i32−1−i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−1+i32−1+i32−1+i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7-1-1-1111-1−iii−i1+i321+i321+i32−1−i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ111−i321−i321−i32−1+i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7
χ63111-1-1-11−iii−i−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7-1-1-1111-1i−i−ii1+i321+i321+i32−1−i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ111−i321−i321−i32−1+i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7
χ6422-22-2000000−1−i3−1−i31+i3−1−i31+i3000000−1+i3−1+i31−i3−1+i31−i3000000-2-22-220000001+i31+i3−1−i31+i3−1−i30000001−i31−i3−1+i31−i3−1+i3000000
χ6522-2-22000000−1−i3−1−i31+i31+i3−1−i3000000−1+i3−1+i31−i31−i3−1+i3000000-2-222-20000001+i31+i3−1−i3−1−i31+i30000001−i31−i3−1+i3−1+i31−i3000000
χ664-4000000000−2−2i32+2i3000000000−2+2i32−2i3000000000-440000000002+2i3−2−2i30000000002−2i3−2+2i3000000000

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