Finite Group Databasebeta

← Group #10596624

Character table — Group #10596624

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size112224444666688888822444888812121212161616161616336661212121218181818242424242424
order1222433662444666612123666123366612121266661212222246666244466661212
χ1111111111111111111111111111111111111111111111111111111111
χ211111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32
χ311111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32
χ4111-1-11111-111-11-11-1-1-1111-1-11111-111-11-11-1-1-1111-1-11111-111-11-11-1-1-1
χ5111-1-1−1+i32−1−i32−1+i32−1−i32-111-1−1+i321−i32−1−i321+i321−i321+i32111-1-1−1+i32−1−i32−1+i32−1−i32-111-1−1+i321−i32−1−i321+i321−i321+i32111-1-1−1+i32−1−i32−1+i32−1−i32-111-1−1+i321−i32−1−i321+i321−i321+i32
χ6111-1-1−1−i32−1+i32−1−i32−1+i32-111-1−1−i321+i32−1+i321−i321+i321−i32111-1-1−1−i32−1+i32−1−i32−1+i32-111-1−1−i321+i32−1+i321−i321+i321−i32111-1-1−1−i32−1+i32−1−i32−1+i32-111-1−1−i321+i32−1+i321−i321+i321−i32
χ711-11-11111-11-11-11-11-1-111-11-11111-11-11-11-11-1-111-11-11111-11-11-11-11-1-1
χ811-11-1−1+i32−1−i32−1+i32−1−i32-11-111−i32−1+i321+i32−1−i321−i321+i3211-11-1−1+i32−1−i32−1+i32−1−i32-11-111−i32−1+i321+i32−1−i321−i321+i3211-11-1−1+i32−1−i32−1+i32−1−i32-11-111−i32−1+i321+i32−1−i321−i321+i32
χ911-11-1−1−i32−1+i32−1−i32−1+i32-11-111+i32−1−i321−i32−1+i321+i321−i3211-11-1−1−i32−1+i32−1−i32−1+i32-11-111+i32−1−i321−i32−1+i321+i321−i3211-11-1−1−i32−1+i32−1−i32−1+i32-11-111+i32−1−i321−i32−1+i321+i321−i32
χ1011-1-11111111-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-111
χ1111-1-11−1+i32−1−i32−1+i32−1−i3211-1-11−i321−i321+i321+i32−1+i32−1−i3211-1-11−1+i32−1−i32−1+i32−1−i3211-1-11−i321−i321+i321+i32−1+i32−1−i3211-1-11−1+i32−1−i32−1+i32−1−i3211-1-11−i321−i321+i321+i32−1+i32−1−i32
χ1211-1-11−1−i32−1+i32−1−i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1+i3211-1-11−1−i32−1+i32−1−i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1+i3211-1-11−1−i32−1+i32−1−i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1+i32
χ13333330000-1-1-1-1000000333330000-1-1-1-1000000333330000-1-1-1-1000000
χ14333-3-300001-1-11000000333-3-300001-1-11000000333-3-300001-1-11000000
χ1533-33-300001-11-100000033-33-300001-11-100000033-33-300001-11-1000000
χ1633-3-330000-1-11100000033-3-330000-1-11100000033-3-330000-1-111000000
χ174-4000-2-22200000000004-4000-2-22200000000004-4000-2-2220000000000
χ184-40001−i31+i3−1+i3−1−i300000000004-40001−i31+i3−1+i3−1−i300000000004-40001−i31+i3−1+i3−1−i30000000000
χ194-40001+i31−i3−1−i3−1+i300000000004-40001+i31−i3−1−i3−1+i300000000004-40001+i31−i3−1−i3−1+i30000000000
χ2011111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1-11−i321+i321−i321+i32-1-1-1-11−i321−i321+i321+i321−i321+i32
χ2211111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1-11+i321−i321+i321−i32-1-1-1-11+i321+i321−i321−i321+i321−i32
χ23111-1-11111-111-11-11-1-1-1111-1-11111-111-11-11-1-1-1-1-1-111-1-1-1-11-1-11-11-1111
χ24111-1-1−1+i32−1−i32−1+i32−1−i32-111-1−1+i321−i32−1−i321+i321−i321+i32111-1-1−1+i32−1−i32−1+i32−1−i32-111-1−1+i321−i32−1−i321+i321−i321+i32-1-1-1111−i321+i321−i321+i321-1-111−i32−1+i321+i32−1−i32−1+i32−1−i32
χ25111-1-1−1−i32−1+i32−1−i32−1+i32-111-1−1−i321+i32−1+i321−i321+i321−i32111-1-1−1−i32−1+i32−1−i32−1+i32-111-1−1−i321+i32−1+i321−i321+i321−i32-1-1-1111+i321−i321+i321−i321-1-111+i32−1−i321−i32−1+i32−1−i32−1+i32
χ2611-11-11111-11-11-11-11-1-111-11-11111-11-11-11-11-1-1-1-11-11-1-1-1-11-11-11-11-111
χ2711-11-1−1+i32−1−i32−1+i32−1−i32-11-111−i32−1+i321+i32−1−i321−i321+i3211-11-1−1+i32−1−i32−1+i32−1−i32-11-111−i32−1+i321+i32−1−i321−i321+i32-1-11-111−i321+i321−i321+i321-11-1−1+i321−i32−1−i321+i32−1+i32−1−i32
χ2811-11-1−1−i32−1+i32−1−i32−1+i32-11-111+i32−1−i321−i32−1+i321+i321−i3211-11-1−1−i32−1+i32−1−i32−1+i32-11-111+i32−1−i321−i32−1+i321+i321−i32-1-11-111+i321−i321+i321−i321-11-1−1−i321+i32−1+i321−i32−1−i32−1+i32
χ2911-1-11111111-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1111111-1-1
χ3011-1-11−1+i32−1−i32−1+i32−1−i3211-1-11−i321−i321+i321+i32−1+i32−1−i3211-1-11−1+i32−1−i32−1+i32−1−i3211-1-11−i321−i321+i321+i32−1+i32−1−i32-1-111-11−i321+i321−i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321+i32
χ3111-1-11−1−i32−1+i32−1−i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1+i3211-1-11−1−i32−1+i32−1−i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1+i32-1-111-11+i321−i321+i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321−i32
χ32333330000-1-1-1-1000000333330000-1-1-1-1000000-3-3-3-3-300001111000000
χ33333-3-300001-1-11000000333-3-300001-1-11000000-3-3-3330000-111-1000000
χ3433-33-300001-11-100000033-33-300001-11-1000000-3-33-330000-11-11000000
χ3533-3-330000-1-11100000033-3-330000-1-111000000-3-333-3000011-1-1000000
χ364-4000-2-22200000000004-4000-2-2220000000000-4400022-2-20000000000
χ374-40001−i31+i3−1+i3−1−i300000000004-40001−i31+i3−1+i3−1−i30000000000-44000−1+i3−1−i31−i31+i30000000000
χ384-40001+i31−i3−1−i3−1+i300000000004-40001+i31−i3−1−i3−1+i30000000000-44000−1−i3−1+i31+i31−i30000000000
χ392222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000
χ4022222−1+i3−1−i3−1+i3−1−i32222−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-1-1-1-1-11−i321+i321−i321+i32-1-1-1-11−i321−i321+i321+i321−i321+i320000000000000000000
χ4122222−1−i3−1+i3−1−i3−1+i32222−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-1-1-1-1-11+i321−i321+i321−i32-1-1-1-11+i321+i321−i321−i321+i321−i320000000000000000000
χ42222-2-22222-222-22-22-2-2-2-1-1-111-1-1-1-11-1-11-11-11110000000000000000000
χ43222-2-2−1+i3−1−i3−1+i3−1−i3-222-2−1+i31−i3−1−i31+i31−i31+i3-1-1-1111−i321+i321−i321+i321-1-111−i32−1+i321+i32−1−i32−1+i32−1−i320000000000000000000
χ44222-2-2−1−i3−1+i3−1−i3−1+i3-222-2−1−i31+i3−1+i31−i31+i31−i3-1-1-1111+i321−i321+i321−i321-1-111+i32−1−i321−i32−1+i32−1−i32−1+i320000000000000000000
χ4522-22-22222-22-22-22-22-2-2-1-11-11-1-1-1-11-11-11-11-1110000000000000000000
χ4622-22-2−1+i3−1−i3−1+i3−1−i3-22-221−i3−1+i31+i3−1−i31−i31+i3-1-11-111−i321+i321−i321+i321-11-1−1+i321−i32−1−i321+i32−1+i32−1−i320000000000000000000
χ4722-22-2−1−i3−1+i3−1−i3−1+i3-22-221+i3−1−i31−i3−1+i31+i31−i3-1-11-111+i321−i321+i321−i321-11-1−1−i321+i32−1+i321−i32−1−i32−1+i320000000000000000000
χ4822-2-22222222-2-2-2-2-2-222-1-111-1-1-1-1-1-1-1111111-1-10000000000000000000
χ4922-2-22−1+i3−1−i3−1+i3−1−i322-2-21−i31−i31+i31+i3−1+i3−1−i3-1-111-11−i321+i321−i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321+i320000000000000000000
χ5022-2-22−1−i3−1+i3−1−i3−1+i322-2-21+i31+i31−i31−i3−1−i3−1+i3-1-111-11+i321−i321+i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321−i320000000000000000000
χ51666660000-2-2-2-2000000-3-3-3-3-3000011110000000000000000000000000
χ52666-6-600002-2-22000000-3-3-3330000-111-10000000000000000000000000
χ5366-66-600002-22-2000000-3-33-330000-11-110000000000000000000000000
χ5466-6-660000-2-222000000-3-333-3000011-1-10000000000000000000000000
χ558-8000-4-4440000000000-4400022-2-200000000000000000000000000000
χ568-80002−2i32+2i3−2+2i3−2−2i30000000000-44000−1+i3−1−i31−i31+i300000000000000000000000000000
χ578-80002+2i32−2i3−2−2i3−2+2i30000000000-44000−1−i3−1+i31+i31−i300000000000000000000000000000

Here i is the imaginary unit (i² = −1).