Finite Group Databasebeta

← Group #64034

Character table — Group #64034

Order 288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size112224444446688121212112224444446688121212112224444446688121212
order1234622812242424662483631266624122424612666122436312666241224246126661224
χ1111111111111111111111111111111111111111111111111111111
χ211111111111-1-111-1-1-111111111111-1-111-1-1-111111111111-1-111-1-1-1
χ3111111-1-11-1-1111-11-1-1111111-1-11-1-1111-11-1-1111111-1-11-1-1111-11-1-1
χ4111111-1-11-1-1-1-11-1-111111111-1-11-1-1-1-11-1-111111111-1-11-1-1-1-11-1-111
χ511111-11-11-1-111-11-11-111111-11-11-1-111-11-11-111111-11-11-1-111-11-11-1
χ611111-11-11-1-1-1-1-111-1111111-11-11-1-1-1-1-111-1111111-11-11-1-1-1-1-111-11
χ711111-1-1111111-1-1-1-1111111-1-1111111-1-1-1-1111111-1-1111111-1-1-1-11
χ811111-1-11111-1-1-1-111-111111-1-11111-1-1-1-111-111111-1-11111-1-1-1-111-1
χ9222-22000-2002-200000222-22000-2002-200000222-22000-2002-200000
χ10222-22000-200-2200000222-22000-200-2200000222-22000-200-2200000
χ1122-12-1222-1-1-100-1-100022-12-1222-1-1-100-1-100022-12-1222-1-1-100-1-1000
χ1222-12-12-2-2-11100-1100022-12-12-2-2-11100-1100022-12-12-2-2-11100-11000
χ1322-12-1-22-2-111001-100022-12-1-22-2-111001-100022-12-1-22-2-111001-1000
χ1422-12-1-2-22-1-1-1001100022-12-1-2-22-1-1-1001100022-12-1-2-22-1-1-10011000
χ1544-2-4-2000200000000044-2-4-2000200000000044-2-4-20002000000000
χ164-440-400000000000004-440-400000000000004-440-40000000000000
χ174-4-2020000i6−i600000004-4-2020000i6−i600000004-4-2020000i6−i60000000
χ184-4-2020000−i6i600000004-4-2020000−i6i600000004-4-2020000−i6i60000000
χ19111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ2011111111111-1-111-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+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−i321+i321+i32−1−i32−1−i321+i321+i321+i32
χ21111111-1-11-1-1111-11-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32
χ22111111-1-11-1-1-1-11-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32
χ2311111-11-11-1-111-11-11-1−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32
χ2411111-11-11-1-1-1-1-111-11−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ2511111-1-1111111-1-1-1-11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32
χ2611111-1-11111-1-1-1-111-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32
χ27222-22000-2002-200000−1+i3−1+i3−1+i31−i3−1+i30001−i300−1+i31−i300000−1−i3−1−i3−1−i31+i3−1−i30001+i300−1−i31+i300000
χ28222-22000-200-2200000−1+i3−1+i3−1+i31−i3−1+i30001−i3001−i3−1+i300000−1−i3−1−i3−1−i31+i3−1−i30001+i3001+i3−1−i300000
χ2922-12-1222-1-1-100-1-1000−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i32001−i321−i32000−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i32001+i321+i32000
χ3022-12-12-2-2-11100-11000−1+i3−1+i31−i32−1+i31−i32−1+i31−i31−i31−i32−1+i32−1+i32001−i32−1+i32000−1−i3−1−i31+i32−1−i31+i32−1−i31+i31+i31+i32−1−i32−1−i32001+i32−1−i32000
χ3122-12-1-22-2-111001-1000−1+i3−1+i31−i32−1+i31−i321−i3−1+i31−i31−i32−1+i32−1+i3200−1+i321−i32000−1−i3−1−i31+i32−1−i31+i321+i3−1−i31+i31+i32−1−i32−1−i3200−1−i321+i32000
χ3222-12-1-2-22-1-1-10011000−1+i3−1+i31−i32−1+i31−i321−i31−i3−1+i31−i321−i321−i3200−1+i32−1+i32000−1−i3−1−i31+i32−1−i31+i321+i31+i3−1−i31+i321+i321+i3200−1−i32−1−i32000
χ3344-2-4-20002000000000−2+2i3−2+2i31−i32−2i31−i3000−1+i3000000000−2−2i3−2−2i31+i32+2i31+i3000−1−i3000000000
χ344-440-40000000000000−2+2i32−2i3−2+2i302−2i30000000000000−2−2i32+2i3−2−2i302+2i30000000000000
χ354-4-2020000i6−i60000000−2+2i32−2i31−i30−1+i30000ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ230000000−2−2i32+2i31+i30−1−i30000−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ230000000
χ364-4-2020000−i6i60000000−2+2i32−2i31−i30−1+i30000−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ230000000−2−2i32+2i31+i30−1−i300002ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ230000000
χ37111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ3811111111111-1-111-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−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+i321−i321−i32−1+i32−1+i321−i321−i321−i32
χ39111111-1-11-1-1111-11-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32
χ40111111-1-11-1-1-1-11-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32
χ4111111-11-11-1-111-11-11-1−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32
χ4211111-11-11-1-1-1-1-111-11−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ4311111-1-1111111-1-1-1-11−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32
χ4411111-1-11111-1-1-1-111-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32
χ45222-22000-2002-200000−1−i3−1−i3−1−i31+i3−1−i30001+i300−1−i31+i300000−1+i3−1+i3−1+i31−i3−1+i30001−i300−1+i31−i300000
χ46222-22000-200-2200000−1−i3−1−i3−1−i31+i3−1−i30001+i3001+i3−1−i300000−1+i3−1+i3−1+i31−i3−1+i30001−i3001−i3−1+i300000
χ4722-12-1222-1-1-100-1-1000−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i32001+i321+i32000−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i32001−i321−i32000
χ4822-12-12-2-2-11100-11000−1−i3−1−i31+i32−1−i31+i32−1−i31+i31+i31+i32−1−i32−1−i32001+i32−1−i32000−1+i3−1+i31−i32−1+i31−i32−1+i31−i31−i31−i32−1+i32−1+i32001−i32−1+i32000
χ4922-12-1-22-2-111001-1000−1−i3−1−i31+i32−1−i31+i321+i3−1−i31+i31+i32−1−i32−1−i3200−1−i321+i32000−1+i3−1+i31−i32−1+i31−i321−i3−1+i31−i31−i32−1+i32−1+i3200−1+i321−i32000
χ5022-12-1-2-22-1-1-10011000−1−i3−1−i31+i32−1−i31+i321+i31+i3−1−i31+i321+i321+i3200−1−i32−1−i32000−1+i3−1+i31−i32−1+i31−i321−i31−i3−1+i31−i321−i321−i3200−1+i32−1+i32000
χ5144-2-4-20002000000000−2−2i3−2−2i31+i32+2i31+i3000−1−i3000000000−2+2i3−2+2i31−i32−2i31−i3000−1+i3000000000
χ524-440-40000000000000−2−2i32+2i3−2−2i302+2i30000000000000−2+2i32−2i3−2+2i302−2i30000000000000
χ534-4-2020000i6−i60000000−2−2i32+2i31+i30−1−i30000−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ230000000−2+2i32−2i31−i30−1+i30000ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ230000000
χ544-4-2020000−i6i60000000−2−2i32+2i31+i30−1−i300002ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ230000000−2+2i32−2i31−i30−1+i30000−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ230000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.