Finite Group Databasebeta

← Group #641

Character table — Group #641

Order 72.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45
size112221122211222112221122211222112221122211222
order124443612121236121212361212123612121236121212361212123612121236121212
χ1111111111111111111111111111111111111111111111
χ2111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1
χ311-11-111-11-111-11-111-11-111-11-111-11-111-11-111-11-111-11-1
χ411-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-11
χ52-20002-20002-20002-20002-20002-20002-20002-20002-2000
χ611111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ7111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32
χ811-11-1−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i3211-11-1−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i3211-11-1−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32
χ911-1-11−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i3211-1-11−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i3211-1-11−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32
χ102-2000−1+i31−i3000−1−i31+i30002-2000−1+i31−i3000−1−i31+i30002-2000−1+i31−i3000−1−i31+i3000
χ1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ12111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32
χ1311-11-1−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i3211-11-1−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i3211-11-1−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32
χ1411-1-11−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i3211-1-11−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i3211-1-11−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32
χ152-2000−1−i31+i3000−1+i31−i30002-2000−1−i31+i3000−1+i31−i30002-2000−1−i31+i3000−1+i31−i3000
χ16111111111111111−1+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
χ17111-1-1111-1-1111-1-1−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32
χ1811-11-111-11-111-11-1−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32
χ1911-1-1111-1-1111-1-11−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ202-20002-20002-2000−1+i31−i3000−1+i31−i3000−1+i31−i3000−1−i31+i3000−1−i31+i3000−1−i31+i3000
χ2111111−1+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−i3211111−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32
χ22111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32111-1-1−1−i32−1−i32−1−i321+i321+i32111-1-1−1+i32−1+i32−1+i321−i321−i32
χ2311-11-1−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i3211-11-1−1−i32−1−i321+i32−1−i321+i3211-11-1−1+i32−1+i321−i32−1+i321−i32
χ2411-1-11−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i3211-1-11−1−i32−1−i321+i321+i32−1−i3211-1-11−1+i32−1+i321−i321−i32−1+i32
χ252-2000−1+i31−i3000−1−i31+i3000−1+i31−i3000−1−i31+i30002-2000−1−i31+i30002-2000−1+i31−i3000
χ2611111−1−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+i3211111−1−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+i3211111
χ27111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32111-1-1−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32111-1-1
χ2811-11-1−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i3211-11-1−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i3211-11-1
χ2911-1-11−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i3211-1-11−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i3211-1-11
χ302-2000−1−i31+i3000−1+i31−i3000−1+i31−i30002-2000−1−i31+i3000−1−i31+i3000−1+i31−i30002-2000
χ31111111111111111−1−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
χ32111-1-1111-1-1111-1-1−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32
χ3311-11-111-11-111-11-1−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32
χ3411-1-1111-1-1111-1-11−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32
χ352-20002-20002-2000−1−i31+i3000−1−i31+i3000−1−i31+i3000−1+i31−i3000−1+i31−i3000−1+i31−i3000
χ3611111−1+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−i3211111−1+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−i3211111
χ37111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32111-1-1−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32111-1-1
χ3811-11-1−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i3211-11-1−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i3211-11-1
χ3911-1-11−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i3211-1-11−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i3211-1-11
χ402-2000−1+i31−i3000−1−i31+i3000−1−i31+i30002-2000−1+i31−i3000−1+i31−i3000−1−i31+i30002-2000
χ4111111−1−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+i3211111−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32
χ42111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32111-1-1−1+i32−1+i32−1+i321−i321−i32111-1-1−1−i32−1−i32−1−i321+i321+i32
χ4311-11-1−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i3211-11-1−1+i32−1+i321−i32−1+i321−i3211-11-1−1−i32−1−i321+i32−1−i321+i32
χ4411-1-11−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i3211-1-11−1+i32−1+i321−i321−i32−1+i3211-1-11−1−i32−1−i321+i321+i32−1−i32
χ452-2000−1−i31+i3000−1+i31−i3000−1−i31+i3000−1+i31−i30002-2000−1+i31−i30002-2000−1−i31+i3000

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