Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | SL(2,𝔽3)2 |
| unambiguous semidirect product | (Q8×SL(2,𝔽3))⋊C3 |
| unambiguous semidirect product | (Q8⋊SL(2,𝔽3))⋊C3 |
| Fitting, derived, Sylow | Q82 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C22 | A42 |
| commutator, Fitting, cosocle, hypocenter | Q82 | C32 |
| LCS | G ▷ Q82 | |
| UCS | C1 ◁ C22 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
49 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5128);