Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #5464 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C22×C3×C42 |
| direct product | C3×#5464 |
| Fitting | C3×H(3,𝔽4) ⋊ C3 |
| derived, Sylow | H(3,𝔽4) ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #5464 |
| commutator, cosocle, hypocenter | H(3,𝔽4) | C32 |
| Frattini | C22 | C3×C22⋊A4 |
| Fitting | C3×H(3,𝔽4) | C3 |
| socle | C22×C3 | C22⋊A4 |
| LCS | G ▷ H(3,𝔽4) | |
| UCS | C1 ◁ C3 | |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
27 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7443);