Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×#3771 |
| derived, Sylow | C32 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C4×C16 |
| Frattini | C22 | C2×AGL(1,𝔽9) |
| Fitting | C2×C32×C4 | C8 |
| socle, prime radical | C22×C32 | C2×C8 |
| cosocle | C2×#622 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C4 | |
73 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#3771, #11771304, #11771316, … |
| maximal normal subgroup of | C8×#3771, #11771304, #11771316, … |
| maximal quotient of | C8×#3771, #11771316, #11772268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5143);