Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#3771 |
| derived, Sylow | C32 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C22×C16 |
| Frattini | C2 | C22×AGL(1,𝔽9) |
| Fitting, socle, prime radical | C23×C32 | C8 |
| cosocle | #622 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23 | |
125 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #11772268, #11772412, C2×C4×#3771, … |
| maximal normal subgroup of | #11772268, #11772412, C2×C4×#3771, … |
| maximal quotient of | C2×C4×#3771, C2×C22⋊#3771, C2×C4⋊#3771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8371);