Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#64213 |
| derived, Sylow | C32 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C2×C4×C16 |
| Frattini | C22 | C22×AGL(1,𝔽9) |
| Fitting | C32×C42 | C8 |
| socle | C22×C32 | C22×C8 |
| prime radical | C22×C3⋊D3 | C2×C8 |
| cosocle | C2×#622 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C42 | |
270 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 29830);