Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D92 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D9×C9⋊C8 |
| unambiguous semidirect product | (C9×D9)⋊C8 |
| derived, Sylow | C92 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D92 |
| commutator, hypocenter | C92 | C2×C8 |
| Frattini | C32×C4 | D32 |
| Fitting, cosocle | C4×C92 | C22 |
| socle | C2×C32 | D3×Dic3 |
| prime radical | C2×C3×D9 | Dic3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C4 | |
127 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 127 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 78);