Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D92 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×D9×Dic9 |
| derived, Sylow | C92 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D92 |
| commutator, hypocenter | C92 | C22×C4 |
| Frattini | C2×C32 | C2×D32 |
| Fitting | C22×C92 | C22 |
| socle | C22×C32 | D32 |
| prime radical | C22×C3×D9 | D3 |
| cosocle | C2×C92 | C23 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C22 | |
299 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 299 conjugacy classes of subgroups — too many to draw. Only its 95 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.
| maximal subgroup of | C2×C4×D92, C2×#13047154, C2×#13047075, … |
| maximal normal subgroup of | C2×C4×D92, C2×#13047154, C2×#13047075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 870);