Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D92 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D92 |
| Fitting | C4×C92 ⋊ C22 |
| derived, Sylow | C92 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D92 |
| commutator, hypocenter | C92 | C22×C4 |
| Frattini, socle | C2×C32 | C2×D32 |
| Fitting | C4×C92 | C22 |
| prime radical | C2×D92 | C2 |
| cosocle | C2×C92 | C23 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C4 | |
299 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 299 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#92265⋊C2, #72219926, D4×D92, … |
| maximal normal subgroup of | C4×#92265⋊C2, #72219926, D4×D92, … |
| maximal quotient of | #72219998, D92×AGL(1,𝔽5), C2×C4×D92 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 797);