Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of D3×#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| Fitting, socle | C22×C3×C13 ⋊ C2×C4 |
| derived, Hall | C3×C13 ⋊ C23×C4 |
| Sylow | C13 ⋊ C22×C4×D3 |
| Sylow | C3 ⋊ C23×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×#261 |
| commutator, hypocenter | C3×C13 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C13 | C2×C4 |
| prime radical | C22×D3×D13 | C2 |
| cosocle | C3×D13 | C24 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C22 | |
472 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3⋊D3×#261, C22×D3×AGL(1,𝔽13), D3×D4×#261, … |
| maximal normal subgroup of | C22×D3×AGL(1,𝔽13), D3×D4×#261, D3×A4×#261, … |
| maximal quotient of | C22×C3⋊D3×#261, D3×D4×#261, C2×D32×#261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1439);