Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of A4×#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×A4×#261 |
| Fitting, socle | C23×C13 ⋊ C3×C4 |
| derived | C22×C13 ⋊ C2×C3×C4 |
| Hall | C23×#261 ⋊ C3 |
| Sylow | C13 ⋊ C2×C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×#261 |
| commutator, hypocenter | C22×C13 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C13 | C3×C4 |
| prime radical | C2×A4×D13 | C2 |
| cosocle | C22×D13 | C22×C3 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C2 | |
132 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 78 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#997, C2×A4×AGL(1,𝔽13), C22×A4×#261, … |
| maximal normal subgroup of | C2×A4×AGL(1,𝔽13), C22×A4×#261, C2×S4×#261, … |
| maximal quotient of | C22×A4×#261, D3×A4×#261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1436);