Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of A4⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×A4⋊#261 |
| unambiguous semidirect product | (C2×A4)⋊#261 |
| unambiguous semidirect product | D13⋊SL(2,ℤ/4) |
| Fitting, socle | C23×C13 ⋊ Dic3 |
| derived | A4×C13 ⋊ C2×C4 |
| Sylow | C13 ⋊ C2×SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4⋊#261 |
| commutator, hypocenter | A4×C13 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C13 | Dic3 |
| prime radical | C2×A4×D13 | C2 |
| cosocle | A4×D13 | C22 |
| LCS | G ▷ A4×C13 | |
| UCS | C1 ◁ C2 | |
126 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 78 |
44 conjugacy classes — view the full character table.
| maximal subgroup of | D3×A4⋊#261, C2×A4⋊AGL(1,𝔽13), C2×S4×#261, … |
| maximal normal subgroup of | C2×A4⋊AGL(1,𝔽13), C2×S4×#261, #72242148, … |
| maximal quotient of | D3×A4⋊#261, #72242148 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1434);