Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C13⋊(#95⋊C3) |
| unambiguous semidirect product | #95⋊(C13⋊C3) |
| Fitting, derived, Hall | C13×#95 ⋊ C3 |
| Sylow | #95 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ #95⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C13⋊(C42⋊C3) |
| commutator, Fitting, cosocle, hypocenter | C13×#95 | C3 |
| Frattini | C23 | C22⋊(C13⋊C3) |
| socle | C23×C13 | A4 |
| LCS | G ▷ C13×#95 | |
| UCS | C1 ◁ C2 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
3,2^2,13,2^3|b^2=e,c^2=ef,b^a=cg,c^a=bc,d^a=d^9,e^a=ef,f^a=g,g^a=fg,c^b=ceg92 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 138);