Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of #120⋊(C13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #120⋊(C13⋊C3) |
| Fitting, Hall | C13×#120 ⋊ C3 |
| derived | C24×C13 ⋊ C2×C3 |
| Sylow | #120 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ #120⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C24×C13 | C2×C3 |
| Frattini | C22 | C2×C22⋊(C13⋊C3) |
| Fitting | C13×#120 | C3 |
| socle | C22×C13 | C2×A4 |
| LCS | G ▷ C24×C13 | |
| UCS | C1 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
Polycyclic presentation:
2,3,2^4,13|c^a=ce,d^a=def,c^b=cd,d^b=c,e^b=f,f^b=ef,g^b=g^366 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 864);