Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of #127⋊(C13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #127⋊(C13⋊C3) |
| Fitting, Hall | C13×#127 ⋊ C3 |
| derived | C42×C13 ⋊ C2×C3 |
| Sylow | #127 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ #127⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C42×C13 | C2×C3 |
| Frattini | C22 | C2×C22⋊(C13⋊C3) |
| Fitting | C13×#127 | C3 |
| socle | C22×C13 | C2×A4 |
| LCS | G ▷ C42×C13 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
2,3,2^2,13,2^2|c^2=f,d^2=fg,c^a=cf,d^a=dfg,c^b=cd,d^b=cfg,e^b=e^3,f^b=g,g^b=fg66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 867);