Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of #11928753 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, Hall | C13×#126 ⋊ C3 |
| derived | C42×C13 ⋊ C2×C3 |
| Sylow | #126 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ #126⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C42×C13 | C2×C3 |
| Frattini | C22 | C2×C22⋊(C13⋊C3) |
| Fitting | C13×#126 | C3 |
| socle | C22×C13 | C2×A4 |
| LCS | G ▷ C42×C13 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2,3,2^2,13,2^2|c^2=f,d^2=fg,c^a=cfg,d^a=dg,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, 865);