Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #88034⋊C3 |
| derived, Sylow | C13 ⋊ C3×C32 |
| Hall | #88034 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D13⋊C3 |
| commutator, hypocenter | C13 | C3×C32 |
| Fitting, cosocle | C13×C16 | C2×C3 |
| socle | C2×C13 | C3×C16 |
| prime radical | C2×C13⋊C3 | C16 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C16 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2,3,2^4,13|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^12,g^b=g^9128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1);