Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of C3⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D13⋊(C3⋊C16) |
| derived, Hall | C3×C13 ⋊ C2×C16 |
| Sylow | C13 ⋊ C2×C3⋊C16 |
| Sylow | C3 ⋊ D13⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C2×C16 |
| Frattini | C4 | C2×C3⋊#261 |
| Fitting | C3×C8×C13 | C4 |
| socle | C2×C3×C13 | C2×C8 |
| prime radical | C2×C3×D13 | C8 |
| cosocle | C3×#1055 | C22 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C8 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 624 |
Polycyclic presentation:
2^5,3,13|a^2=c,b^2=d,c^2=d,d^2=e,f^a=f^2,g^a=g^8,g^c=g^12120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 471);