Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of C3⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊#6092 |
| unambiguous semidirect product | (C2×C3)⋊#6092 |
| derived, Hall | C3×C13 ⋊ C2×C16 |
| Sylow | C13 ⋊ C2×C3⋊C16 |
| Sylow | C3 ⋊ C2×#6092 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C2×C16 |
| Frattini | C4 | C2×C3⋊#261 |
| Fitting | C2×C3×C4×C13 | C4 |
| socle, prime radical | C22×C3×C13 | C8 |
| cosocle | C3×#1055 | C22 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2×C4 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1248 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 479);