Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of C3⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×C3⋊#1057 |
| derived, Hall | C3×C13 ⋊ C4×C8 |
| Sylow | C13 ⋊ C4×C3⋊C8 |
| Sylow | C3 ⋊ C4×#1057 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C4×C8 |
| Frattini | C22 | C2×C3⋊#261 |
| Fitting | C2×C3×C4×C13 | C4 |
| socle, prime radical | C22×C3×C13 | C2×C4 |
| cosocle | C2×C3×Dic13 | C22 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2×C4 | |
88 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, 482);