Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C3×C4×#1057 |
| derived, Sylow | C13 ⋊ C3×C4×C8 |
| Hall | C3×C13 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C4 | #261 |
| commutator, hypocenter | C13 | C3×C4×C8 |
| Frattini | C22 | C2×C3×#261 |
| Fitting | C2×C3×C4×C13 | C4 |
| socle, prime radical | C22×C3×C13 | C2×C4 |
| cosocle | C2×Dic13 | C22×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C3×C4 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1248 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 457);