Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×#1057 |
| derived, Sylow | C13 ⋊ C22×C3×C8 |
| Hall | C3×C13 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | #261 |
| commutator, hypocenter | C13 | C22×C3×C8 |
| Frattini | C2 | C22×C3×#261 |
| Fitting, socle, prime radical | C23×C3×C13 | C4 |
| cosocle | Dic13 | C23×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C23×C3 | |
152 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, 1289);