Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#994 |
| Fitting, Hall | C13×H(5,𝔽2) ⋊ C3 |
| Sylow | H(5,𝔽2) ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C22×A4 |
| commutator, cosocle, hypocenter | Q8 | C22×C3×C13 |
| Frattini | C2 | C22×A4×C13 |
| Fitting | C13×H(5,𝔽2) | C3 |
| hypercenter | Q8×C13 | A4 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C13 ◁ Q8×C13 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
247 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1369);