Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×#226 |
| Sylow | C13 ⋊ C2×#226 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | S4×D13 |
| commutator, cosocle, hypocenter | C13×SL(2,𝔽3) | C22 |
| Fitting | Q8×C13 | C2×D3 |
| socle | C2×C13 | C2×S4 |
| prime radical | SL(2,𝔽3)×D13 | C2 |
| LCS | G ▷ C13×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
64 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1178);