Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic13⋊SL(2,𝔽3) |
| derived | Q8×C13 ⋊ C3×C4 |
| Hall | Q8×Dic13 ⋊ C3 |
| Sylow | C13 ⋊ C4×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D13⋊A4 |
| commutator, hypocenter | Q8×C13 | C3×C4 |
| Fitting, cosocle | C2×Q8×C13 | C2×C3 |
| socle | C22×C13 | C2×A4 |
| prime radical | C2×Q8⋊(C13⋊C3) | C2 |
| LCS | G ▷ Q8×C13 | |
| UCS | C1 ◁ C22 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2,3,2^3,13,2|a^2=c,d^2=g,e^2=g,f^a=f^12,d^b=de,e^b=d,f^b=f^9,e^d=eg48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 443);