Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C4⋊(D13⋊A4) |
| unambiguous semidirect product | D52⋊A4 |
| Fitting | C22×C4×C13 ⋊ C2×C3 |
| Hall | C22×D52 ⋊ C3 |
| Sylow | C13 ⋊ D4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D13⋊A4 |
| commutator, socle, cosocle | C23×C13 | C22×C3 |
| Fitting | C22×C4×C13 | C2×C3 |
| hypercenter | C4 | D13⋊A4 |
| hypocenter | C22×C13 | C3×D4 |
| LCS | G ▷ C23×C13 ▷ C22×C13 | |
| UCS | C1 ◁ C2 ◁ C4 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
2^2,3,2^3,13|b^2=d,b^a=bd,g^a=g^12,e^c=ef,f^c=e,g^c=g^352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1270);