Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D13⋊(#41⋊C3) |
| Fitting | C13×#41 ⋊ C2×C3 |
| Hall | #41×D13 ⋊ C3 |
| Sylow | C13 ⋊ C2×#41⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D13⋊A4 |
| commutator, cosocle, hypocenter | Q8×C13 | C22×C3 |
| Frattini | C2 | C2×D13⋊A4 |
| Fitting | C13×#41 | C2×C3 |
| socle | C2×C13 | C22×A4 |
| LCS | G ▷ Q8×C13 | |
| UCS | C1 ◁ C4 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^2,3,2^2,13,2|b^2=g,d^2=g,e^2=g,f^a=f^12,d^c=de,e^c=d,f^c=f^3,e^d=eg48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1275);