Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#41 ⋊ C2×C3 |
| Hall | #88257 ⋊ C3 |
| Hall | C13⋊C3 ⋊ 2−1+4 |
| Sylow | C13 ⋊ C3×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D13⋊C3 |
| commutator, socle, cosocle | C2×C13 | C24×C3 |
| Fitting | C13×#41 | C2×C3 |
| hypercenter | #41 | D13⋊C3 |
| hypocenter | C13 | C3×2−1+4 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ #41 | |
292 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^4,3,2,13|b^2=f,c^2=f,d^2=f,d^a=df,g^a=g^12,c^b=cf,g^e=g^371 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1254);