Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×Q8×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ 2−1+4 |
| Sylow | C13 ⋊ #1007 |
| Sylow | C3 ⋊ #88254 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D39 |
| commutator, socle, cosocle | C2×C3×C13 | C24 |
| Fitting | C2×C3×Q8×C13 | C2 |
| hypercenter | C2×Q8 | D39 |
| hypocenter | C3×C13 | 2−1+4 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
292 conjugacy classes of subgroups.
| transitive degree | μt(G) = 624 |
Polycyclic presentation:
2^5,3,13|b^2=e,c^2=e,d^a=de,f^a=f^2,g^a=g^12,c^b=ce207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1421);