Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | #88202 ⋊ C3 |
| Sylow | C13 ⋊ #131⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D13⋊A4 |
| commutator, hypocenter | Q8×C13 | C3×C4 |
| Fitting, cosocle | C13×#41 | C2×C3 |
| socle | C2×C13 | C4×A4 |
| prime radical | #41⋊(C13⋊C3) | C2 |
| LCS | G ▷ Q8×C13 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2,3,2^3,13,2|a^2=c,c^2=g,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, 444);