Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C13 ⋊ M32 |
| Sylow | C13 ⋊ #798 |
| Sylow | C3 ⋊ #88106 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×#261 |
| commutator, socle | C2×C3×C13 | C2×C8 |
| Fitting | C3×C4×C13 | C2×C4 |
| prime radical | C2×D3×C13 | C8 |
| cosocle | C3×#1055 | C22 |
| hypocenter | C3×C13 | M32 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C4 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 624 |
Polycyclic presentation:
2^5,3,13|a^2=c,c^2=d,d^2=e,b^a=be,g^a=g^8,f^b=f^2,g^c=g^1272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 324);