Finite Group DatabasebetaFinite Group Databasebeta| order | 24852 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊#89137 |
| Fitting, socle, derived, Hall | C19×C109 ⋊ C3×C4 |
| Hall | C19⋊#89137 ⋊ C3 |
| Hall | C19⋊C3×C109 ⋊ C4 |
| Sylow | C109 ⋊ (C19⋊C3)⋊C4 |
| Hall | C19⋊C3 ⋊ #89137 |
| Sylow | C19 ⋊ C3×#89137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C109 | C3×C4 |
| prime radical | C19⋊C3×D109 | C2 |
| cosocle | C19×D109 | C2×C3 |
| LCS | G ▷ C19×C109 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2071 |
Polycyclic presentation:
2,3,2,19,109|a^2=c,d^a=d^18,e^a=e^76,d^b=d^7,e^c=e^108261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24852, 31);