Finite Group DatabasebetaFinite Group Databasebeta| order | 24548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C361⋊#595 |
| Fitting, derived, Hall | C17×C361 ⋊ C4 |
| Sylow | C361 ⋊ #595 |
| Sylow | C17 ⋊ Dic361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C17×C361 | C4 |
| Frattini | C19 | C19⋊#595 |
| socle | C17×C19 | Dic19 |
| prime radical | C19×D17 | D19 |
| cosocle | D17×C361 | C2 |
| LCS | G ▷ C17×C361 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6137 |
Polycyclic presentation:
2^2,17,19^2|a^2=b,d^19=e^18,c^a=c^13,d^a=d^18e,e^a=e^18,c^b=c^161808 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24548, 7);