Finite Group DatabasebetaFinite Group Databasebeta| order | 25194 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊#13093361 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C17×C19 | C2×C3 |
| LCS | G ▷ C13×C17×C19 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4199 |
Polycyclic presentation:
2,3,13,17,19|d^a=d^16,e^a=e^18,c^b=c^3,e^b=e^11733 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25194, 32);