Finite Group DatabasebetaFinite Group Databasebeta| order | 19025 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C761⋊C25 |
| derived, Sylow | C761 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C761⋊C5 |
| commutator, hypocenter | C761 | C25 |
| Fitting, socle, prime radical, cosocle | C5×C761 | C5 |
| LCS | G ▷ C761 | |
| UCS | C1 ◁ C5 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19025 |
Polycyclic presentation:
5^2,761|a^5=b,c^a=c^67785 conjugacy classes — view the full character table.
| maximal subgroup of | D761⋊C25, C2×C761⋊C25 |
| maximal normal subgroup of | D761⋊C25, C2×C761⋊C25 |
| maximal quotient of | C2×C761⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19025, 1);