Finite Group DatabasebetaFinite Group Databasebeta| order | 34025 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C5 |
| direct product | C5×C1361⋊C5 |
| unambiguous semidirect product | C1361⋊C52 |
| unambiguous semidirect product | (C5×C1361)⋊C5 |
| Fitting, socle | C5×C1361 ⋊ C5 |
| derived, Sylow | C1361 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C1361⋊C5 |
| commutator, cosocle, hypocenter | C1361 | C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C1361 | C5 |
| LCS | G ▷ C1361 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6805 |
1385 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34025, 3);