Finite Group DatabasebetaFinite Group Databasebeta| order | 34375 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C252 · Schur multiplier (H2) = C52×C25 |
| direct product | C252×C11⋊C5 |
| Fitting | C11×C252 ⋊ C5 |
| derived, Sylow | C11 ⋊ C5×C252 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C252 | C11⋊C5 |
| commutator, hypocenter | C11 | C5×C252 |
| Frattini | C52 | C52×C11⋊C5 |
| Fitting | C11×C252 | C5 |
| socle, cosocle | C52×C11 | C53 |
| prime radical | C52×C11⋊C5 | C52 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C252 | |
852 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6875 |
4375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34375, 237);