Finite Group DatabasebetaFinite Group Databasebeta| order | 23925 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25×C29 · Schur multiplier (H2) = C1 |
| derived, Sylow | C11 ⋊ C3×C25×C29 |
| Hall | C3×C11×C29 ⋊ C25 |
| Hall | C11×C29 ⋊ C3×C25 |
| Hall | C3×C11 ⋊ C25×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C29 | C11⋊C5 |
| commutator, hypocenter | C11 | C3×C25×C29 |
| Frattini | C5 | C3×C29×C11⋊C5 |
| Fitting, socle, prime radical | C3×C5×C11×C29 | C5 |
| cosocle | C5×C11 | C3×C5×C29 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C3×C5×C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23925 |
3045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23925, 2);