Finite Group DatabasebetaFinite Group Databasebeta| order | 25012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×#3866 |
| Fitting, socle, Hall | C132×C37 ⋊ C4 |
| derived, Sylow | C37 ⋊ C4×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | #3866 |
| commutator, hypocenter | C37 | C4×C132 |
| Frattini | C1 | G |
| Fitting, socle | C132×C37 | C4 |
| prime radical | C132×D37 | C2 |
| cosocle | D37 | C2×C132 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C132 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6253 |
2197 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25012, 23);