Finite Group DatabasebetaFinite Group Databasebeta| order | 25636 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#11725133 |
| Fitting, socle, Hall | C13×C17×C29 ⋊ C4 |
| derived, Hall | C13×C17 ⋊ C4×C29 |
| Hall | C17×C29 ⋊ Dic13 |
| Hall | C13×C29 ⋊ #595 |
| Sylow | C17 ⋊ C29×Dic13 |
| Sylow | C13 ⋊ C29×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #11725133 |
| commutator, hypocenter | C13×C17 | C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C29 | C4 |
| prime radical | C13×C29×D17 | C2 |
| cosocle | C13×D17 | C2×C29 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 ◁ C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6409 |
1972 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25636, 35);