Finite Group DatabasebetaFinite Group Databasebeta| order | 26700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×C3⋊#67063 |
| unambiguous semidirect product | C3⋊(C52×#67063) |
| Fitting, socle, Hall | C3×C52×C89 ⋊ C4 |
| derived, Hall | C3×C89 ⋊ C4×C52 |
| Hall | C52×C89 ⋊ Dic3 |
| Sylow | C89 ⋊ C52×Dic3 |
| Hall | C3×C52 ⋊ #67063 |
| Sylow | C3 ⋊ C52×#67063 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C3⋊#67063 |
| commutator, hypocenter | C3×C89 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C89 | C4 |
| prime radical | C3×C52×D89 | C2 |
| cosocle | C3×D89 | C2×C52 |
| LCS | G ▷ C3×C89 | |
| UCS | C1 ◁ C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6675 |
1800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26700, 99);