Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | Dic25×#3861 |
| derived, Hall | C72×C25 ⋊ C3×C4 |
| Hall | C72×Dic25 ⋊ C3 |
| Hall | C25×#3861 ⋊ C4 |
| Sylow | C72 ⋊ C3×Dic25 |
| Sylow | C25 ⋊ C4×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D25×#3861 |
| commutator, hypocenter | C72×C25 | C3×C4 |
| Frattini | C2×C5 | D5×#3861 |
| Fitting, cosocle | C2×C72×C25 | C2×C3 |
| socle | C2×C5×C72 | C3×D5 |
| prime radical | C2×C5×#3861 | D5 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 86);