Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| isoclinism | isoclinic class of #64480 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C5 |
| direct product | C49×#64480 |
| Fitting, Hall | C52×C49 ⋊ Dic3 |
| derived, Hall | C52⋊C3 ⋊ C4×C49 |
| Hall | C49×C52⋊C3 ⋊ C4 |
| Sylow | C52 ⋊ Dic3×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | #64480 |
| commutator, hypocenter | C52⋊C3 | C4×C49 |
| Frattini | C7 | C7×#64480 |
| Fitting | C52×C49 | Dic3 |
| socle | C52×C7 | C7×Dic3 |
| prime radical, cosocle | C7×(C5⋊D5)⋊C3 | C2×C7 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C49 | |
54 conjugacy classes of subgroups.
392 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 125);