Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5×C7 |
| direct product | C4×C52⋊#3862 |
| unambiguous semidirect product | (C4×C52)⋊#3862 |
| Fitting, Hall | C4×C52×C72 ⋊ C3 |
| derived, Hall | C52×C72 ⋊ C3×C4 |
| Hall | C4×C72 ⋊ C52⋊C3 |
| Hall | C4×C52 ⋊ #3862 |
| Sylow | C72 ⋊ C4×C52⋊C3 |
| Sylow | C52 ⋊ C4×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C52⋊#3862 |
| commutator, hypocenter | C52×C72 | C3×C4 |
| Frattini | C2 | C2×C52⋊#3862 |
| Fitting | C4×C52×C72 | C3 |
| socle, cosocle | C2×C52×C72 | C2×C3 |
| prime radical | C2×C52⋊#3862 | C2 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 ◁ C4 | |
120 conjugacy classes of subgroups.
1644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 373);