Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | C7⋊D7×D75 |
| Fitting, derived, Hall | C3×C72×C25 ⋊ C22 |
| Hall | C72×C25 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D25 |
| Hall | C3×C25 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×D75 |
| Sylow | C25 ⋊ D3×C7⋊D7 |
| Sylow | C3 ⋊ D25×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C72×C25 | C22 |
| Frattini | C5 | D15×C7⋊D7 |
| socle | C3×C5×C72 | C2×D5 |
| LCS | G ▷ C3×C72×C25 | |
| UCS | C1 | |
300 conjugacy classes of subgroups.
1014 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 278);