Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C3×C72×D52 |
| unambiguous semidirect product | (C5×D5)⋊(C2×C3×C72) |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C22 |
| derived, Sylow | C52 ⋊ C22×C3×C72 |
| Hall | C52×C72 ⋊ C22×C3 |
| Hall | C3×C52 ⋊ C22×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | D52 |
| commutator, cosocle, hypocenter | C52 | C22×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C72 | |
480 conjugacy classes of subgroups.
2352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 663);