Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D5×C5⋊(D49⋊C3) |
| unambiguous semidirect product | (C5×D5)⋊(D49⋊C3) |
| unambiguous semidirect product | (D5×C49⋊C3)⋊D5 |
| unambiguous semidirect product | (D5×D245)⋊C3 |
| Fitting, derived, Hall | C52×C49 ⋊ C22×C3 |
| Hall | D5×D245 ⋊ C3 |
| Hall | C52×C49⋊C3 ⋊ C22 |
| Hall | C49⋊C3 ⋊ D52 |
| Sylow | C49 ⋊ C3×D52 |
| Sylow | C52 ⋊ C2×D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C49 | C22×C3 |
| Frattini | C7 | D5×C5⋊AGL(1,𝔽7) |
| socle | C52×C7 | C2×AGL(1,𝔽7) |
| LCS | G ▷ C52×C49 | |
| UCS | C1 | |
144 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 114);