Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | D7×D7⋊(C52⋊C3) |
| unambiguous semidirect product | D7⋊(D7×C52⋊C3) |
| Fitting, socle, derived, Hall | C52×C72 ⋊ C22×C3 |
| Hall | C52×D72 ⋊ C3 |
| Hall | C7×C7⋊(C52⋊C3) ⋊ C22 |
| Hall | D72 ⋊ C52⋊C3 |
| Sylow | C72 ⋊ C22×C52⋊C3 |
| Sylow | C52 ⋊ D7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C72 | C22×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
136 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
235 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 575);