Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C25⋊#64422 |
| unambiguous semidirect product | (C2×C25)⋊#64422 |
| Fitting | C2×C72×C25 ⋊ C2×C3 |
| derived, Hall | C72×C25 ⋊ C22×C3 |
| Hall | C2×C7×D175 ⋊ C3 |
| Hall | C25×#3862 ⋊ C22 |
| Hall | #3862 ⋊ C2×D25 |
| Sylow | C72 ⋊ C2×C3×D25 |
| Sylow | C25 ⋊ C2×#64422 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C25⋊#64422 |
| commutator, cosocle, hypocenter | C72×C25 | C22×C3 |
| Frattini | C5 | C2×C5⋊#64422 |
| Fitting | C2×C72×C25 | C2×C3 |
| socle | C2×C5×C72 | C3×D5 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 ◁ C2 | |
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 251);