Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×C7⋊#3874 |
| unambiguous semidirect product | (C7×D7)⋊#3874 |
| Fitting, socle, Hall | C52×C72 ⋊ C2×D3 |
| derived, Hall | C72×C52⋊C3 ⋊ C22 |
| Hall | C52⋊C3 ⋊ D72 |
| Sylow | C72 ⋊ C2×#3874 |
| Sylow | C52 ⋊ D7×D21 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C72×C52⋊C3 | C22 |
| Fitting, socle | C52×C72 | C2×D3 |
| LCS | G ▷ C72×C52⋊C3 | |
| UCS | C1 | |
156 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 527);