Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5×C7 |
| direct product | C7⋊D7×(C5⋊D5)⋊C3 |
| Fitting, socle, derived, Hall | C52×C72 ⋊ C22×C3 |
| Hall | C5⋊D5×C7⋊D7 ⋊ C3 |
| Hall | C72×C52⋊C3 ⋊ C22 |
| Hall | C52⋊C3 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×(C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C2×C3×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C72 | C22×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
300 conjugacy classes of subgroups.
260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 568);