Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C22×C52⋊#3861 |
| Fitting, socle, Hall | C22×C52×C72 ⋊ C3 |
| derived, Hall | C52×C72 ⋊ C22×C3 |
| Hall | C22×C72 ⋊ C52⋊C3 |
| Hall | C22×C52 ⋊ #3861 |
| Sylow | C72 ⋊ C22×C52⋊C3 |
| Sylow | C52 ⋊ C22×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C52⋊#3861 |
| commutator, cosocle, hypocenter | C52×C72 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52×C72 | C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 ◁ C22 | |
300 conjugacy classes of subgroups.
1644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 748);