Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| isoclinism | isoclinic class of #5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5×C7 |
| direct product | C3×C52×#5997 |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C4 |
| derived, Sylow | C72 ⋊ C3×C4×C52 |
| Hall | C52×C72 ⋊ C3×C4 |
| Hall | C3×C72 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | #5997 |
| commutator, hypocenter | C72 | C3×C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C4 |
| prime radical | C3×C52×C7⋊D7 | C2 |
| cosocle | C7⋊D7 | C2×C3×C52 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C52 | |
224 conjugacy classes of subgroups.
1200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 636);