Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| isoclinism | isoclinic class of #64423 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×#64423 |
| Fitting, socle | C2×C52×C72 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C22×C3×C52 |
| Hall | C2×C52×C7×D7 ⋊ C3 |
| Hall | C52×#3861 ⋊ C22 |
| Hall | C52×C72 ⋊ C22×C3 |
| Hall | C2×C7×D7 ⋊ C3×C52 |
| Hall | #3861 ⋊ C22×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | #64423 |
| commutator, cosocle, hypocenter | C72 | C22×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C72 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C52 | |
416 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
850 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 582);