Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | D5×C3⋊(C5⋊(C7⋊D7)) |
| unambiguous semidirect product | (C3×D5)⋊(C5⋊(C7⋊D7)) |
| unambiguous semidirect product | (C5×D5)⋊(C3⋊(C7⋊D7)) |
| unambiguous semidirect product | (C7×D5)⋊D105 |
| Fitting, socle, derived, Hall | C3×C52×C72 ⋊ C22 |
| Hall | C52×C72 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ D52 |
| Hall | C3×C52 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ D5×D15 |
| Sylow | C52 ⋊ C2×C3⋊(C7⋊D7) |
| Sylow | C3 ⋊ D5×C5⋊(C7⋊D7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C72 | C22 |
| LCS | G ▷ C3×C52×C72 | |
| UCS | C1 | |
480 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 725);