Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| Fitting | C2×C52×C49 ⋊ C2×C3 |
| derived | C5×C49 ⋊ C22×C3×C5 |
| Hall | C2×C5×D5×C49 ⋊ C3 |
| Hall | C52×C49⋊C3 ⋊ C22 |
| Hall | C52×C49 ⋊ C22×C3 |
| Sylow | C49 ⋊ C2×C3×C5×D5 |
| Sylow | C52 ⋊ C22×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D5×C49⋊C3 |
| commutator, cosocle, hypocenter | C5×C49 | C22×C3×C5 |
| Frattini | C7 | C2×C5×D5×ΓL(1,𝔽8) |
| Fitting | C2×C52×C49 | C2×C3 |
| socle | C2×C52×C7 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C2×C5 | |
144 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 131);