Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C5⋊#11725071 |
| unambiguous semidirect product | C5⋊(C5×#11725071) |
| derived | C5×#89205 ⋊ C2×C5 |
| Hall | C52×#89205 ⋊ C2 |
| Hall | C52×C72 ⋊ D9 |
| Hall | #89205 ⋊ C5×D5 |
| Sylow | C72 ⋊ C5×D45 |
| Sylow | C52 ⋊ #11725071 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C5⋊#11725071 |
| commutator, cosocle, hypocenter | C5×#89205 | C2×C5 |
| Frattini | C3 | C5×C5⋊#64418 |
| Fitting, socle | C3×C52×C72 | D3 |
| LCS | G ▷ C5×#89205 | |
| UCS | C1 ◁ C5 | |
124 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 630 |
765 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 240);