Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C32×C7⋊D175 |
| unambiguous semidirect product | C25⋊(C32×C7⋊D7) |
| Fitting, Hall | C32×C72×C25 ⋊ C2 |
| derived, Hall | C72×C25 ⋊ C2×C32 |
| Hall | C32×C72 ⋊ D25 |
| Hall | C32×C25 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C32×D25 |
| Sylow | C25 ⋊ C32×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C7⋊D175 |
| commutator, cosocle, hypocenter | C72×C25 | C2×C32 |
| Frattini | C5 | C32×C5⋊(C7⋊D7) |
| Fitting | C32×C72×C25 | C2 |
| socle | C32×C5×C72 | D5 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 ◁ C32 | |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11025 |
5526 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 208);