Finite Group DatabasebetaFinite Group Databasebeta| order | 25550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D2555 |
| unambiguous semidirect product | C7⋊(C5⋊D365) |
| unambiguous semidirect product | C73⋊(C5⋊D35) |
| Fitting, socle, derived, Hall | C52×C7×C73 ⋊ C2 |
| Hall | C52×C73 ⋊ D7 |
| Hall | C7×C73 ⋊ C5⋊D5 |
| Hall | C52×C7 ⋊ D73 |
| Sylow | C73 ⋊ C5⋊D35 |
| Sylow | C52 ⋊ D511 |
| Sylow | C7 ⋊ C5⋊D365 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C73 | C2 |
| LCS | G ▷ C52×C7×C73 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12775 |
Polycyclic presentation:
2,5^2,7,73|b^a=b^4,c^a=c^4,d^a=d^6,e^a=e^726389 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25550, 20);