Finite Group DatabasebetaFinite Group Databasebeta| order | 26450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D2645 |
| unambiguous semidirect product | C529⋊(C5⋊D5) |
| Fitting, derived, Hall | C52×C529 ⋊ C2 |
| Sylow | C529 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C529 | C2 |
| Frattini | C23 | C5⋊D115 |
| socle | C52×C23 | D23 |
| LCS | G ▷ C52×C529 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13225 |
Polycyclic presentation:
2,5^2,23^2|d^23=e^22,b^a=b^4,c^a=c^4,d^a=d^22e,e^a=e^226614 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26450, 10);