Finite Group DatabasebetaFinite Group Databasebeta| order | 26450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C23⋊D575 |
| unambiguous semidirect product | C25⋊(C23⋊D23) |
| Fitting, derived, Hall | C232×C25 ⋊ C2 |
| Sylow | C232 ⋊ D25 |
| Sylow | C25 ⋊ C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C232×C25 | C2 |
| Frattini | C5 | C5⋊(C23⋊D23) |
| socle | C5×C232 | D5 |
| LCS | G ▷ C232×C25 | |
| UCS | C1 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13225 |
Polycyclic presentation:
2,5,23^2,5|b^5=e^4,b^a=b^4e,c^a=c^22,d^a=d^22,e^a=e^46614 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26450, 16);