Finite Group DatabasebetaFinite Group Databasebeta| order | 25524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#15667778 |
| Fitting, derived, Hall | C9×C709 ⋊ C4 |
| Sylow | C709 ⋊ Dic9 |
| Sylow | C9 ⋊ #15667778 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C709 | C4 |
| Frattini | C3 | C3⋊#15667778 |
| socle | C3×C709 | Dic3 |
| prime radical | C3×D709 | D3 |
| cosocle | C9×D709 | C2 |
| LCS | G ▷ C9×C709 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6381 |
Polycyclic presentation:
2^2,3,709,3|a^2=b,c^3=e^2,c^a=c^2e,d^a=d^96,e^a=e^2,d^b=d^7081605 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25524, 11);