Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(C23⋊#1035) |
| unambiguous semidirect product | C23⋊(C11⋊#1035) |
| Fitting, derived, Hall | C11×C23×C25 ⋊ C4 |
| Hall | C23×C25 ⋊ Dic11 |
| Hall | C11×C25 ⋊ Dic23 |
| Hall | C11×C23 ⋊ #1035 |
| Sylow | C25 ⋊ Dic253 |
| Sylow | C23 ⋊ C11⋊#1035 |
| Sylow | C11 ⋊ C23⋊#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C11×C23×C25 | C4 |
| Frattini | C5 | C11⋊(C23⋊AGL(1,𝔽5)) |
| socle | C5×C11×C23 | AGL(1,𝔽5) |
| prime radical, cosocle | C11×C23×D25 | C2 |
| LCS | G ▷ C11×C23×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6325 |
Polycyclic presentation:
2^2,5,11,23,5|a^2=b,c^5=f,c^a=c^2f,d^a=d^10,e^a=e^22,f^a=f^2,c^b=c^4f^4,f^b=f^41774 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 34);