Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C361⋊#1043 |
| Fitting, derived, Hall | C52×C361 ⋊ C4 |
| Sylow | C361 ⋊ #1043 |
| Sylow | C52 ⋊ Dic361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C361 | C4 |
| Frattini | C19 | C19⋊#1043 |
| socle | C52×C19 | Dic19 |
| prime radical | C19×C5⋊D5 | D19 |
| cosocle | C5⋊D5×C361 | C2 |
| LCS | G ▷ C52×C361 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9025 |
Polycyclic presentation:
2^2,5^2,19^2|a^2=b,e^19=f^18,c^a=c^2,d^a=d^2,e^a=e^18f,f^a=f^18,c^b=c^4,d^b=d^42530 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 22);