Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C19⋊(C19⋊#1035) |
| Fitting, derived, Hall | C192×C25 ⋊ C4 |
| Sylow | C192 ⋊ #1035 |
| Sylow | C25 ⋊ C19⋊Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C192×C25 | C4 |
| Frattini | C5 | C19⋊(C19⋊AGL(1,𝔽5)) |
| socle | C5×C192 | AGL(1,𝔽5) |
| prime radical, cosocle | C192×D25 | C2 |
| LCS | G ▷ C192×C25 | |
| UCS | C1 | |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9025 |
Polycyclic presentation:
2^2,5,19^2,5|a^2=b,c^5=f,c^a=c^2f,d^a=d^18,e^a=e^18,f^a=f^2,c^b=c^4f^4,f^b=f^42530 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 57);