Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C19⋊Dic475 |
| derived, Hall | C192×C25 ⋊ C4 |
| Sylow | C192 ⋊ Dic25 |
| Sylow | C25 ⋊ C19⋊Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C19⋊D475 |
| commutator, hypocenter | C192×C25 | C4 |
| Frattini | C2×C5 | C5⋊(C19⋊D19) |
| Fitting, cosocle | C2×C192×C25 | C2 |
| socle, prime radical | C2×C5×C192 | D5 |
| LCS | G ▷ C192×C25 | |
| UCS | C1 ◁ C2 | |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36100 |
Polycyclic presentation:
2,5,19^2,2,5|a^2=e,b^5=f^4,b^a=b^4f,c^a=c^18,d^a=d^18,f^a=f^49028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 45);