Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | #13089659⋊C25 |
| derived, Sylow | C192 ⋊ C4×C25 |
| Hall | C192⋊C25 ⋊ C4 |
| Hall | #13089659 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #13089659⋊C5 |
| commutator, hypocenter | C192 | C4×C25 |
| Fitting, socle | C5×C192 | C4×C5 |
| prime radical, cosocle | C5×C19⋊D19 | C2×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C5 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 950 |
Polycyclic presentation:
2,5,2,19^2,5|a^2=c,b^5=f,d^a=d^4e^16,e^a=d^12e^15,d^b=d^18e^7,e^b=d^10e^5,d^c=d^18,e^c=e^18190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 49);