Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
No aliases for this group.
| derived, Hall | C192⋊C25 ⋊ C4 |
| Sylow | C192 ⋊ Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C192⋊C25 | C4 |
| Frattini | C5 | #20297981 |
| Fitting, socle | C5×C192 | Dic5 |
| prime radical | C5×C19⋊D19 | D5 |
| cosocle | (C19⋊D19)⋊C25 | C2 |
| LCS | G ▷ C192⋊C25 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 950 |
Polycyclic presentation:
2^2,5,19^2,5|a^2=b,c^5=f^4,c^a=c^4f,d^a=e^10,e^a=d^17,f^a=f^4,d^b=d^18,e^b=e^18,d^c=d^15e^5,e^c=de^8118 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 48);