Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C192⋊C25 ⋊ C4 |
| Sylow | C192 ⋊ Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #31825265 |
| commutator, hypocenter | C192⋊C25 | C4 |
| Frattini | C2×C5 | #16813380 |
| Fitting, socle, prime radical | C2×C5×C192 | D5 |
| cosocle | C2×C192⋊C25 | C2 |
| LCS | G ▷ C192⋊C25 | |
| UCS | C1 ◁ C2 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1900 |
Polycyclic presentation:
2,5,19^2,2,5|a^2=e,b^5=f^4,b^a=b^4f,d^a=cd^18,f^a=f^4,c^b=c^12d^18,d^b=c^2d^11442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 38);