Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20259076⋊C3 |
| Fitting, derived, Hall | C25×C61 ⋊ C3×C4 |
| Hall | #20259076 ⋊ C3 |
| Hall | C25×C61⋊C3 ⋊ C4 |
| Hall | C61⋊C3 ⋊ #1035 |
| Sylow | C61 ⋊ C3×#1035 |
| Sylow | C25 ⋊ #6923⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C61 | C3×C4 |
| Frattini | C5 | #11927412⋊C3 |
| socle | C5×C61 | C3×AGL(1,𝔽5) |
| prime radical | C25⋊(D61⋊C3) | C2 |
| cosocle | D1525 | C2×C3 |
| LCS | G ▷ C25×C61 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1525 |
Polycyclic presentation:
2,3,2,5,61,5|a^2=c,d^5=f,d^a=d^2f,e^a=e^50,f^a=f^2,e^b=e^13,d^c=d^4f^4,e^c=e^60,f^c=f^4155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 29);