Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20259122⋊C3 |
| Fitting, socle, derived, Hall | C52×C61 ⋊ C3×C4 |
| Hall | #20259122 ⋊ C3 |
| Hall | C52×C61⋊C3 ⋊ C4 |
| Hall | C61⋊C3 ⋊ #1042 |
| Sylow | C61 ⋊ C3×#1042 |
| Sylow | C52 ⋊ #6923⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C61 | C3×C4 |
| prime radical | C5×C5⋊(D61⋊C3) | C2 |
| cosocle | C5×D305 | C2×C3 |
| LCS | G ▷ C52×C61 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1220 |
Polycyclic presentation:
2,3,2,5^2,61|a^2=c,d^a=d^2,e^a=e^4,f^a=f^11,f^b=f^13,d^c=d^4,f^c=f^60164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 159);