Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #1035×C61⋊C3 |
| unambiguous semidirect product | (C61×#1035)⋊C3 |
| Fitting, derived, Hall | C25×C61 ⋊ C3×C4 |
| Hall | C61×#1035 ⋊ C3 |
| Hall | C25×C61⋊C3 ⋊ C4 |
| Sylow | C61 ⋊ C3×#1035 |
| Sylow | C25 ⋊ C4×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C61 | C3×C4 |
| Frattini | C5 | AGL(1,𝔽5)×C61⋊C3 |
| socle | C5×C61 | C3×AGL(1,𝔽5) |
| prime radical | D25×C61⋊C3 | C2 |
| cosocle | D25×C61 | C2×C3 |
| LCS | G ▷ C25×C61 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1525 |
230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 32);