Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1805 |
| unambiguous semidirect product | C361⋊(C5×Dic5) |
| derived | C5×C361 ⋊ C4×C5 |
| Hall | C52×C361 ⋊ C4 |
| Sylow | C361 ⋊ C5×Dic5 |
| Sylow | C52 ⋊ Dic361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1805 |
| commutator, hypocenter | C5×C361 | C4×C5 |
| Frattini | C2×C19 | C5×D95 |
| Fitting | C2×C52×C361 | C2 |
| socle, prime radical | C2×C52×C19 | D19 |
| cosocle | C2×C5×C361 | C2×C5 |
| LCS | G ▷ C5×C361 | |
| UCS | C1 ◁ C2×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7220 |
9040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 15);