Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×Dic361 |
| unambiguous semidirect product | C361⋊(C4×C52) |
| derived, Sylow | C361 ⋊ C4×C52 |
| Hall | C52×C361 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D361 |
| commutator, hypocenter | C361 | C4×C52 |
| Frattini | C2×C19 | C52×D19 |
| Fitting | C2×C52×C361 | C2 |
| socle, prime radical | C2×C52×C19 | D19 |
| cosocle | C2×C361 | C2×C52 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C2×C52 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36100 |
9100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 13);