Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C5 |
| direct product | C41×#11744634 |
| derived, Hall | C52⋊C9 ⋊ C4×C41 |
| Hall | C41×C52⋊C9 ⋊ C4 |
| Hall | C52×C41 ⋊ Dic9 |
| Sylow | C52 ⋊ Dic9×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | #11744634 |
| commutator, hypocenter | C52⋊C9 | C4×C41 |
| Frattini | C3 | C41×#64480 |
| Fitting, socle | C3×C52×C41 | Dic3 |
| prime radical | C3×C41×C5⋊D5 | D3 |
| cosocle | (C5⋊D5)⋊C9 | C2×C41 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 ◁ C41 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1845 |
738 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 205);