Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊(D41⋊C5))⋊D15 |
| unambiguous semidirect product | (D123⋊D15)⋊C5 |
| Fitting, socle, derived | C32×C5×C41 ⋊ C22×C5 |
| Hall | C32×C5×C41⋊C5 ⋊ C22 |
| Hall | C5×C41⋊C5 ⋊ D32 |
| Hall | C32×C41 ⋊ C2×C5×D5 |
| Sylow | C41 ⋊ C5×D3×D15 |
| Sylow | C32 ⋊ D5×D41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C41 | C22×C5 |
| LCS | G ▷ C32×C5×C41 | |
| UCS | C1 | |
212 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1230 |
Polycyclic presentation:
2^2,5,3^2,5,41|e^a=e^2,g^a=g^40,d^b=d^2,e^b=e^2,f^b=f^4,g^c=g^10231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 373);