Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C41 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | C22×C3×C41×C52⋊C3 |
| Fitting, socle | C22×C3×C52×C41 ⋊ C3 |
| derived, Sylow | C52 ⋊ C22×C32×C41 |
| Hall | C22×C52×C41 ⋊ C32 |
| Hall | C52×C41 ⋊ C22×C32 |
| Hall | C22×C52 ⋊ C32×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C41 | C52⋊C3 |
| commutator, cosocle, hypocenter | C52 | C22×C32×C41 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52×C41 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C3×C41 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7380 |
5412 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 604);