Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C52 · Schur multiplier (H2) = C2×C3×C5 |
| Fitting, socle | C22×C3×C5×C41 ⋊ C3×C5 |
| derived, Hall | C22×C41 ⋊ C32×C52 |
| Hall | C22×C5×C41⋊C5 ⋊ C32 |
| Hall | C3×A4×C41 ⋊ C52 |
| Sylow | C41 ⋊ C3×C52×A4 |
| Sylow | C22 ⋊ C32×C5×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | A4×C41⋊C5 |
| commutator, cosocle, hypocenter | C22×C41 | C32×C52 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C5×C41 | C3×C5 |
| LCS | G ▷ C22×C41 | |
| UCS | C1 ◁ C3×C5 | |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2460 |
780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 391);