Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#1035 |
| Fitting, Hall | C32×C25 ⋊ C4 |
| derived, Sylow | C25 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #1035 |
| commutator, hypocenter | C25 | C32×C4 |
| Frattini | C5 | C32×AGL(1,𝔽5) |
| Fitting | C32×C25 | C4 |
| socle | C32×C5 | AGL(1,𝔽5) |
| prime radical | C32×D25 | C2 |
| cosocle | D25 | C2×C32 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C32 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 225 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#1035, C3⋊D3×#1035, C2×C32×#1035, … |
| maximal normal subgroup of | C3×D3×#1035, C3⋊D3×#1035, C2×C32×#1035, … |
| maximal quotient of | C32×#6016, C2×C32×#1035, C3×#13049908⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 28);