Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#1042 |
| Fitting, Hall | C52×C9 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #1042 |
| commutator, hypocenter | C52 | C4×C9 |
| Frattini | C3 | C3×#1042 |
| Fitting | C52×C9 | C4 |
| socle | C3×C52 | C3×C4 |
| prime radical, cosocle | C3×C5×D5 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C9 | |
39 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C9×D5×AGL(1,𝔽5), #1042⋊D9, D9×#1042, … |
| maximal normal subgroup of | C9×D5×AGL(1,𝔽5), #1042⋊D9, D9×#1042, … |
| maximal quotient of | C9×#6032, C2×C9×#1042, #13049935⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 52);