Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic25 |
| derived, Sylow | C25 ⋊ C32×C4 |
| Hall | C32×C25 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D25 |
| commutator, hypocenter | C25 | C32×C4 |
| Frattini | C2×C5 | C32×D5 |
| Fitting | C2×C32×C25 | C2 |
| socle, prime radical | C2×C32×C5 | D5 |
| cosocle | C2×C25 | C2×C32 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C32 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 900 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#6016, C3×C3⋊#6016, C3⋊(C3⋊#6016), … |
| maximal normal subgroup of | C32×#6016, C3×C3⋊#6016, C3⋊(C3⋊#6016), … |
| maximal quotient of | C32×#6014, C2×C32×Dic25, C3×C13⋊C3×Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 13);