Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #4380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×#4380 |
| Fitting, socle, Hall | C32×C52 ⋊ C4 |
| derived | C32×C5 ⋊ C4×C5 |
| Sylow | C52 ⋊ #157 |
| Sylow | C32 ⋊ C5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #4380 |
| commutator, hypocenter | C32×C5 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52 | C4 |
| prime radical | C5×C3⋊D15 | C2 |
| cosocle | C3⋊D15 | C2×C5 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C5 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D5⋊#157, D5×#4380, #4380⋊D5, … |
| maximal normal subgroup of | C5×D5⋊#157, D5×#4380, #4380⋊D5, … |
| maximal quotient of | C5×#67127, C2×C5×#4380, C5×C13×#4380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 117);