Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C5×D15 |
| unambiguous semidirect product | (C2×C3)⋊(C3×C5×D5) |
| unambiguous semidirect product | (C2×C5)⋊(C3×C5×D3) |
| Fitting, socle | C2×C32×C52 ⋊ C2 |
| derived | C3×C5 ⋊ C22×C3×C5 |
| Hall | C32×C52 ⋊ C22 |
| Sylow | C52 ⋊ C2×C3×D3 |
| Sylow | C32 ⋊ C2×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C3×C5 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×#1200, C3×C5×#1202, C3×C5×#1203, … |
| maximal normal subgroup of | C3×C5×#1200, C3×C5×#1202, C3×C5×#1203, … |
| maximal quotient of | C3×C5×Dic30, C3×C4×C5×D15, C3×C5×D60, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 145);