Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D152 |
| Fitting, socle, derived, Hall | C32×C52 ⋊ C22 |
| Sylow | C52 ⋊ D32 |
| Sylow | C32 ⋊ D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C52 | C22 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | #14268470, D3×D5×D15, #14268487, … |
| maximal normal subgroup of | #14268470, D3×D5×D15, #14268487, … |
| maximal quotient of | D15×Dic15, #14268302, #14268303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 137);