Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D15⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D15 |
| 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 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^2,3^2,5^2|c^a=c^2,d^a=d^2,f^a=f^4,c^b=c^2,e^b=e^475 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×D15, D3×D15⋊D5, D5×(C3⋊D3)⋊D5, … |
| maximal normal subgroup of | D3×D5×D15, D3×D15⋊D5, D5×(C3⋊D3)⋊D5, … |
| maximal quotient of | #14268306, #14268307, #14268308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 138);