Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #1039⋊C9 |
| derived, Sylow | C52 ⋊ C4×C9 |
| Hall | C52⋊C9 ⋊ C4 |
| Hall | #1039 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | (C5⋊D5)⋊C3 |
| commutator, hypocenter | C52 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C52 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2,3,2,3,5^2|a^2=c,b^3=d,e^a=e^4,f^a=f^4,e^b=e^3f^3,f^b=e^4f60 conjugacy classes — view the full character table.
| maximal subgroup of | #14267932, #6033⋊C9, #14267934, … |
| maximal normal subgroup of | #14267932, #6033⋊C9, #14267934, … |
| maximal quotient of | #6029⋊C9, C2×#1039⋊C9, C13×#1039⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 20);