Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #1043⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #1043⋊C9 |
| derived, Sylow | C52 ⋊ C4×C9 |
| Hall | C52⋊C9 ⋊ C4 |
| Hall | #1043 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #1043⋊C3 |
| commutator, hypocenter | C52 | C4×C9 |
| Fitting, socle | C3×C52 | C3×C4 |
| prime radical, cosocle | C3×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
Polycyclic presentation:
2,3,2,3,5^2|a^2=c,b^3=d,e^a=e^2,f^a=f^2,e^b=ef,f^b=e^2f^3,e^c=e^4,f^c=f^442 conjugacy classes — view the full character table.
| maximal subgroup of | #14268076, #6053⋊C9, #11744634⋊C2, … |
| maximal normal subgroup of | #14268076, #6053⋊C9, #11744634⋊C2, … |
| maximal quotient of | #6033⋊C9, C2×#1043⋊C9, C13×#1043⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 47);