Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #90646 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C52⋊C9 ⋊ C4 |
| Sylow | C52 ⋊ Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #90646 |
| commutator, hypocenter | C52⋊C9 | C4 |
| Frattini | C2×C3 | #3874 |
| Fitting, socle, prime radical | C2×C3×C52 | D3 |
| cosocle | C2×C52⋊C9 | C2 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^2,3^2,5^2|a^2=b,c^3=d,c^a=c^2d^2,d^a=d^2,e^a=e^2f,f^a=e^2f^3,e^c=e^2f^4,f^c=e^2f^248 conjugacy classes — view the full character table.
| maximal subgroup of | #14267934, #14267935, #14267937, … |
| maximal normal subgroup of | #14267934, #14267935, #14267937, … |
| maximal quotient of | #14267857, C2×#11744607, C13×#11744607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 19);