Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #11744620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Hall | C32×C25 ⋊ C4 |
| Sylow | C25 ⋊ #157 |
| Sylow | C32 ⋊ Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C25 | C4 |
| Frattini | C5 | #4379 |
| socle | C32×C5 | Dic5 |
| prime radical | C5×C3⋊D3 | D5 |
| cosocle | C3⋊D3×C25 | C2 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
Polycyclic presentation:
2^2,3^2,5^2|a^2=b,e^5=f,c^a=cd,d^a=cd^2,e^a=e^4f^4,f^a=f^4,c^b=c^2,d^b=d^278 conjugacy classes — view the full character table.
| maximal subgroup of | #14268023, #157×D25, D32⋊D25, … |
| maximal normal subgroup of | #14268023, #157×D25, D32⋊D25, … |
| maximal quotient of | #14267870, C2×#11744620, C13×#11744620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 32);