Finite Group DatabasebetaFinite Group Databasebeta| order | 11325 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16836849⋊C3 |
| derived, Sylow | C151 ⋊ C3×C25 |
| Hall | #16836849 ⋊ C3 |
| Hall | C151⋊C3 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | (C151⋊C3)⋊C5 |
| commutator, hypocenter | C151 | C3×C25 |
| Fitting, socle, cosocle | C5×C151 | C3×C5 |
| prime radical | C5×C151⋊C3 | C5 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,151,5|b^5=d,c^a=c^32,c^b=c^59125 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11325, 2);